Vehicular Traffic Capacity at Unsignalized Crosswalks with Probabilistic Yielding Behavior

Motorists' probabilistic yielding behavior is often observed at unsignalized crosswalks, but its impedance on traffic capacity has not been thoroughly examined. The uniqueness of this problem, which is also the challenge, is that neither pedestrians nor motorists hold absolute priority because of uncertainty in yielding behavior. Therefore, from the perspective of queuing theory, understanding the service mechanism is key to determining system performance. In this study, based on explicit analyses of complete yielding scenarios, the distribution of service time for queuing vehicles is derived. Traffic capacity is then determined on the basis of mean service time for queuers. In the special case of drivers fully respecting the priority of pedestrian flow, the capacity model reduces to the classic formula with absolute priority. The solutions from the proposed capacity model precisely match the results from stochastic simulations. To facilitate practical applications, an approximation is also developed that greatly simplifies the capacity formula but still gives very close estimations to the exact solutions. This simplified formula is recommended for practical applications. The proposed capacity formula, as well as the service time distribution, can also be applied to develop performance measures such as traffic delay and queue length through use of sophisticated queuing formulas.