Optimal Control Theory in Intelligent Transportation Systems Research - A Review
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paper_title: An arterial signal optimization model for intersections experiencing queue spillback and lane blockage

paper_content:

This paper presents an arterial signal optimization model that features its effectiveness on: (1) explicitly modeling physical queue evolution on arterial links by lane-group to account for shared-lane traffic interactions; and (2) capturing the dynamic interactions of spillback queues among lane groups and between neighboring intersections due to high demand, geometric constraints, or signal settings. Depending on the detected traffic patterns, one can select the control objective to be either minimizing the total travel time or maximizing the total throughput over the target area. The solution procedures developed with the Genetic Algorithm (GA) have been tested with an example arterial of four intersections under different demand scenarios. Extensive experimental analyses in comparison with results from TRANSYT-7F (version 8) reveal that the proposed model and solution method are quite promising for use in design of arterial signals, especially under congested, high demand traffic conditions.
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paper_title: Optimal Control Theory: Applications to Management Science and Economics

paper_content:

Preface to First Edition.- Preface to Second Edition.- What is Optimal Control Theory?.- The Maximum Principle: Continuous Time.- The Maximum Principle: Mixed Inequality Constraints.- The Maximum Principle: General Inequality Constraints.- Applications to Finance.- Applications to Production and Inventory.- Applications to Marketing.- The Maximum Principle: Discrete Time.- Maintenance and Replacement.- Applications to Natural Resources.- Economic Applications.- Differential Games, Distributed Systems, and Impulse Control.- Stochastic Optimal Control.- Solutions of Linear Differential Equations.- Calculus of Variations and Optimal Control Theory.- An Alternative Derivation of the Maximum Principle.- Special Topics in Optimal Control.- Answers to Selected Exercises.- Bibliography.- Index.- List of Figures.- List of Tables.
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paper_title: ON OPTIMAL FREEWAY RAMP CONTROL POLICIES FOR CONGESTED TRAFFIC CORRIDORS

paper_content:

This paper examines the conditions for which ramp metering can be beneficial to the overall system in terms of travel time savings for a simple traffic corridor that consists of a freeway and a set of parallel arterials connected by entrance ramps. The focus is on analyzing state and control relationships to arrive at general analytical results regarding optimal metering policies, rather than on either developing specific control algorithms or solving a specific application. The analysis is concerned with the general behavior of the system under ramp control and traffic diversion. The analysis assumes that time-varying traffic demands that originate from various locations are destined for a single location and that the freeway is uniformly congested throughout the control period. Under these assumptions, some general results are obtained regarding the effectiveness of ramp metering for various traffic diversion propensities and differentials between freeway and arterial traffic conditions. It is shown that the optimal ramp control policies are determined by the magnitudes of two co-state vectors that depend on traffic conditions on the freeway and its alternative, and the drivers diversion propensity. The results of two limiting cases imply that when the freeway is uniformly congested ramp control is counter-productive unless diversion occurs, and where drivers have a high propensity to divert, the optimal policy is dependent on the travel speed on the freeway alternative and on the wave speed of backward propagating waves on the freeway.
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paper_title: Optimal driving for single-vehicle fuel economy

paper_content:

Abstract This study uses fuel consumption simulators for 15 late-model automobiles to determine how one ought to drive to maximize fuel economy. The simulation is based on extensive on-road and dynamometer testing of the 15 cars. Dynamic programming is used to determine the optimal way to accelerate from rest to cruising speed, to drive a block between stop signs, and to cruise on hilly terrain while maintaining a given average speed. The dependence of fuel economy on cruising speed is also characterized for various road grades. Findings include that optimal speeds are generally higher for larger cars and higher on downgrades than on upgrades, and that the relative fuel penalty for exceeding the speed limit is no worse for small cars than large cars. Optimal control for accelerate-and-cruise and for driving between stop signs varies considerably from car to car; in the latter case fuel economy is much improved by achieving a rather low peak speed. Optimal control on hills is consistent from car to car and can achieve fuel economy 7% to 30% better than that of constant-speed driving on 3% to 6% grades. Results that appear generalizable to other cars are reduced to advice for the fuel-conscious driver.
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paper_title: Optimal scheduling of rehabilitation activities for multiple pavement facilities: Exact and approximate solutions

paper_content:

This paper presents a mathematical programming model for optimal highway pavement rehabilitation planning which minimizes the life-cycle cost for a finite horizon. It extends previous researches in this area by solving the problem of multiple rehabilitation activities on multiple facilities, with realistic empirical models of deterioration and rehabilitation effectiveness. The formulation is based on discrete control theory. A nonlinear pavement performance model and integer decision variables are incorporated into a mixed-integer nonlinear programming (MINLP). Two solution approaches, a branch-and-bound algorithm and a greedy heuristic, are proposed for this model. It is shown that the heuristic results provide a good approximation to the exact optima, but with much lower computational costs.
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paper_title: Solving the Dynamic Network User Equilibrium Problem with State-Dependent Time Shifts

paper_content:

In this paper we consider the infinite dimensional variational inequality (VI) formulation of dynamic user equilibrium (DUE) put forward by Friesz et al. (1993) [A variational inequality formulation of the dynamic network user equilibrium problem. Operations Research 41, 179-191] as well as the differential variational inequality (DVI) version reported in Friesz et al. (2001) [Dynamic network user equilibrium with state-dependent time lags. Networks and Spatial Economics 1, 319-347]. We show how the theory of optimal control and the theory of infinite dimensional variational inequalities may be combined to create a simple and effective fixed point algorithm for calculating DUE network flows that are solutions of both formulations. A numerical example is provided.
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paper_title: Control strategies of traffic signal timing transition for emergency vehicle preemption

paper_content:

Emergency vehicle (EV) operation saves lives and reduces property damage. This paper reports two new control strategies for EV signal pre-emption (EVSP) that reduce the response time and minimize the impact of EV operation on general traffic. A real-time control strategy is developed that enables signal transitioning from normal operation to EVSP (transition 1) so that the approaching EV can cross the intersection safely at its operating speed and also the impact of the EVSP on general traffic is decreased. The green time that is not required for the EV is dynamically allotted to the traffic on the cross road by taking into account the prevailing traffic condition at the intersection and the state of signal indication. The second control strategy, implemented by an optimal control algorithm, is used for the signal transitioning from the EVSP back to normal operation (transition 2). A two-phase algorithm, consisting of a relaxation method and a stepwise search strategy, is adopted to overcome the difficulty in solving the optimal control model, which results from the interrelationship between successive signal sequences. Software was developed in the MATLAB environment for simulations of the EVSP process under different signal timing transitioning control strategies. Results indicate that the real-time control and the optimal control strategies and their associated methods perform better than the commonly used existing approaches. It is also demonstrated that the two control strategies are applicable to different traffic conditions up to and slightly over-saturated level, and can be used to deal with a single EVSP occurrence as well as multiple EVSP occurrences.
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paper_title: An arterial signal optimization model for intersections experiencing queue spillback and lane blockage

paper_content:

This paper presents an arterial signal optimization model that features its effectiveness on: (1) explicitly modeling physical queue evolution on arterial links by lane-group to account for shared-lane traffic interactions; and (2) capturing the dynamic interactions of spillback queues among lane groups and between neighboring intersections due to high demand, geometric constraints, or signal settings. Depending on the detected traffic patterns, one can select the control objective to be either minimizing the total travel time or maximizing the total throughput over the target area. The solution procedures developed with the Genetic Algorithm (GA) have been tested with an example arterial of four intersections under different demand scenarios. Extensive experimental analyses in comparison with results from TRANSYT-7F (version 8) reveal that the proposed model and solution method are quite promising for use in design of arterial signals, especially under congested, high demand traffic conditions.
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paper_title: Trend curve optimal control model for highway pavement maintenance: Case study and evaluation

paper_content:

This paper presents a control theoretic dynamic model for optimizing the timing and intensity of major highway pavement maintenance actions. The solution procedure is demonstrated through a simple case study, and the worthiness as a problem-solving tool is discussed through a systematic evaluation of the solutions.
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paper_title: OPTIMAL FLEET UTILIZATION AND REPLACEMENT

paper_content:

The fleet replacement problem of a profit-maximizing manager is examined using an optimal control model that captures both utilization and replacement decisions. Conditions for optimal utilization of each vessel in the fleet and optimal vessel acquisition and retirement strategies are discussed. The results indicate that the optimal replacement schedule and fleet size are influenced by utilization schedules, and vice versa. Thus, replacement and utilization strategies should be determined jointly. We develop a numerical example to illustrate the model's potential as a practical management decision tool and the procedures to solve it.
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paper_title: Neural approximations for feedback optimal control of freeway systems

paper_content:

The problem of clearing congestion situations in freeway traffic is addressed for both an N-stage and an infinite-stage control horizon (in the latter case, a receding-horizon control mechanism is used). Traffic is controlled by regulating the vehicle access to the freeway and by limiting the vehicle speed by means of variable message signs. To describe the traffic behavior, a "classical" macroscopic model, first proposed by Payne (1971), is adapted. Even though the problem is stated within a deterministic context, an optimal control law in feedback form is sought to react to unpredictable events. The resulting functional optimization problem is reduced to a nonlinear programming problem by constraining the control law to take on a fixed structure in which free parameters have to be optimized. For such a structure, a multilayer feedforward neural mapping is chosen. Simulation results show the effectiveness of the proposed method in two different case studies. For the simulation of the second case study, real traffic data are used, which allows one to very well represent critical traffic conditions on freeways.
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paper_title: Stochastic Optimal-Control Approach to Automatic Incident-Responsive Coordinated Ramp Control

paper_content:

This paper presents a stochastic optimal-control-based approach to real-time incident-responsive coordinated ramp control. The proposed coordinated ramp-control methodology includes two major functions, i.e., 1) identification of control-zone-based congestion patterns using the modified generalized-sequential-probability-ratio-testing technology and 2) group-based ramp control using stochastic optimal control coupled with extended Kalman filtering technologies. With the aid of the Paramics microscopic traffic simulator, numerical studies under various simulated incident-induced congestion conditions were conducted. Corresponding numerical results indicate the feasibility of the proposed ramp-control method in responding to diverse lane-blocking incident-induced traffic-congestion conditions
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paper_title: Optimal use of telemetry by parallel hybrid vehicles in urban driving

paper_content:

