Queue length and delay distributions at traffic signals

Some new analytical results on statistical distributions of queue lengths and delays at traffic signals are derived. For this purpose, the probability generating function of the queue length distribution is developed, from which the Laplace-transform of the delay distribution is obtained. A Poisson arrival process and fixed-time control are assumed. Similar techniques have successfully been employed to obtain the queue-length and delay distributions at priority intersections. Thus, a unified theory for both signalized and unsignalized intersections results.