An Improved Expected Waiting Time Model for Passengers in Public Transport

Abstract

Passengers' expected waiting time (EWT) has been a primary performance indicator of public transport services. Accurate estimation of EWT plays a vital role in public transit planning and operations. An extensive literature review indicates that existing EWT models were usually developed based on three assumptions: (i) passengers arrive at transit stops randomly; (ii) a large sample size of transit vehicles arriving/departing within a scheduling horizon; and (iii) passengers can always board the first-arrival vehicle. These assumptions, however, do not always hold in practice. We recognize that the number of vehicle arrivals/departures is often quite limited during the study period (e.g., a morning peak). Thus, it is evident to relax assumption (ii) to develop more realistic and accurate EWT models. To this end, we propose an approximate model for EWT estimation only based on assumptions (i) and (iii). The approximation is conducted using a Taylor expansion with an inherent minimization of the approximation error. For the sake of practical applications, simple closed-form expressions of the proposed model are given for the Jth order Taylor expansion, where J=0,1,2,3,4. Numerical experiments are conducted to compare the new model with the existing ones under various scenarios. The results demonstrate the improved accuracy of the new model than its counterparts in estimating EWT in realistic situations (where headways follow asymmetric distributions). A real-world case study of a bus line in Chengdu, China, including the case of common lines, further demonstrates the advantages of the new model. Potential applications and extensions of the new model are discussed.

Keywords: Transportation, Public Transit, expected waiting time, approximate model, Taylor expansion, closed-form expression