The benefit of telemetry systems that can provide information about future traffic conditions has been previously established, with both vehicle velocity and torque split controllers in hybrid vehicles able to improve fuel economy and emissions. However, many existing algorithms are either computationally intractable for real application or do not maximise the potential savings available. Here, a computationally efficient approach for the optimal control of both velocity and torque split of a parallel hybrid electric vehicle with vehicle telemetry is proposed. The optimal control inputs are determined using Pontryagin’s Minimum Principle and applied in a receding horizon fashion over realistic drive cycles. Although developed on a relatively simple model, the proposed controller is tested on a complex hybrid vehicle simulation. The effectiveness of the proposed controller in improving fuel consumption is investigated as preview information is varied, and in the presence of modelling error and measurement noise.
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paper_title: A Stochastic Optimal Control Approach to Real-time, Incident-Responsive Traffic Signal Control at Isolated Intersections

paper_content:

Real-time, incident-responsive traffic control and management is vital to development of advanced incident management systems in ITS. More importantly, it provides, from an academic point of view, the linkages between incident detection, incident management, and traffic signal control. This study explores the application of a stochastic optimal control approach to real-time, incident-responsive traffic control at isolated intersections. In the methodology development, time-varying lane traffic state variables and control variables are specified to characterize sectionwide interlane and intralane traffic states under conditions of lane-blocking incidents. Following specification of system states, we formulated a discrete-time nonlinear stochastic model that comprises four types of equations, namely (1) recursive equations, (2) measurement equations, (3) incident-induced delay equations, and (4) boundary constraints. From the proposed stochastic model we then developed a stochastic optimal control algorithm to update the time-varying control variables and lane traffic state variables in real-time with lane-blocking incidents at isolated intersections. To generate traffic data used in model tests efficiently, we employed an advanced microscopic traffic simulator, Paramics, Version 3.0, which is developed to model and analyze ITS traffic flow conditions. The preliminary test results indicate that the proposed method can accomplish the goal of real-time, incident-responsive traffic signal control. In addition to proposing a new methodology, we hope that this study can initiate investigation into real-time, incident-responsive traffic control and management to achieve the final goal of networkwide incident-responsive, traffic-optimal control for incident management.
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paper_title: TRAFFIC NOISE AND TRAFFIC LIGHT CONTROL

paper_content:

Abstract An optimal control problem of traffic light duration is considered. The traffic noise level is introduced as a state variable in a dynamical optimization problem. A closed loop control system is designed which influences the green duration of the lights according to the equivalent noise level. Real time considerations lead to sub-optimal control implementation. This control policy decreases the noise levels at intensive traffic intersections. The traffic lights adapt their duration according to the noise pollution. Simulation and experimental results are discussed.
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paper_title: Dynamic bus holding strategies for schedule reliability: Optimal linear control and performance analysis

paper_content:

As is well known, bus systems are naturally unstable. Without control, buses on a single line tend to bunch, reducing their punctuality in meeting a schedule. Although conventional schedule-based strategies that hold buses at control points can alleviate this problem these methods require too much slack, which slows buses. This delays on-board passengers and increases operating costs.
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paper_title: A model of optimal transport maintenance with demand responsiveness

paper_content:

Maintenance activities can be performed throughout the lifetime of a particular facility or piece of equipment, thereby affecting its quality in a continuous fashion. It is assumed in this paper that quality of a facility is determined by natural factors, rate of use and maintenance investments while demand for the facility is assumed to be a function of its quality. A dynamic optimization model in the form of a simple linear optimal control problem is then developed in order to determine optimal maintenance policies under these circumstances. Bang-bang and singular policies are derived and given economic interpretations. An algorithm is presented for numerical solution of the Pontryagin necessary conditions. Finally, sufficiency conditions are obtained for the model structure considered.
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paper_title: Influence of Demand-Quality Interrelationships on Optimal Policies for Stage Construction of Transportation Facilities

paper_content:

The time staging of investment decisions for transportation facilities has generally been analyzed using models which assume a complete independence between transportation level of service and demand for the use of the facility considered. Through the use of a dynamic optimal control model, we analyze the implications of explicitly considering the interrelationship between level of service and demand on the time staging of optimal investment decisions. This analysis leads to a more general time staging decision rule than those previously proposed in the literature; an economic interpretation of that decision rule is given. Second order conditions are developed for various cases of practical significance. Finally, a numerical example is introduced to illustrate the dramatic effect that demand-quality interrelationships can have on the optimal time staging policy.
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paper_title: ON OPTIMAL FREEWAY RAMP CONTROL POLICIES FOR CONGESTED TRAFFIC CORRIDORS

paper_content:

This paper examines the conditions for which ramp metering can be beneficial to the overall system in terms of travel time savings for a simple traffic corridor that consists of a freeway and a set of parallel arterials connected by entrance ramps. The focus is on analyzing state and control relationships to arrive at general analytical results regarding optimal metering policies, rather than on either developing specific control algorithms or solving a specific application. The analysis is concerned with the general behavior of the system under ramp control and traffic diversion. The analysis assumes that time-varying traffic demands that originate from various locations are destined for a single location and that the freeway is uniformly congested throughout the control period. Under these assumptions, some general results are obtained regarding the effectiveness of ramp metering for various traffic diversion propensities and differentials between freeway and arterial traffic conditions. It is shown that the optimal ramp control policies are determined by the magnitudes of two co-state vectors that depend on traffic conditions on the freeway and its alternative, and the drivers diversion propensity. The results of two limiting cases imply that when the freeway is uniformly congested ramp control is counter-productive unless diversion occurs, and where drivers have a high propensity to divert, the optimal policy is dependent on the travel speed on the freeway alternative and on the wave speed of backward propagating waves on the freeway.
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paper_title: Optimal mainstream traffic flow control of large scale motorway networks

paper_content:

Summary form only given. The continuously increasing daily traffic congestions on motorway networks around the world call for innovative control measures that would drastically improve the current traffic conditions. Mainstream traffic flow control (MTFC) is proposed as a novel and efficient motorway traffic management tool, and its possible implementation and principal impact on traffic flow efficiency is analysed. Variable speed limits, suitably operated and enforced, are considered as one (out of several possible) way(s) for MTFC realisation, either as a stand-alone measure or in combination with ramp metering. A computationally efficient software tool for optimal integrated motorway network traffic control including MTFC is applied to a large-scale motorway ring-road. It is demonstrated via several investigated control scenarios that traffic flow can be substantially improved via MTFC with or without integration with coordinated ramp metering actions.
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paper_title: Optimal driving for single-vehicle fuel economy

paper_content:

Abstract This study uses fuel consumption simulators for 15 late-model automobiles to determine how one ought to drive to maximize fuel economy. The simulation is based on extensive on-road and dynamometer testing of the 15 cars. Dynamic programming is used to determine the optimal way to accelerate from rest to cruising speed, to drive a block between stop signs, and to cruise on hilly terrain while maintaining a given average speed. The dependence of fuel economy on cruising speed is also characterized for various road grades. Findings include that optimal speeds are generally higher for larger cars and higher on downgrades than on upgrades, and that the relative fuel penalty for exceeding the speed limit is no worse for small cars than large cars. Optimal control for accelerate-and-cruise and for driving between stop signs varies considerably from car to car; in the latter case fuel economy is much improved by achieving a rather low peak speed. Optimal control on hills is consistent from car to car and can achieve fuel economy 7% to 30% better than that of constant-speed driving on 3% to 6% grades. Results that appear generalizable to other cars are reduced to advice for the fuel-conscious driver.
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paper_title: Dynamic Systems, Variational Inequalities and Control Theoretic Models for Predicting Time-Varying Urban Network Flows

paper_content:

In this paper, we set forth certain axioms for a positive theory of dynamic urban network flows. We then show that mathematical models which fulfill these axioms may be created by adapting and extending certain fundamental notions from microeconomics and nonlinear systems theory. We further show that models created in this fashion, using concepts of fast and slow dynamic processes, may be manipulated into a variety of mathematical forms, thereby providing a synthesis of dynamic systems, variational inequality and control theoretic perspectives for predicting dynamic urban network flows. We close with a discussion of the implications of this synthesis for route guidance and intelligent vehicle infrastructure. Throughout, our presentation is at a conceptual level; the mathematical arguments are purposely not rigorous to embrace the widest possible readership.
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paper_title: On optimal cooperative conflict resolution for air traffic management systems

paper_content:

We consider optimal resolution of air traffic (AT) conflicts. Aircraft are assumed to cruise within a given altitude layer and are modeled as a kinematic system with constant velocity and curvature bounds. Aircraft cannot get closer to each other than a predefined safety distance. For such a system of multiple aircraft, we consider the problem of planning optimal paths among given waypoints. Necessary conditions for optimality of solutions are derived and used to devise a parametrization of possible trajectories that turns into efficient numerical solutions to the problem. Simulation results for a realistic aircraft conflict scenario are provided. A decentralized implementation of the optimal conflict resolution scheme is introduced that may allow free-flight coordination in a cooperative airspace management scheme. Impact of decentralization on performance and safety is finally discussed with the help of extensive simulations.
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paper_title: Dynamic user equilibrium with side constraints for a traffic network: Theoretical development and numerical solution algorithm

paper_content:

This paper investigates a traffic volume control scheme for a dynamic traffic network model which aims to ensure that traffic volumes on specified links do not exceed preferred levels. The problem is formulated as a dynamic user equilibrium problem with side constraints (DUE-SC) in which the side constraints represent the restrictions on the traffic volumes. Travelers choose their departure times and routes to minimize their generalized travel costs, which include early/late arrival penalties. An infinite-dimensional variational inequality (VI) is formulated to model the DUE-SC. Based on this VI formulation, we establish an existence result for the DUE-SC by showing that the VI admits at least one solution. To analyze the necessary condition for the DUE-SC, we restate the VI as an equivalent optimal control problem. The Lagrange multipliers associated with the side constraints as derived from the optimality condition of the DUE-SC provide the traffic volume control scheme. The control scheme can be interpreted as additional travel delays (either tolls or access delays) imposed upon drivers for using the controlled links. This additional delay term derived from the Lagrange multiplier is compared with its counterpart in a static user equilibrium assignment model. If the side constraint is chosen as the storage capacity of a link, the additional delay can be viewed as the effort needed to prevent the link from spillback. Under this circumstance, it is found that the flow is incompressible when the link traffic volume is equal to its storage capacity. An algorithm based on Euler's discretization scheme and nonlinear programming is proposed to solve the DUE-SC. Numerical examples are presented to illustrate the mechanism of the proposed traffic volume control scheme.
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paper_title: Analysis of the time-varying pricing of a bottleneck with elastic demand using optimal control theory

paper_content:

