Vehicle delay estimation at unsignalised pedestrian crosswalks with probabilistic yielding behaviour

Unsignalised pedestrian crosswalks are commonly adopted in school and residential areas. To enhance pedestrian safety, various types of signs and crosswalk markings have been implemented, which results in motorists' probabilistic yielding behaviour and interrupted traffic flow patterns. Predicting the vehicular delay is of central importance to evaluate the level of service. However, as the interaction involves two random streams and is governed by the uncertain yielding behaviour, the analysis could be fairly challenging. In this paper, a novel method is proposed to estimate vehicular delay, which decomposes the vehicular stream into free-flow and queuing traffic. By explicitly considering the relation between the vehicular headway and the critical gap, the probability of a yielding event is derived to the expected proportion of queue formation, queue dispersion and free-flow periods. Equations of the average vehicular delay are given as a function of the vehicle volume, pedestrian volume and the yielding rate. The validation experiment using a stochastic simulation indicates that the proposed method consistently gives close estimations with absolute error less than 1s.