Equilibrium Queueing Patterns at a Two-Tandem Bottleneck during the Morning Peak

Several researchers have analyzed queueing patterns at bottleneck sites on freeways during the morning peak. However, all previous studies have assumed that each commuter passes only one bottleneck during his commuting trip. Here, we consider the possibility that some commuters pass two bottlenecks on their way to work. The objective is to obtain cumulative arrival curves at each of the two bottlenecks, given who passes both bottlenecks and who passes only one, and their desired arrival times at their work places (work starting times). Each commuter using the freeway is assumed to have the same travel cost function which consists of time-dependent costs due to queueing delay (waiting time in a queue) and schedule delay (the time difference between his actual and desired arrival time at the work place). Commuter trips are assigned temporally so as to establish an equilibrium in which each commuter seeks to minimize his travel cost. The queue evolutions illustrate a service priority at the downstream bottleneck in favor of commuters passing only the downstream bottleneck. One of the countermeasures for this equity problem in the service priority would be to meter the favored commuters.