In this paper, a time-varying pricing model of a road bottleneck with elastic traffic demand is formulated using the optimal control theory. It is assumed that the optimal use of the bottleneck is achieved when social benefit over the whole time horizon of study is maximized. The necessary conditions for optimal solution are derived and their economic interpretations are given. Different from conventional analyses, queuing is not pre-assumed to be zero when obtaining the optimal time-varying toll, and the exit capacity of the bottleneck is assumed either to be constant or to vary with queue length. An approximate iterative algorithm is proposed for solving the model in a discrete time version. Three numerical examples are presented to demonstrate the applications of the proposed model and algorithm.
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paper_title: ENERGY-EFFICIENT OPERATION OF RAIL VEHICLES

paper_content:

This paper describes an analytical process that computes the optimal operating successions of a rail vehicle to minimize energy consumption. Rising energy prices and environmental concerns have made energy conservation a high priority for transportation operations. The cost of energy consumption makes up a large portion of the Operation and Maintenance (O&M) costs of transit especially rail transit systems. Energy conservation or reduction in energy cost may be one of the effective ways to reduce transit operating cost, therefore improve the efficiency of transit operations. From a theoretical point of view, the problem of energy efficient train control can be formulated as one of the functions of Optimal Control Theory. However, the classic numerical optimization methods such as discrete method of optimum programming are too slow to be used in an on-board computer even with the much improved computation power, today. The contribution of this particular research is the analytical solution that gives the sequence of optimal controls and equations to find the control change points. As a result, a calculation algorithm and a computer program for energy efficient train control has been developed. This program is also capable of developing energy efficient operating schedules by optimizing distributions of running time for an entire route or any part of rail systems. We see the major application of the proposed algorithms in fully or partially automated Train Control Systems. The modern train control systems, often referred as "positive" train control (PTC), have collected a large amount of information to ensure safety of train operations. The same data can be utilized to compute the optimum controls on-board to minimize energy consumption based on the algorithms proposed in this paper. Most of the input data, such as track plan, track profile, traction and braking characteristics, speed limits and required trip time are located in an on-board database and/or they can be transmitted via radio link to be processed by the proposed algorithm and program.
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paper_title: RAPID COMPUTATION OF OPTIMAL CONTROL FOR VEHICLES

paper_content:

This paper describes a rapid computational method of optimal control for vehicles and the software realizing it. The optimal control problem is solved with the dynamic programming technique. A traditional engineering simulator is used to predict the vehicle's performance and economy. An objective function is suggested that permits high-speed computation. Results show the dependence of optimal fuel consumption on average speed for various vehicle masses in a number of situations: acceleration from rest to cruising speed, driving between stop signs and driving on hilly terrain. Findings include that one can travel up to 20 to 80% (depending on the situation) faster than the most economical average speed without increasing fuel consumption more than an equal amount.
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paper_title: On an optimal control problem of train operation

paper_content:

This paper examines the operation of a train on a variable grade profile subject to arbitrary speed restrictions. The purpose of the study is to determine a detailed program for traction and brake applications, which minimizes energy consumption in moving the train along a given route for a given time. Stated in the form of optimal control, this problem is solved by constructing a numerical algorithm which essentially exploits analytical properties of the optimal solution obtained from the maximum principle analysis. Due to its analytical origin, the algorithm has inherent accuracy and adequate quick-operation that are demonstrated in numerical examples.
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paper_title: Dynamic congestion pricing models for general traffic networks

paper_content:

In this paper we develop two types of dynamic congestion pricing model, based on the theory of marginal cost pricing. The first model is appropriate for situations where commuters have the ability to learn the best route choices through day-to-day explorations on a network with arc capacities and travel demands that are stable from day to day. The second model is appropriate for situations where commuters optimize their routing decisions each day on a network with arc capacities and travel demands that fluctuate significantly from day to day. We show that two types of time-varying congestion tolls can be determined by solving a convex control formulation of the dynamic system optimal traffic assignment problem on a network with many origins and many destinations. We also show that the dynamic system optimal traffic assignment is an equilibrium for commuters under the tolls in both cases.
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paper_title: Modeling user adoption of advanced traveler information systems: a control theoretic approach for optimal endogenous growth

paper_content:

This study is a subsequent development of the dynamic evolution model of the market penetration of advanced traveler information systems (ATIS) proposed by Yang and Meng [Transport. Res. A 35 (2001) 895]. In previous study we have shown that a benefit-driven, user-optimal ATIS market does not necessarily lead to a socially optimal growth and optimal stationary equilibrium level of market penetration of ATIS products or services. The current study proposes an optimal time-dependent service pricing strategy so as to minimize total system cost throughout the time horizon of growth or optimally reach a socially desirable target level of ATIS market penetration in a final stationary equilibrium. We formulate the problem of interest as an optimal control problem and propose an efficient solution algorithm together with a numerical demonstration of the characteristics of the study problem.
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paper_title: Environmental-regulation pricing strategies for green supply chain management

paper_content:

This paper demonstrates that a proper design of environmental-regulation pricing strategies is able to promote Extended Product Responsibility for green supply chain firms in a competitive market. A differential game model comprising Vidale-Wolfe equation has been established in light of sales competition and recycling dynamics as well as regulation related profit function. Analytic solutions of Markovian Nash equilibriums are provided with the necessary condition derived from Hamilton-Jacobi-Bellman equations. We found that governments should opt to gradually raise regulation standards so that rational manufacturers will gradually improve its product recyclability, and, in turn, Extended Product Responsibility will get promoted.
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paper_title: Optimal scheduling of rehabilitation activities for multiple pavement facilities: Exact and approximate solutions

paper_content:

This paper presents a mathematical programming model for optimal highway pavement rehabilitation planning which minimizes the life-cycle cost for a finite horizon. It extends previous researches in this area by solving the problem of multiple rehabilitation activities on multiple facilities, with realistic empirical models of deterioration and rehabilitation effectiveness. The formulation is based on discrete control theory. A nonlinear pavement performance model and integer decision variables are incorporated into a mixed-integer nonlinear programming (MINLP). Two solution approaches, a branch-and-bound algorithm and a greedy heuristic, are proposed for this model. It is shown that the heuristic results provide a good approximation to the exact optima, but with much lower computational costs.
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paper_title: A time series analysis framework for transportation infrastructure management

paper_content:

We present an integrated framework to address performance prediction and maintenance optimization for transportation infrastructure facilities. The framework is based on formulating the underlying resource allocation problem as discrete-time, stochastic optimal control problem with linear dynamics and a quadratic criterion. Facility deterioration is represented as a time series which provides an attractive and rigorous approach to specify and estimate performance models. The state and decision variables in the framework are continuous which allows the framework to overcome important computational and statistical limitations that do not allow existing optimization models to address various problems that arise the management of transportation infrastructure. To illustrate the advantages of the proposed approach, we conduct a numerical study where we examine the case of multiple technologies being used simultaneously to collect condition data. Specifically, we illustrate how the framework can be used to quantify the effect of the capabilities of inspection technologies, i.e., precision, accuracy and relationships, on life-cycle costs. This information can be used to compute the operational value of combining technologies, and thus, to guide in their selection based on economic criteria.
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paper_title: A new strategy for minimum usage of external yaw moment in vehicle dynamic control system

paper_content:

Due to the loss of vehicle directional stability in emergency maneuvers, a new complete desired model for vehicle handling based on the linear two-degrees-of-freedom (2DOF) model and tire/road conditions is presented to be tracked by the direct yaw moment control (DYC) system. In order to maintain the vehicle actual motions, yaw rate and side-slip angle, close to the proposed desired responses without excessively large external yaw moment, a complete linear quadratic (LQ) optimal problem is formulated and its analytical solution is obtained. Here, the derived control law is evaluated and its different versions are discussed. It is shown that the side-slip tracking by DYC is more effective than the yaw rate control to stabilize vehicle motions in nonlinear regimes. Also, optimal property of the control law provides the possibility of reducing the external yaw moment as low as possible, at the cost of some admissible tracking errors. Simulation studies of vehicle handling, with and without control, have been conducted using a full nonlinear vehicle dynamic model. The results, obtained during various maneuvers, indicate that when the proposed optimal controller is engaged with the model, improvements in the handling performance through a reduced external yaw moment can be acquired.
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paper_title: Some general results on the optimal ramp control problem

paper_content:

In an effort to relieve peak hour congestion on freeways, various ramp metering algorithms have been employed to regulate the inputs to freeways from entry ramps. In this paper, we consider a freeway system comprised of a freeway section and its entry/exit ramps, and formulate the ramp control problem as a dynamic optimal process to minimize the total time spent in this system. Within this framework, we are able to show when ramp metering is beneficial to the system in terms of total time savings, and when it is not, under the restriction that the controlled freeway has to serve all of its ramp demand, and the traffic flow process follows the rules prescribed by the LWR theory with a triangular flow-density relationship. We also provide solution techniques to the problem and present some preliminary numerical results and empirical validation.
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paper_title: Efficiency and equity properties of freeway network-wide ramp metering with AMOC

paper_content:

Abstract The Advanced Motorway Optimal Control (AMOC) strategy for optimal freeway network-wide ramp metering is applied to the ring-road of Amsterdam, The Netherlands, in the aim of investigating some important and interesting problems arising in ubiquitous ramp metering systems. A number of suitably chosen scenarios along with a thorough analysis, interpretation, and suitable visualization of the obtained results provide a basis for the better understanding of some complex interrelationships of competing performance criteria. More precisely, the strategy’s efficiency and equity properties as well as their trade-off are studied and their partially competitive behaviour is discussed. This trade-off is implicitly addressed by the AMOC strategy through consideration of the available ramp storage space and may be used as a tool to establish a desired policy of the system’s efficiency versus equity.
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paper_title: Coordinated and integrated control of motorway networks via non-linear optimal control

paper_content:

The problem of designing integrated traffic control strategies for motorway networks with the use of ramp metering, route guidance, and motorway-to-motorway control measures is considered in this paper. A generic problem formulation is presented in the format of a discrete-time optimal control problem whose numerical solution is achieved by use of a feasible-direction algorithm. As an illustrative example, a relatively simple motorway network is considered under different control scenarios. In each case the optimal control strategy is discussed along with its effect on the traffic flow process. The results demonstrate the efficiency of the proposed approach as well as the genuinely intelligent behaviour of the designed control strategy.
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paper_title: The optimal control of collision avoidance trajectories in air traffic management

paper_content:

