 The busy period is the time spent in states 1, 2, 3... between visits to the state 0.The expected length of a busy period is 1/(μ−λ) where 1/μ is the expected length of service time and λ the rate of the Poisson process governing arrivals.The busy period probability density function formula_4 can be shown to obey the Kendall functional equation
where as above g is the Laplace–Stieltjes transform of the service time distribution function.