Models of Bus Queueing at Curbside Stops

We consider curbside bus stops of the kind that serve multiple bus routes, and that are isolated from the effects of traffic signals and other stops. A Markov chain embedded in the bus queueing process is used to develop steady-state queueing models for two special cases of this stop type. The models estimate the maximum rate that buses can arrive to, and be served by the stop, and still satisfy a specified target of average bus delay. These models can be used to determine, for example, a stop's suitable number of bus berths, given the bus demand and the specified delay target. The solutions for the two special cases are used to derive a closed-form, parsimonious approximation model for general cases. Our approximations closely match simulations for a range of conditions that arise in real settings. And the approximations unveil how suitable choices for the number of bus berths are influenced by both, the variation in the time that buses spend serving passengers at the stop, and the specified delay target. The models further show why the proxy measure that is used for the delay target in other bus-stop studies is a poor one.