A collision avoidance/conflict resolution model for aircraft traversing planar intersecting trajectories is developed based on the actual flight dynamics of each aircraft and the criteria that a flight regime correction is optimal if it represents a minimum-time safe deviation from a preassigned flight program. The formulation of the model leads to a singular optimal control problem where the control variable constraint is the maximum acceptable aircraft turn rate for passenger comfort and safety and the state variable constraint is defined in terms of the radius of the protected zone about a potentially conflicting aircraft. A robust, accurate real-time solution procedure is derived for computing the steering program for the execution of the optimal safe avoidance maneuver. Several representative examples of pairwise trajectory conflicts are analysed in detail. A brief discussion of how the model might be generalized to incorporate changes in airspeed and altitude as well as more comprehensive dynamics is included.
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paper_title: Solving the Dynamic Network User Equilibrium Problem with State-Dependent Time Shifts

paper_content:

In this paper we consider the infinite dimensional variational inequality (VI) formulation of dynamic user equilibrium (DUE) put forward by Friesz et al. (1993) [A variational inequality formulation of the dynamic network user equilibrium problem. Operations Research 41, 179-191] as well as the differential variational inequality (DVI) version reported in Friesz et al. (2001) [Dynamic network user equilibrium with state-dependent time lags. Networks and Spatial Economics 1, 319-347]. We show how the theory of optimal control and the theory of infinite dimensional variational inequalities may be combined to create a simple and effective fixed point algorithm for calculating DUE network flows that are solutions of both formulations. A numerical example is provided.
---
paper_title: A dynamic programming algorithm based on expected revenue approximation for the network revenue management problem

paper_content:

Since American Airlines successfully applied revenue management (RM) to raise its revenue, RM has become a common technique in the airline industry. Due to the current hub-and-spoke operation of the airline industry, the focus of RM research has shifted from the traditional single-leg problem to the network-type problem. The mainstream approaches, bid price and virtual nesting, are faced with some limitations such as inaccuracy due to their suboptimal nature and operation interruption caused by the required updates. This study developed an algorithm to generate a seat control policy by approximating the expected revenue function in a dynamic programming (DP) model. In order to deal with the issue of dimensionality for the DP model in a network context, this study used a suitable parameterized function and a sampling concept to achieve the approximation. In the numerical experiment, the objective function value of the developed algorithm was very close to the one achieved by the optimal control. We believe that this approach can serve as an alternative to the current mainstream approaches for the network RM problem for airlines and will provide an inspiring concept for other types of multi-resource RM problems.
---
paper_title: Urban Rail Emergency Response Using Pedestrian Dynamics

paper_content:

An urban rail-transit emergency response system is developed based on existing artificial systems by analyzing human behaviors from a pedestrian dynamics viewpoint. This enables necessary computational experiments on the systems that can ultimately lead to the establishment of a database of emergency response strategies and schemes.
---
paper_title: Trend curve optimal control model for highway pavement maintenance: Case study and evaluation

paper_content:

This paper presents a control theoretic dynamic model for optimizing the timing and intensity of major highway pavement maintenance actions. The solution procedure is demonstrated through a simple case study, and the worthiness as a problem-solving tool is discussed through a systematic evaluation of the solutions.
---
paper_title: OPTIMAL FLEET UTILIZATION AND REPLACEMENT

paper_content:

The fleet replacement problem of a profit-maximizing manager is examined using an optimal control model that captures both utilization and replacement decisions. Conditions for optimal utilization of each vessel in the fleet and optimal vessel acquisition and retirement strategies are discussed. The results indicate that the optimal replacement schedule and fleet size are influenced by utilization schedules, and vice versa. Thus, replacement and utilization strategies should be determined jointly. We develop a numerical example to illustrate the model's potential as a practical management decision tool and the procedures to solve it.
---
paper_title: Stochastic Optimal-Control Approach to Automatic Incident-Responsive Coordinated Ramp Control

paper_content:

This paper presents a stochastic optimal-control-based approach to real-time incident-responsive coordinated ramp control. The proposed coordinated ramp-control methodology includes two major functions, i.e., 1) identification of control-zone-based congestion patterns using the modified generalized-sequential-probability-ratio-testing technology and 2) group-based ramp control using stochastic optimal control coupled with extended Kalman filtering technologies. With the aid of the Paramics microscopic traffic simulator, numerical studies under various simulated incident-induced congestion conditions were conducted. Corresponding numerical results indicate the feasibility of the proposed ramp-control method in responding to diverse lane-blocking incident-induced traffic-congestion conditions
---
paper_title: A Stochastic Optimal Control Approach to Real-time, Incident-Responsive Traffic Signal Control at Isolated Intersections

paper_content:

Real-time, incident-responsive traffic control and management is vital to development of advanced incident management systems in ITS. More importantly, it provides, from an academic point of view, the linkages between incident detection, incident management, and traffic signal control. This study explores the application of a stochastic optimal control approach to real-time, incident-responsive traffic control at isolated intersections. In the methodology development, time-varying lane traffic state variables and control variables are specified to characterize sectionwide interlane and intralane traffic states under conditions of lane-blocking incidents. Following specification of system states, we formulated a discrete-time nonlinear stochastic model that comprises four types of equations, namely (1) recursive equations, (2) measurement equations, (3) incident-induced delay equations, and (4) boundary constraints. From the proposed stochastic model we then developed a stochastic optimal control algorithm to update the time-varying control variables and lane traffic state variables in real-time with lane-blocking incidents at isolated intersections. To generate traffic data used in model tests efficiently, we employed an advanced microscopic traffic simulator, Paramics, Version 3.0, which is developed to model and analyze ITS traffic flow conditions. The preliminary test results indicate that the proposed method can accomplish the goal of real-time, incident-responsive traffic signal control. In addition to proposing a new methodology, we hope that this study can initiate investigation into real-time, incident-responsive traffic control and management to achieve the final goal of networkwide incident-responsive, traffic-optimal control for incident management.
---
paper_title: A model of optimal transport maintenance with demand responsiveness

paper_content:

Maintenance activities can be performed throughout the lifetime of a particular facility or piece of equipment, thereby affecting its quality in a continuous fashion. It is assumed in this paper that quality of a facility is determined by natural factors, rate of use and maintenance investments while demand for the facility is assumed to be a function of its quality. A dynamic optimization model in the form of a simple linear optimal control problem is then developed in order to determine optimal maintenance policies under these circumstances. Bang-bang and singular policies are derived and given economic interpretations. An algorithm is presented for numerical solution of the Pontryagin necessary conditions. Finally, sufficiency conditions are obtained for the model structure considered.
---
paper_title: Influence of Demand-Quality Interrelationships on Optimal Policies for Stage Construction of Transportation Facilities

paper_content:

The time staging of investment decisions for transportation facilities has generally been analyzed using models which assume a complete independence between transportation level of service and demand for the use of the facility considered. Through the use of a dynamic optimal control model, we analyze the implications of explicitly considering the interrelationship between level of service and demand on the time staging of optimal investment decisions. This analysis leads to a more general time staging decision rule than those previously proposed in the literature; an economic interpretation of that decision rule is given. Second order conditions are developed for various cases of practical significance. Finally, a numerical example is introduced to illustrate the dramatic effect that demand-quality interrelationships can have on the optimal time staging policy.
---
paper_title: Dynamic Systems, Variational Inequalities and Control Theoretic Models for Predicting Time-Varying Urban Network Flows

paper_content:

In this paper, we set forth certain axioms for a positive theory of dynamic urban network flows. We then show that mathematical models which fulfill these axioms may be created by adapting and extending certain fundamental notions from microeconomics and nonlinear systems theory. We further show that models created in this fashion, using concepts of fast and slow dynamic processes, may be manipulated into a variety of mathematical forms, thereby providing a synthesis of dynamic systems, variational inequality and control theoretic perspectives for predicting dynamic urban network flows. We close with a discussion of the implications of this synthesis for route guidance and intelligent vehicle infrastructure. Throughout, our presentation is at a conceptual level; the mathematical arguments are purposely not rigorous to embrace the widest possible readership.
---
paper_title: On optimal cooperative conflict resolution for air traffic management systems

paper_content:

We consider optimal resolution of air traffic (AT) conflicts. Aircraft are assumed to cruise within a given altitude layer and are modeled as a kinematic system with constant velocity and curvature bounds. Aircraft cannot get closer to each other than a predefined safety distance. For such a system of multiple aircraft, we consider the problem of planning optimal paths among given waypoints. Necessary conditions for optimality of solutions are derived and used to devise a parametrization of possible trajectories that turns into efficient numerical solutions to the problem. Simulation results for a realistic aircraft conflict scenario are provided. A decentralized implementation of the optimal conflict resolution scheme is introduced that may allow free-flight coordination in a cooperative airspace management scheme. Impact of decentralization on performance and safety is finally discussed with the help of extensive simulations.
---
paper_title: Dynamic user equilibrium with side constraints for a traffic network: Theoretical development and numerical solution algorithm

paper_content:

This paper investigates a traffic volume control scheme for a dynamic traffic network model which aims to ensure that traffic volumes on specified links do not exceed preferred levels. The problem is formulated as a dynamic user equilibrium problem with side constraints (DUE-SC) in which the side constraints represent the restrictions on the traffic volumes. Travelers choose their departure times and routes to minimize their generalized travel costs, which include early/late arrival penalties. An infinite-dimensional variational inequality (VI) is formulated to model the DUE-SC. Based on this VI formulation, we establish an existence result for the DUE-SC by showing that the VI admits at least one solution. To analyze the necessary condition for the DUE-SC, we restate the VI as an equivalent optimal control problem. The Lagrange multipliers associated with the side constraints as derived from the optimality condition of the DUE-SC provide the traffic volume control scheme. The control scheme can be interpreted as additional travel delays (either tolls or access delays) imposed upon drivers for using the controlled links. This additional delay term derived from the Lagrange multiplier is compared with its counterpart in a static user equilibrium assignment model. If the side constraint is chosen as the storage capacity of a link, the additional delay can be viewed as the effort needed to prevent the link from spillback. Under this circumstance, it is found that the flow is incompressible when the link traffic volume is equal to its storage capacity. An algorithm based on Euler's discretization scheme and nonlinear programming is proposed to solve the DUE-SC. Numerical examples are presented to illustrate the mechanism of the proposed traffic volume control scheme.
---
paper_title: Dynamic congestion pricing models for general traffic networks

paper_content:

In this paper we develop two types of dynamic congestion pricing model, based on the theory of marginal cost pricing. The first model is appropriate for situations where commuters have the ability to learn the best route choices through day-to-day explorations on a network with arc capacities and travel demands that are stable from day to day. The second model is appropriate for situations where commuters optimize their routing decisions each day on a network with arc capacities and travel demands that fluctuate significantly from day to day. We show that two types of time-varying congestion tolls can be determined by solving a convex control formulation of the dynamic system optimal traffic assignment problem on a network with many origins and many destinations. We also show that the dynamic system optimal traffic assignment is an equilibrium for commuters under the tolls in both cases.
---
paper_title: Optimal scheduling of rehabilitation activities for multiple pavement facilities: Exact and approximate solutions

paper_content:

