As the calculations of the LSA progress, the collision rates of particles may and usually do increase. Still the LSA successfully approaches the jamming state as long as those rates remain comparable among all the particles, except for the rattlers. (Rattlers experience consistently low collision rates. This property allows one to detect rattlers.) However, it is possible for a few particles, even just for a single particle, to experience a very high collision rate along the approach to a certain simulated time. The rate will be increasing without a bound in proportion to the rates of collisions in the rest of the particle ensemble. If this happens, then the simulation will be stuck in time, it won't be able to progress toward the state of jamming.