Traffic Delay at a Signalized Intersection with Binomial Arrivals

Delay formulas are derived for vehicles at an isolated intersection at which the vehicle arrivals are supposed generated by a binomial process, the departure rates are assumed constant, and the control strategy is to switch the lights when the favored queue empties. The mean delay is calculated using a discrete analog of the method used by Darroch, Morris, and Newell for the case of random arrivals. Later a probability generating function for delay is developed yielding, in particular, the variance of the delay.