This paper presents a mathematical programming model for optimal highway pavement rehabilitation planning which minimizes the life-cycle cost for a finite horizon. It extends previous researches in this area by solving the problem of multiple rehabilitation activities on multiple facilities, with realistic empirical models of deterioration and rehabilitation effectiveness. The formulation is based on discrete control theory. A nonlinear pavement performance model and integer decision variables are incorporated into a mixed-integer nonlinear programming (MINLP). Two solution approaches, a branch-and-bound algorithm and a greedy heuristic, are proposed for this model. It is shown that the heuristic results provide a good approximation to the exact optima, but with much lower computational costs.
---
paper_title: A time series analysis framework for transportation infrastructure management

paper_content:

We present an integrated framework to address performance prediction and maintenance optimization for transportation infrastructure facilities. The framework is based on formulating the underlying resource allocation problem as discrete-time, stochastic optimal control problem with linear dynamics and a quadratic criterion. Facility deterioration is represented as a time series which provides an attractive and rigorous approach to specify and estimate performance models. The state and decision variables in the framework are continuous which allows the framework to overcome important computational and statistical limitations that do not allow existing optimization models to address various problems that arise the management of transportation infrastructure. To illustrate the advantages of the proposed approach, we conduct a numerical study where we examine the case of multiple technologies being used simultaneously to collect condition data. Specifically, we illustrate how the framework can be used to quantify the effect of the capabilities of inspection technologies, i.e., precision, accuracy and relationships, on life-cycle costs. This information can be used to compute the operational value of combining technologies, and thus, to guide in their selection based on economic criteria.
---
paper_title: A new strategy for minimum usage of external yaw moment in vehicle dynamic control system

paper_content:

Due to the loss of vehicle directional stability in emergency maneuvers, a new complete desired model for vehicle handling based on the linear two-degrees-of-freedom (2DOF) model and tire/road conditions is presented to be tracked by the direct yaw moment control (DYC) system. In order to maintain the vehicle actual motions, yaw rate and side-slip angle, close to the proposed desired responses without excessively large external yaw moment, a complete linear quadratic (LQ) optimal problem is formulated and its analytical solution is obtained. Here, the derived control law is evaluated and its different versions are discussed. It is shown that the side-slip tracking by DYC is more effective than the yaw rate control to stabilize vehicle motions in nonlinear regimes. Also, optimal property of the control law provides the possibility of reducing the external yaw moment as low as possible, at the cost of some admissible tracking errors. Simulation studies of vehicle handling, with and without control, have been conducted using a full nonlinear vehicle dynamic model. The results, obtained during various maneuvers, indicate that when the proposed optimal controller is engaged with the model, improvements in the handling performance through a reduced external yaw moment can be acquired.
---
paper_title: Emergency Management of Urban Rail Transportation Based on Parallel Systems

paper_content:

Integrating artificial systems, computational experiments, and parallel execution (ACP) is an effective approach to modeling, simulating, and intervening real complex systems. Emergency response is an important issue in the operation of urban rail transport systems for ensuring the safety of people and property. Inspired by the ACP method, this paper introduces a basic framework of parallel control and management (PCM) for emergency response of urban rail transportation systems. The proposed framework is elaborated from three interdependent aspects: Points, Lines, and Networks. Points represent the modeling of urban rail stations, Lines describe the microscopic characteristics of urban rail connections between designated stations, and Networks present the macroscopic properties of all the urban rail connections. Based on the given framework, a series of parallel experiments, which were impossible to achieve in real systems, can now be conducted in the constructed artificial system. Furthermore, the constructed artificial system can be used to test and develop effective emergency control and management strategies for real rail transport systems. Therefore, this proposed framework will be able to enhance the reliability, security, robustness, and maneuverability of urban rail transport systems in case of an emergency.
---
paper_title: The optimal control of collision avoidance trajectories in air traffic management

paper_content:

A collision avoidance/conflict resolution model for aircraft traversing planar intersecting trajectories is developed based on the actual flight dynamics of each aircraft and the criteria that a flight regime correction is optimal if it represents a minimum-time safe deviation from a preassigned flight program. The formulation of the model leads to a singular optimal control problem where the control variable constraint is the maximum acceptable aircraft turn rate for passenger comfort and safety and the state variable constraint is defined in terms of the radius of the protected zone about a potentially conflicting aircraft. A robust, accurate real-time solution procedure is derived for computing the steering program for the execution of the optimal safe avoidance maneuver. Several representative examples of pairwise trajectory conflicts are analysed in detail. A brief discussion of how the model might be generalized to incorporate changes in airspeed and altitude as well as more comprehensive dynamics is included.
---
paper_title: Solving the Dynamic Network User Equilibrium Problem with State-Dependent Time Shifts

paper_content:

In this paper we consider the infinite dimensional variational inequality (VI) formulation of dynamic user equilibrium (DUE) put forward by Friesz et al. (1993) [A variational inequality formulation of the dynamic network user equilibrium problem. Operations Research 41, 179-191] as well as the differential variational inequality (DVI) version reported in Friesz et al. (2001) [Dynamic network user equilibrium with state-dependent time lags. Networks and Spatial Economics 1, 319-347]. We show how the theory of optimal control and the theory of infinite dimensional variational inequalities may be combined to create a simple and effective fixed point algorithm for calculating DUE network flows that are solutions of both formulations. A numerical example is provided.
---
paper_title: Trend curve optimal control model for highway pavement maintenance: Case study and evaluation

paper_content:

This paper presents a control theoretic dynamic model for optimizing the timing and intensity of major highway pavement maintenance actions. The solution procedure is demonstrated through a simple case study, and the worthiness as a problem-solving tool is discussed through a systematic evaluation of the solutions.
---
paper_title: OPTIMAL FLEET UTILIZATION AND REPLACEMENT

paper_content:

The fleet replacement problem of a profit-maximizing manager is examined using an optimal control model that captures both utilization and replacement decisions. Conditions for optimal utilization of each vessel in the fleet and optimal vessel acquisition and retirement strategies are discussed. The results indicate that the optimal replacement schedule and fleet size are influenced by utilization schedules, and vice versa. Thus, replacement and utilization strategies should be determined jointly. We develop a numerical example to illustrate the model's potential as a practical management decision tool and the procedures to solve it.
---
paper_title: Neural approximations for feedback optimal control of freeway systems

paper_content:

The problem of clearing congestion situations in freeway traffic is addressed for both an N-stage and an infinite-stage control horizon (in the latter case, a receding-horizon control mechanism is used). Traffic is controlled by regulating the vehicle access to the freeway and by limiting the vehicle speed by means of variable message signs. To describe the traffic behavior, a "classical" macroscopic model, first proposed by Payne (1971), is adapted. Even though the problem is stated within a deterministic context, an optimal control law in feedback form is sought to react to unpredictable events. The resulting functional optimization problem is reduced to a nonlinear programming problem by constraining the control law to take on a fixed structure in which free parameters have to be optimized. For such a structure, a multilayer feedforward neural mapping is chosen. Simulation results show the effectiveness of the proposed method in two different case studies. For the simulation of the second case study, real traffic data are used, which allows one to very well represent critical traffic conditions on freeways.
---
paper_title: A Stochastic Optimal Control Approach to Real-time, Incident-Responsive Traffic Signal Control at Isolated Intersections

paper_content:

Real-time, incident-responsive traffic control and management is vital to development of advanced incident management systems in ITS. More importantly, it provides, from an academic point of view, the linkages between incident detection, incident management, and traffic signal control. This study explores the application of a stochastic optimal control approach to real-time, incident-responsive traffic control at isolated intersections. In the methodology development, time-varying lane traffic state variables and control variables are specified to characterize sectionwide interlane and intralane traffic states under conditions of lane-blocking incidents. Following specification of system states, we formulated a discrete-time nonlinear stochastic model that comprises four types of equations, namely (1) recursive equations, (2) measurement equations, (3) incident-induced delay equations, and (4) boundary constraints. From the proposed stochastic model we then developed a stochastic optimal control algorithm to update the time-varying control variables and lane traffic state variables in real-time with lane-blocking incidents at isolated intersections. To generate traffic data used in model tests efficiently, we employed an advanced microscopic traffic simulator, Paramics, Version 3.0, which is developed to model and analyze ITS traffic flow conditions. The preliminary test results indicate that the proposed method can accomplish the goal of real-time, incident-responsive traffic signal control. In addition to proposing a new methodology, we hope that this study can initiate investigation into real-time, incident-responsive traffic control and management to achieve the final goal of networkwide incident-responsive, traffic-optimal control for incident management.
---
paper_title: A model of optimal transport maintenance with demand responsiveness

paper_content:

Maintenance activities can be performed throughout the lifetime of a particular facility or piece of equipment, thereby affecting its quality in a continuous fashion. It is assumed in this paper that quality of a facility is determined by natural factors, rate of use and maintenance investments while demand for the facility is assumed to be a function of its quality. A dynamic optimization model in the form of a simple linear optimal control problem is then developed in order to determine optimal maintenance policies under these circumstances. Bang-bang and singular policies are derived and given economic interpretations. An algorithm is presented for numerical solution of the Pontryagin necessary conditions. Finally, sufficiency conditions are obtained for the model structure considered.
---
paper_title: Influence of Demand-Quality Interrelationships on Optimal Policies for Stage Construction of Transportation Facilities

paper_content:

The time staging of investment decisions for transportation facilities has generally been analyzed using models which assume a complete independence between transportation level of service and demand for the use of the facility considered. Through the use of a dynamic optimal control model, we analyze the implications of explicitly considering the interrelationship between level of service and demand on the time staging of optimal investment decisions. This analysis leads to a more general time staging decision rule than those previously proposed in the literature; an economic interpretation of that decision rule is given. Second order conditions are developed for various cases of practical significance. Finally, a numerical example is introduced to illustrate the dramatic effect that demand-quality interrelationships can have on the optimal time staging policy.
---
paper_title: Optimal mainstream traffic flow control of large scale motorway networks

paper_content:

