Multi-state semi-Markov modeling of recurrent events: Estimating driver waiting time at semi-controlled crosswalks

Abstract

At “semi-controlled” crosswalks, signs and markings are present, but delay to pedestrians and motorists is largely the result of the “negotiation” between the two parties to determine who yields. This paper proposes a novel approach using multi-state semi-Markov models to investigate motorists’ delay and their interactions with pedestrians. Motorist waiting behavior can be divided into a series of gap acceptance decisions as part of a Markov Chain. Each gap acceptance decision is modeled as a specific transition between two states in the Markov Chain.To demonstrate the reliability of the proposed models, multi-state semi-Markov models are estimated for the waiting behavior of more than 1,000 drivers in the presence of pedestrians at semi-controlled crosswalks. The multi-state semi-Markov models are capable of dealing with specific challenges related to (i) the need to account for recurrent events and (ii) a generalized framework for vehicle delay estimation and simulation at semi-controlled crosswalks. The extent to which motorists behave more aggressively and impatiently as their delay increases is demonstrated. Differences in behavior for operators of buses and trucks were also identified. The semi-Markov method is also able to deal effectively with the “pulsing” arrival patterns of pedestrians at crosswalks as university classes begin and end nearby and handle temporal heterogeneity. Finally, to address aggressive driver behavior, several safety implications are discussed.