Distribution-Free Model for Estimating Random Queues in Signalized Networks

A general-arrival, bulk service time queueing model is formulated for studying the distribution of random queues in signalized networks. The model is predicated on the occurrence of three traffic stream transformations: merging, splitting, and filtering. The model is applied to steady-state conditions (traffic intensity < 1.0) but can be eventually converted to a time-dependent form to account for oversaturation effects. A comparison of the results of the model with those of comparable models in the literature confirms that the use of random queue estimates derived from the assumption of a Poisson arrival process is inappropriate for networks. Marginal adjustments to the Poisson process by including a variance-to-mean ratio of the departure distribution improve the random queue estimate to a point. The results also confirm recent observations by Newell about the relationship of stochastic queues in an arterial network with their counterparts at isolated intersections. Ih general queue estimates for the network case are substantially smaller than those incurred at an isolated intersection with similar traffic intensity. The difference is attributable primarily to the process of traffic filtering.