Summary form only given. The continuously increasing daily traffic congestions on motorway networks around the world call for innovative control measures that would drastically improve the current traffic conditions. Mainstream traffic flow control (MTFC) is proposed as a novel and efficient motorway traffic management tool, and its possible implementation and principal impact on traffic flow efficiency is analysed. Variable speed limits, suitably operated and enforced, are considered as one (out of several possible) way(s) for MTFC realisation, either as a stand-alone measure or in combination with ramp metering. A computationally efficient software tool for optimal integrated motorway network traffic control including MTFC is applied to a large-scale motorway ring-road. It is demonstrated via several investigated control scenarios that traffic flow can be substantially improved via MTFC with or without integration with coordinated ramp metering actions.
---
paper_title: Optimal scheduling of rehabilitation activities for multiple pavement facilities: Exact and approximate solutions

paper_content:

This paper presents a mathematical programming model for optimal highway pavement rehabilitation planning which minimizes the life-cycle cost for a finite horizon. It extends previous researches in this area by solving the problem of multiple rehabilitation activities on multiple facilities, with realistic empirical models of deterioration and rehabilitation effectiveness. The formulation is based on discrete control theory. A nonlinear pavement performance model and integer decision variables are incorporated into a mixed-integer nonlinear programming (MINLP). Two solution approaches, a branch-and-bound algorithm and a greedy heuristic, are proposed for this model. It is shown that the heuristic results provide a good approximation to the exact optima, but with much lower computational costs.
---
paper_title: A time series analysis framework for transportation infrastructure management

paper_content:

We present an integrated framework to address performance prediction and maintenance optimization for transportation infrastructure facilities. The framework is based on formulating the underlying resource allocation problem as discrete-time, stochastic optimal control problem with linear dynamics and a quadratic criterion. Facility deterioration is represented as a time series which provides an attractive and rigorous approach to specify and estimate performance models. The state and decision variables in the framework are continuous which allows the framework to overcome important computational and statistical limitations that do not allow existing optimization models to address various problems that arise the management of transportation infrastructure. To illustrate the advantages of the proposed approach, we conduct a numerical study where we examine the case of multiple technologies being used simultaneously to collect condition data. Specifically, we illustrate how the framework can be used to quantify the effect of the capabilities of inspection technologies, i.e., precision, accuracy and relationships, on life-cycle costs. This information can be used to compute the operational value of combining technologies, and thus, to guide in their selection based on economic criteria.
---
paper_title: Coordinated and integrated control of motorway networks via non-linear optimal control

paper_content:

The problem of designing integrated traffic control strategies for motorway networks with the use of ramp metering, route guidance, and motorway-to-motorway control measures is considered in this paper. A generic problem formulation is presented in the format of a discrete-time optimal control problem whose numerical solution is achieved by use of a feasible-direction algorithm. As an illustrative example, a relatively simple motorway network is considered under different control scenarios. In each case the optimal control strategy is discussed along with its effect on the traffic flow process. The results demonstrate the efficiency of the proposed approach as well as the genuinely intelligent behaviour of the designed control strategy.
---
paper_title: Urban Rail Emergency Response Using Pedestrian Dynamics

paper_content:

An urban rail-transit emergency response system is developed based on existing artificial systems by analyzing human behaviors from a pedestrian dynamics viewpoint. This enables necessary computational experiments on the systems that can ultimately lead to the establishment of a database of emergency response strategies and schemes.
---
paper_title: Control strategies of traffic signal timing transition for emergency vehicle preemption

paper_content:

Emergency vehicle (EV) operation saves lives and reduces property damage. This paper reports two new control strategies for EV signal pre-emption (EVSP) that reduce the response time and minimize the impact of EV operation on general traffic. A real-time control strategy is developed that enables signal transitioning from normal operation to EVSP (transition 1) so that the approaching EV can cross the intersection safely at its operating speed and also the impact of the EVSP on general traffic is decreased. The green time that is not required for the EV is dynamically allotted to the traffic on the cross road by taking into account the prevailing traffic condition at the intersection and the state of signal indication. The second control strategy, implemented by an optimal control algorithm, is used for the signal transitioning from the EVSP back to normal operation (transition 2). A two-phase algorithm, consisting of a relaxation method and a stepwise search strategy, is adopted to overcome the difficulty in solving the optimal control model, which results from the interrelationship between successive signal sequences. Software was developed in the MATLAB environment for simulations of the EVSP process under different signal timing transitioning control strategies. Results indicate that the real-time control and the optimal control strategies and their associated methods perform better than the commonly used existing approaches. It is also demonstrated that the two control strategies are applicable to different traffic conditions up to and slightly over-saturated level, and can be used to deal with a single EVSP occurrence as well as multiple EVSP occurrences.
---
paper_title: An arterial signal optimization model for intersections experiencing queue spillback and lane blockage

paper_content:

This paper presents an arterial signal optimization model that features its effectiveness on: (1) explicitly modeling physical queue evolution on arterial links by lane-group to account for shared-lane traffic interactions; and (2) capturing the dynamic interactions of spillback queues among lane groups and between neighboring intersections due to high demand, geometric constraints, or signal settings. Depending on the detected traffic patterns, one can select the control objective to be either minimizing the total travel time or maximizing the total throughput over the target area. The solution procedures developed with the Genetic Algorithm (GA) have been tested with an example arterial of four intersections under different demand scenarios. Extensive experimental analyses in comparison with results from TRANSYT-7F (version 8) reveal that the proposed model and solution method are quite promising for use in design of arterial signals, especially under congested, high demand traffic conditions.
---
paper_title: Trend curve optimal control model for highway pavement maintenance: Case study and evaluation

paper_content:

This paper presents a control theoretic dynamic model for optimizing the timing and intensity of major highway pavement maintenance actions. The solution procedure is demonstrated through a simple case study, and the worthiness as a problem-solving tool is discussed through a systematic evaluation of the solutions.
---
paper_title: OPTIMAL FLEET UTILIZATION AND REPLACEMENT

paper_content:

The fleet replacement problem of a profit-maximizing manager is examined using an optimal control model that captures both utilization and replacement decisions. Conditions for optimal utilization of each vessel in the fleet and optimal vessel acquisition and retirement strategies are discussed. The results indicate that the optimal replacement schedule and fleet size are influenced by utilization schedules, and vice versa. Thus, replacement and utilization strategies should be determined jointly. We develop a numerical example to illustrate the model's potential as a practical management decision tool and the procedures to solve it.
---
paper_title: Neural approximations for feedback optimal control of freeway systems

paper_content:

The problem of clearing congestion situations in freeway traffic is addressed for both an N-stage and an infinite-stage control horizon (in the latter case, a receding-horizon control mechanism is used). Traffic is controlled by regulating the vehicle access to the freeway and by limiting the vehicle speed by means of variable message signs. To describe the traffic behavior, a "classical" macroscopic model, first proposed by Payne (1971), is adapted. Even though the problem is stated within a deterministic context, an optimal control law in feedback form is sought to react to unpredictable events. The resulting functional optimization problem is reduced to a nonlinear programming problem by constraining the control law to take on a fixed structure in which free parameters have to be optimized. For such a structure, a multilayer feedforward neural mapping is chosen. Simulation results show the effectiveness of the proposed method in two different case studies. For the simulation of the second case study, real traffic data are used, which allows one to very well represent critical traffic conditions on freeways.
---
paper_title: Stochastic Optimal-Control Approach to Automatic Incident-Responsive Coordinated Ramp Control

paper_content:

This paper presents a stochastic optimal-control-based approach to real-time incident-responsive coordinated ramp control. The proposed coordinated ramp-control methodology includes two major functions, i.e., 1) identification of control-zone-based congestion patterns using the modified generalized-sequential-probability-ratio-testing technology and 2) group-based ramp control using stochastic optimal control coupled with extended Kalman filtering technologies. With the aid of the Paramics microscopic traffic simulator, numerical studies under various simulated incident-induced congestion conditions were conducted. Corresponding numerical results indicate the feasibility of the proposed ramp-control method in responding to diverse lane-blocking incident-induced traffic-congestion conditions
---
paper_title: Optimal use of telemetry by parallel hybrid vehicles in urban driving

paper_content:

The benefit of telemetry systems that can provide information about future traffic conditions has been previously established, with both vehicle velocity and torque split controllers in hybrid vehicles able to improve fuel economy and emissions. However, many existing algorithms are either computationally intractable for real application or do not maximise the potential savings available. Here, a computationally efficient approach for the optimal control of both velocity and torque split of a parallel hybrid electric vehicle with vehicle telemetry is proposed. The optimal control inputs are determined using Pontryagin’s Minimum Principle and applied in a receding horizon fashion over realistic drive cycles. Although developed on a relatively simple model, the proposed controller is tested on a complex hybrid vehicle simulation. The effectiveness of the proposed controller in improving fuel consumption is investigated as preview information is varied, and in the presence of modelling error and measurement noise.
---
paper_title: A Stochastic Optimal Control Approach to Real-time, Incident-Responsive Traffic Signal Control at Isolated Intersections

paper_content:

Real-time, incident-responsive traffic control and management is vital to development of advanced incident management systems in ITS. More importantly, it provides, from an academic point of view, the linkages between incident detection, incident management, and traffic signal control. This study explores the application of a stochastic optimal control approach to real-time, incident-responsive traffic control at isolated intersections. In the methodology development, time-varying lane traffic state variables and control variables are specified to characterize sectionwide interlane and intralane traffic states under conditions of lane-blocking incidents. Following specification of system states, we formulated a discrete-time nonlinear stochastic model that comprises four types of equations, namely (1) recursive equations, (2) measurement equations, (3) incident-induced delay equations, and (4) boundary constraints. From the proposed stochastic model we then developed a stochastic optimal control algorithm to update the time-varying control variables and lane traffic state variables in real-time with lane-blocking incidents at isolated intersections. To generate traffic data used in model tests efficiently, we employed an advanced microscopic traffic simulator, Paramics, Version 3.0, which is developed to model and analyze ITS traffic flow conditions. The preliminary test results indicate that the proposed method can accomplish the goal of real-time, incident-responsive traffic signal control. In addition to proposing a new methodology, we hope that this study can initiate investigation into real-time, incident-responsive traffic control and management to achieve the final goal of networkwide incident-responsive, traffic-optimal control for incident management.
---
paper_title: TRAFFIC NOISE AND TRAFFIC LIGHT CONTROL

paper_content:

Abstract An optimal control problem of traffic light duration is considered. The traffic noise level is introduced as a state variable in a dynamical optimization problem. A closed loop control system is designed which influences the green duration of the lights according to the equivalent noise level. Real time considerations lead to sub-optimal control implementation. This control policy decreases the noise levels at intensive traffic intersections. The traffic lights adapt their duration according to the noise pollution. Simulation and experimental results are discussed.
---
paper_title: Dynamic bus holding strategies for schedule reliability: Optimal linear control and performance analysis

paper_content:

