Accurate Estimation of Average Waiting Time in Public Transportation Systems

Public transportation is one of the most essential services in urban areas. The average passenger waiting time at a stop is an important criterion in evaluating the quality of public transportation systems. Accurate measurement of the average waiting time (AWT) at stops leads to more appropriate and timely schedules. Researchers in the past developed formulations for measuring the AWT at stops based on the assumptions that passengers arrive at stops in a uniform manner and buses arrive at stops independently. Studies on transportation systems in different cities indicate that using these formulations does not result in an accurate measure of the AWT and that there is a significant difference between the observed AWT and the one estimated by these formulations. Researchers related the cause of this discrepancy to the violation of the assumptions of uniform passenger arrival times and independent headways. We show that when the number of buses is not large (even when these assumptions hold true) the existing formulations still lack adequate accuracy. In this paper, we examine the process of formula development that resulted in a formulation that overestimates the AWT; we then propose accurate formulas for estimating the AWT with dependent and independent headways. A discrete simulation model has also been developed to further verify the inaccuracy of the existing formulations and to evaluate the performance of the proposed formulations. Furthermore, as a case study, the AWT at a bus stop in the Tehran bus transportation system has been studied and the accuracy of the proposed formulations has been examined and compared with that of the existing one.