Performance Analysis of Overtaking Maneuvers at Bus Stops with Tandem Berths

Bus queues are common at bus stops and may cause significant delays. Overtaking is a standard maneuver used by buses at curbside stops. In general, there are two kinds of overtaking maneuvers, namely overtaking in and overtaking out. When overtaking is allowed, the analysis of the bus queues becomes more difficult because such maneuvers violate the first-in, first-out rule and affect the capacity of the bus stop as well as the average waiting delay. It is important to understand the effects that overtaking maneuvers have on the operations at bus stops. In our study, we consider four different bus overtaking rules at curbside bus stops and analyze four associated queuing models with finite tandem berths. To be more specific, low, moderate, and high bus frequencies are analyzed assuming exponentially distributed dwell times. Analytic expressions for the expected average waiting delays are developed. Further, a general queueing model with overtaking maneuvers occurring at random is presented. Through simulation, the accuracy of the models and the effects of the coefficient of variation of the dwell times on waiting delays are examined. Theoretical analyses as well as simulation results show the positive effects of overtaking maneuvers on the bus stop capacity and on expected average delays at curbside stops when dwell times are varied. The comparison of different overtaking maneuvers reveals performance differences among the various rules and shows why buses should rather be encouraged to overtake when departing a stop than when entering it. In addition, we discuss some practical factors that may impede the implementation of overtaking. Some managerial insights are obtained, and our formulations and results may help with the assignments of bus lines to bus stops and bus frequency-setting problems. The online appendix is available at https://doi.org/10.1287/trsc.2018.0841 .