As is well known, bus systems are naturally unstable. Without control, buses on a single line tend to bunch, reducing their punctuality in meeting a schedule. Although conventional schedule-based strategies that hold buses at control points can alleviate this problem these methods require too much slack, which slows buses. This delays on-board passengers and increases operating costs.
---
paper_title: A model of optimal transport maintenance with demand responsiveness

paper_content:

Maintenance activities can be performed throughout the lifetime of a particular facility or piece of equipment, thereby affecting its quality in a continuous fashion. It is assumed in this paper that quality of a facility is determined by natural factors, rate of use and maintenance investments while demand for the facility is assumed to be a function of its quality. A dynamic optimization model in the form of a simple linear optimal control problem is then developed in order to determine optimal maintenance policies under these circumstances. Bang-bang and singular policies are derived and given economic interpretations. An algorithm is presented for numerical solution of the Pontryagin necessary conditions. Finally, sufficiency conditions are obtained for the model structure considered.
---
paper_title: Influence of Demand-Quality Interrelationships on Optimal Policies for Stage Construction of Transportation Facilities

paper_content:

The time staging of investment decisions for transportation facilities has generally been analyzed using models which assume a complete independence between transportation level of service and demand for the use of the facility considered. Through the use of a dynamic optimal control model, we analyze the implications of explicitly considering the interrelationship between level of service and demand on the time staging of optimal investment decisions. This analysis leads to a more general time staging decision rule than those previously proposed in the literature; an economic interpretation of that decision rule is given. Second order conditions are developed for various cases of practical significance. Finally, a numerical example is introduced to illustrate the dramatic effect that demand-quality interrelationships can have on the optimal time staging policy.
---
paper_title: ON OPTIMAL FREEWAY RAMP CONTROL POLICIES FOR CONGESTED TRAFFIC CORRIDORS

paper_content:

This paper examines the conditions for which ramp metering can be beneficial to the overall system in terms of travel time savings for a simple traffic corridor that consists of a freeway and a set of parallel arterials connected by entrance ramps. The focus is on analyzing state and control relationships to arrive at general analytical results regarding optimal metering policies, rather than on either developing specific control algorithms or solving a specific application. The analysis is concerned with the general behavior of the system under ramp control and traffic diversion. The analysis assumes that time-varying traffic demands that originate from various locations are destined for a single location and that the freeway is uniformly congested throughout the control period. Under these assumptions, some general results are obtained regarding the effectiveness of ramp metering for various traffic diversion propensities and differentials between freeway and arterial traffic conditions. It is shown that the optimal ramp control policies are determined by the magnitudes of two co-state vectors that depend on traffic conditions on the freeway and its alternative, and the drivers diversion propensity. The results of two limiting cases imply that when the freeway is uniformly congested ramp control is counter-productive unless diversion occurs, and where drivers have a high propensity to divert, the optimal policy is dependent on the travel speed on the freeway alternative and on the wave speed of backward propagating waves on the freeway.
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paper_title: Optimal mainstream traffic flow control of large scale motorway networks

paper_content:

Summary form only given. The continuously increasing daily traffic congestions on motorway networks around the world call for innovative control measures that would drastically improve the current traffic conditions. Mainstream traffic flow control (MTFC) is proposed as a novel and efficient motorway traffic management tool, and its possible implementation and principal impact on traffic flow efficiency is analysed. Variable speed limits, suitably operated and enforced, are considered as one (out of several possible) way(s) for MTFC realisation, either as a stand-alone measure or in combination with ramp metering. A computationally efficient software tool for optimal integrated motorway network traffic control including MTFC is applied to a large-scale motorway ring-road. It is demonstrated via several investigated control scenarios that traffic flow can be substantially improved via MTFC with or without integration with coordinated ramp metering actions.
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paper_title: Optimal driving for single-vehicle fuel economy

paper_content:

Abstract This study uses fuel consumption simulators for 15 late-model automobiles to determine how one ought to drive to maximize fuel economy. The simulation is based on extensive on-road and dynamometer testing of the 15 cars. Dynamic programming is used to determine the optimal way to accelerate from rest to cruising speed, to drive a block between stop signs, and to cruise on hilly terrain while maintaining a given average speed. The dependence of fuel economy on cruising speed is also characterized for various road grades. Findings include that optimal speeds are generally higher for larger cars and higher on downgrades than on upgrades, and that the relative fuel penalty for exceeding the speed limit is no worse for small cars than large cars. Optimal control for accelerate-and-cruise and for driving between stop signs varies considerably from car to car; in the latter case fuel economy is much improved by achieving a rather low peak speed. Optimal control on hills is consistent from car to car and can achieve fuel economy 7% to 30% better than that of constant-speed driving on 3% to 6% grades. Results that appear generalizable to other cars are reduced to advice for the fuel-conscious driver.
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paper_title: Dynamic Systems, Variational Inequalities and Control Theoretic Models for Predicting Time-Varying Urban Network Flows

paper_content:

In this paper, we set forth certain axioms for a positive theory of dynamic urban network flows. We then show that mathematical models which fulfill these axioms may be created by adapting and extending certain fundamental notions from microeconomics and nonlinear systems theory. We further show that models created in this fashion, using concepts of fast and slow dynamic processes, may be manipulated into a variety of mathematical forms, thereby providing a synthesis of dynamic systems, variational inequality and control theoretic perspectives for predicting dynamic urban network flows. We close with a discussion of the implications of this synthesis for route guidance and intelligent vehicle infrastructure. Throughout, our presentation is at a conceptual level; the mathematical arguments are purposely not rigorous to embrace the widest possible readership.
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paper_title: On optimal cooperative conflict resolution for air traffic management systems

paper_content:

We consider optimal resolution of air traffic (AT) conflicts. Aircraft are assumed to cruise within a given altitude layer and are modeled as a kinematic system with constant velocity and curvature bounds. Aircraft cannot get closer to each other than a predefined safety distance. For such a system of multiple aircraft, we consider the problem of planning optimal paths among given waypoints. Necessary conditions for optimality of solutions are derived and used to devise a parametrization of possible trajectories that turns into efficient numerical solutions to the problem. Simulation results for a realistic aircraft conflict scenario are provided. A decentralized implementation of the optimal conflict resolution scheme is introduced that may allow free-flight coordination in a cooperative airspace management scheme. Impact of decentralization on performance and safety is finally discussed with the help of extensive simulations.
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paper_title: Dynamic user equilibrium with side constraints for a traffic network: Theoretical development and numerical solution algorithm

paper_content:

This paper investigates a traffic volume control scheme for a dynamic traffic network model which aims to ensure that traffic volumes on specified links do not exceed preferred levels. The problem is formulated as a dynamic user equilibrium problem with side constraints (DUE-SC) in which the side constraints represent the restrictions on the traffic volumes. Travelers choose their departure times and routes to minimize their generalized travel costs, which include early/late arrival penalties. An infinite-dimensional variational inequality (VI) is formulated to model the DUE-SC. Based on this VI formulation, we establish an existence result for the DUE-SC by showing that the VI admits at least one solution. To analyze the necessary condition for the DUE-SC, we restate the VI as an equivalent optimal control problem. The Lagrange multipliers associated with the side constraints as derived from the optimality condition of the DUE-SC provide the traffic volume control scheme. The control scheme can be interpreted as additional travel delays (either tolls or access delays) imposed upon drivers for using the controlled links. This additional delay term derived from the Lagrange multiplier is compared with its counterpart in a static user equilibrium assignment model. If the side constraint is chosen as the storage capacity of a link, the additional delay can be viewed as the effort needed to prevent the link from spillback. Under this circumstance, it is found that the flow is incompressible when the link traffic volume is equal to its storage capacity. An algorithm based on Euler's discretization scheme and nonlinear programming is proposed to solve the DUE-SC. Numerical examples are presented to illustrate the mechanism of the proposed traffic volume control scheme.
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paper_title: ENERGY-EFFICIENT OPERATION OF RAIL VEHICLES

paper_content:

This paper describes an analytical process that computes the optimal operating successions of a rail vehicle to minimize energy consumption. Rising energy prices and environmental concerns have made energy conservation a high priority for transportation operations. The cost of energy consumption makes up a large portion of the Operation and Maintenance (O&M) costs of transit especially rail transit systems. Energy conservation or reduction in energy cost may be one of the effective ways to reduce transit operating cost, therefore improve the efficiency of transit operations. From a theoretical point of view, the problem of energy efficient train control can be formulated as one of the functions of Optimal Control Theory. However, the classic numerical optimization methods such as discrete method of optimum programming are too slow to be used in an on-board computer even with the much improved computation power, today. The contribution of this particular research is the analytical solution that gives the sequence of optimal controls and equations to find the control change points. As a result, a calculation algorithm and a computer program for energy efficient train control has been developed. This program is also capable of developing energy efficient operating schedules by optimizing distributions of running time for an entire route or any part of rail systems. We see the major application of the proposed algorithms in fully or partially automated Train Control Systems. The modern train control systems, often referred as "positive" train control (PTC), have collected a large amount of information to ensure safety of train operations. The same data can be utilized to compute the optimum controls on-board to minimize energy consumption based on the algorithms proposed in this paper. Most of the input data, such as track plan, track profile, traction and braking characteristics, speed limits and required trip time are located in an on-board database and/or they can be transmitted via radio link to be processed by the proposed algorithm and program.
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paper_title: RAPID COMPUTATION OF OPTIMAL CONTROL FOR VEHICLES

paper_content:

This paper describes a rapid computational method of optimal control for vehicles and the software realizing it. The optimal control problem is solved with the dynamic programming technique. A traditional engineering simulator is used to predict the vehicle's performance and economy. An objective function is suggested that permits high-speed computation. Results show the dependence of optimal fuel consumption on average speed for various vehicle masses in a number of situations: acceleration from rest to cruising speed, driving between stop signs and driving on hilly terrain. Findings include that one can travel up to 20 to 80% (depending on the situation) faster than the most economical average speed without increasing fuel consumption more than an equal amount.
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paper_title: On an optimal control problem of train operation

paper_content:

This paper examines the operation of a train on a variable grade profile subject to arbitrary speed restrictions. The purpose of the study is to determine a detailed program for traction and brake applications, which minimizes energy consumption in moving the train along a given route for a given time. Stated in the form of optimal control, this problem is solved by constructing a numerical algorithm which essentially exploits analytical properties of the optimal solution obtained from the maximum principle analysis. Due to its analytical origin, the algorithm has inherent accuracy and adequate quick-operation that are demonstrated in numerical examples.
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paper_title: Modeling user adoption of advanced traveler information systems: a control theoretic approach for optimal endogenous growth

paper_content:

