Traffic queuing at unsignalized crosswalks with probabilistic priority

Abstract

Probabilistic yielding behavior is often observed at unsignalized crosswalks, but its impacts on the traffic flow in terms of traffic capacity and associated vehicular delay have not been examined before. The uniqueness of this problem is that neither traffic nor pedestrian flow holds the absolute priority as normally assumed in existing literature. Based on queuing theory, this paper developed traffic capacity and delay formulas considering the probabilistic priority. The proposed capacity equation reduces to the classic formula when the yielding rate equals one. The service time distributions for both queuers and non-queuers were derived, and M/G2/1 queuing model was applied to determine queue length and vehicular delay. Stochastic simulations showed that the proposed capacity and delay formulas precisely match the simulation results. For ease of practical applications, simpler queuing formulas including M/G/1, M/M/1 and M/D/1 were also examined. Noting that the differences between M/G2/1 and M/G/1 model are only marginal, especially for low yielding rates, we recommend the M/G/1 model for practical applications. In addition, when the pedestrian volume is relatively low, the M/M/1 model is also applicable due to its sufficient accuracy and simplicity.

Keywords:

• Yielding
• traffic capacity
• traffic delay
• queuing theory

Notes

No potential conflict of interest was reported by the authors.

1 The use of hesitation time is firstly proposed by Hawkes (1968) for ease of analysis in the framework of M/G2/1 queuing models. This hesitation time is also adopted and discussed in Heidemann and Wegmann (1997).

2 The crossing time is calculated based on a walking speed of 4 feet per second, a lane width of 12 feet, and a start time of 3 s. Vehicle flow is assumed to be uniform unless local vehicle data are known.