Weihua Gu

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 of this stop type, as illustrated by two special cases. The models estimate the maximum number of buses that can arrive at and serve a stop and still satisfy a specified target of average bus delay. These models can be used to determine, for example, a stops suitable number of bus berths, given the bus demand and the specified delay target. The solutions for the two cases are used to derive a closed-form, parsimonious approximation model for general cases. This approximation matches simulations reasonably well for many conditions that arise in real settings; differences of less than 10% were common. Our results 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 commonly used for the delay target in previous bus stop studies is a poor one.

On the impact of obstructions on the capacity of nearby signalised intersections

Various obstructions exist that can impede maximum vehicle flow through signalised intersections. Examples include buses or freight vehicles dwelling at loading areas near the intersection, stalled vehicles, pre-signals that temporarily block car traffic to provide bus priority, on-street parking manoeuvres and permanent road fixtures. If the effects of these obstructions are not recognised or accounted for, vehicle discharge capacities at these critical locations can be overestimated, leading to ineffective traffic management strategies. This paper examines the capacity of an isolated signalised intersection when a nearby roadway obstruction is present in either the upstream or downstream direction. To quantify the loss of capacity caused by an obstruction, the paper applies the variational theory of kinematic waves in a moving-time coordinate system, which simplifies the traditional variational theory by reducing the number of local path costs that must be considered. The result is a simple recipe that requires few calculations and can be used to gain insights into signal operations when obstructions are present. Capacity formulae for general cases are also developed from the recipe. The results, recipe and formulae can be used to guide policies on the location of obstructions that can be controlled, like bus stops, pre-signals or permanent road fixtures and to develop strategies to mitigate the effects of obstructions that can be identified in real time. As an example, a simple adaptive signal control scheme is created using this methodology to more efficiently allocate green time between competing directions when an obstruction is present.