On a Paper by Andre de Palma, Moshe Ben-Akiva, Claude Lefèvre, and Nicolaos Litinas Entitled “Stochastic Equilibrium Model of Peak Period Traffic Congestion”

A paper published in 1983 in this journal by A. de Palma et al. uses a deterministic queueing supply model in combination with a random utility demand model to predict the pattern of traffic flows during a peak period. Two different versions of the supply model are included, a “basic model” which is identical to the supply model used by a number of other authors investigating the same general problem (e.g., M. J. Smith [Smith, M. J. 1984. The existence of a time-dependent equilibrium distribution of arrivals at a single bottleneck. Trans. Sci.18 385–394.]), and a more complicated “extended model.” As detailed below, there is a mathematical discrepancy in the analysis. Because of this discrepancy, some of the conclusions about the traffic flow pattern in the case of the extended model are incorrect and all are unproven. For the simpler—and seemingly more realistic—basic model, the discrepancy vanishes and the conclusions remain valid.