This study is a subsequent development of the dynamic evolution model of the market penetration of advanced traveler information systems (ATIS) proposed by Yang and Meng [Transport. Res. A 35 (2001) 895]. In previous study we have shown that a benefit-driven, user-optimal ATIS market does not necessarily lead to a socially optimal growth and optimal stationary equilibrium level of market penetration of ATIS products or services. The current study proposes an optimal time-dependent service pricing strategy so as to minimize total system cost throughout the time horizon of growth or optimally reach a socially desirable target level of ATIS market penetration in a final stationary equilibrium. We formulate the problem of interest as an optimal control problem and propose an efficient solution algorithm together with a numerical demonstration of the characteristics of the study problem.
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paper_title: Optimal scheduling of rehabilitation activities for multiple pavement facilities: Exact and approximate solutions

paper_content:

This paper presents a mathematical programming model for optimal highway pavement rehabilitation planning which minimizes the life-cycle cost for a finite horizon. It extends previous researches in this area by solving the problem of multiple rehabilitation activities on multiple facilities, with realistic empirical models of deterioration and rehabilitation effectiveness. The formulation is based on discrete control theory. A nonlinear pavement performance model and integer decision variables are incorporated into a mixed-integer nonlinear programming (MINLP). Two solution approaches, a branch-and-bound algorithm and a greedy heuristic, are proposed for this model. It is shown that the heuristic results provide a good approximation to the exact optima, but with much lower computational costs.
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paper_title: A time series analysis framework for transportation infrastructure management

paper_content:

We present an integrated framework to address performance prediction and maintenance optimization for transportation infrastructure facilities. The framework is based on formulating the underlying resource allocation problem as discrete-time, stochastic optimal control problem with linear dynamics and a quadratic criterion. Facility deterioration is represented as a time series which provides an attractive and rigorous approach to specify and estimate performance models. The state and decision variables in the framework are continuous which allows the framework to overcome important computational and statistical limitations that do not allow existing optimization models to address various problems that arise the management of transportation infrastructure. To illustrate the advantages of the proposed approach, we conduct a numerical study where we examine the case of multiple technologies being used simultaneously to collect condition data. Specifically, we illustrate how the framework can be used to quantify the effect of the capabilities of inspection technologies, i.e., precision, accuracy and relationships, on life-cycle costs. This information can be used to compute the operational value of combining technologies, and thus, to guide in their selection based on economic criteria.
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paper_title: A new strategy for minimum usage of external yaw moment in vehicle dynamic control system

paper_content:

Due to the loss of vehicle directional stability in emergency maneuvers, a new complete desired model for vehicle handling based on the linear two-degrees-of-freedom (2DOF) model and tire/road conditions is presented to be tracked by the direct yaw moment control (DYC) system. In order to maintain the vehicle actual motions, yaw rate and side-slip angle, close to the proposed desired responses without excessively large external yaw moment, a complete linear quadratic (LQ) optimal problem is formulated and its analytical solution is obtained. Here, the derived control law is evaluated and its different versions are discussed. It is shown that the side-slip tracking by DYC is more effective than the yaw rate control to stabilize vehicle motions in nonlinear regimes. Also, optimal property of the control law provides the possibility of reducing the external yaw moment as low as possible, at the cost of some admissible tracking errors. Simulation studies of vehicle handling, with and without control, have been conducted using a full nonlinear vehicle dynamic model. The results, obtained during various maneuvers, indicate that when the proposed optimal controller is engaged with the model, improvements in the handling performance through a reduced external yaw moment can be acquired.
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paper_title: Some general results on the optimal ramp control problem

paper_content:

In an effort to relieve peak hour congestion on freeways, various ramp metering algorithms have been employed to regulate the inputs to freeways from entry ramps. In this paper, we consider a freeway system comprised of a freeway section and its entry/exit ramps, and formulate the ramp control problem as a dynamic optimal process to minimize the total time spent in this system. Within this framework, we are able to show when ramp metering is beneficial to the system in terms of total time savings, and when it is not, under the restriction that the controlled freeway has to serve all of its ramp demand, and the traffic flow process follows the rules prescribed by the LWR theory with a triangular flow-density relationship. We also provide solution techniques to the problem and present some preliminary numerical results and empirical validation.
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paper_title: Efficiency and equity properties of freeway network-wide ramp metering with AMOC

paper_content:

Abstract The Advanced Motorway Optimal Control (AMOC) strategy for optimal freeway network-wide ramp metering is applied to the ring-road of Amsterdam, The Netherlands, in the aim of investigating some important and interesting problems arising in ubiquitous ramp metering systems. A number of suitably chosen scenarios along with a thorough analysis, interpretation, and suitable visualization of the obtained results provide a basis for the better understanding of some complex interrelationships of competing performance criteria. More precisely, the strategy’s efficiency and equity properties as well as their trade-off are studied and their partially competitive behaviour is discussed. This trade-off is implicitly addressed by the AMOC strategy through consideration of the available ramp storage space and may be used as a tool to establish a desired policy of the system’s efficiency versus equity.
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paper_title: Coordinated and integrated control of motorway networks via non-linear optimal control

paper_content:

The problem of designing integrated traffic control strategies for motorway networks with the use of ramp metering, route guidance, and motorway-to-motorway control measures is considered in this paper. A generic problem formulation is presented in the format of a discrete-time optimal control problem whose numerical solution is achieved by use of a feasible-direction algorithm. As an illustrative example, a relatively simple motorway network is considered under different control scenarios. In each case the optimal control strategy is discussed along with its effect on the traffic flow process. The results demonstrate the efficiency of the proposed approach as well as the genuinely intelligent behaviour of the designed control strategy.
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paper_title: Emergency Management of Urban Rail Transportation Based on Parallel Systems

paper_content:

Integrating artificial systems, computational experiments, and parallel execution (ACP) is an effective approach to modeling, simulating, and intervening real complex systems. Emergency response is an important issue in the operation of urban rail transport systems for ensuring the safety of people and property. Inspired by the ACP method, this paper introduces a basic framework of parallel control and management (PCM) for emergency response of urban rail transportation systems. The proposed framework is elaborated from three interdependent aspects: Points, Lines, and Networks. Points represent the modeling of urban rail stations, Lines describe the microscopic characteristics of urban rail connections between designated stations, and Networks present the macroscopic properties of all the urban rail connections. Based on the given framework, a series of parallel experiments, which were impossible to achieve in real systems, can now be conducted in the constructed artificial system. Furthermore, the constructed artificial system can be used to test and develop effective emergency control and management strategies for real rail transport systems. Therefore, this proposed framework will be able to enhance the reliability, security, robustness, and maneuverability of urban rail transport systems in case of an emergency.
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paper_title: The optimal control of collision avoidance trajectories in air traffic management

paper_content:

A collision avoidance/conflict resolution model for aircraft traversing planar intersecting trajectories is developed based on the actual flight dynamics of each aircraft and the criteria that a flight regime correction is optimal if it represents a minimum-time safe deviation from a preassigned flight program. The formulation of the model leads to a singular optimal control problem where the control variable constraint is the maximum acceptable aircraft turn rate for passenger comfort and safety and the state variable constraint is defined in terms of the radius of the protected zone about a potentially conflicting aircraft. A robust, accurate real-time solution procedure is derived for computing the steering program for the execution of the optimal safe avoidance maneuver. Several representative examples of pairwise trajectory conflicts are analysed in detail. A brief discussion of how the model might be generalized to incorporate changes in airspeed and altitude as well as more comprehensive dynamics is included.
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paper_title: Solving the Dynamic Network User Equilibrium Problem with State-Dependent Time Shifts

paper_content:

In this paper we consider the infinite dimensional variational inequality (VI) formulation of dynamic user equilibrium (DUE) put forward by Friesz et al. (1993) [A variational inequality formulation of the dynamic network user equilibrium problem. Operations Research 41, 179-191] as well as the differential variational inequality (DVI) version reported in Friesz et al. (2001) [Dynamic network user equilibrium with state-dependent time lags. Networks and Spatial Economics 1, 319-347]. We show how the theory of optimal control and the theory of infinite dimensional variational inequalities may be combined to create a simple and effective fixed point algorithm for calculating DUE network flows that are solutions of both formulations. A numerical example is provided.
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paper_title: A dynamic programming algorithm based on expected revenue approximation for the network revenue management problem

paper_content:

Since American Airlines successfully applied revenue management (RM) to raise its revenue, RM has become a common technique in the airline industry. Due to the current hub-and-spoke operation of the airline industry, the focus of RM research has shifted from the traditional single-leg problem to the network-type problem. The mainstream approaches, bid price and virtual nesting, are faced with some limitations such as inaccuracy due to their suboptimal nature and operation interruption caused by the required updates. This study developed an algorithm to generate a seat control policy by approximating the expected revenue function in a dynamic programming (DP) model. In order to deal with the issue of dimensionality for the DP model in a network context, this study used a suitable parameterized function and a sampling concept to achieve the approximation. In the numerical experiment, the objective function value of the developed algorithm was very close to the one achieved by the optimal control. We believe that this approach can serve as an alternative to the current mainstream approaches for the network RM problem for airlines and will provide an inspiring concept for other types of multi-resource RM problems.
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Title: Optimal Control Theory in Intelligent Transportation Systems Research - A Review

Section 1: Introduction
Description 1: Introductory remarks on the importance of ITS and the relevance of optimal control theory in addressing transportation problems.

Section 2: Review methodology
Description 2: Explanation of the review process, selection criteria, and the scope of literature reviewed for the study.

Section 3: Categorize articles by academic journals
Description 3: Analysis of how the selected articles are distributed across different academic journals.

Section 4: Categorize articles by traffic types in the research
Description 4: Categorization of the reviewed articles based on different types of traffic (highways, urban roads, railways, air traffic).

Section 5: Categorize articles by ITS research objectives
Description 5: Categorization of the articles based on key research objectives in ITS, such as mitigation of traffic congestion, efficiency improvement, maintenance, and safety.

Section 6: Categorize articles by research methods of reducing traffic congestion
Description 6: Detailed discussion of the different methods used in ITS for reducing traffic congestion, categorized by research approach.

Section 7: Categorize articles by areas in ITS research
Description 7: Categorization of articles based on the different areas within ITS, such as Advanced Traveler Information Systems, Advanced Transportation Management Systems, ITS-Enabled Transportation Pricing Systems, Advanced Public Transportation Systems, and Fully Integrated Intelligent Transportation Systems.

Section 8: Research gaps and possible future research directions
Description 8: Identification of current research gaps and suggestions for future research directions within the field of ITS using optimal control theory.