Modelling bus delay at bus stop

Abstract

A bus may be blocked from entering and exiting a stop by other buses and traffic lights. The objective of this paper is to model each type of delay under these phenomena and the overall delay a bus experiences at a stop. Occupy-based delay, transfer block-based delay and block-based delay are defined and modelled. Bus delay at stop is just the sum of these three types of delay. Bus arrival rate, bus service rate, berth number and traffic lights are taken into consideration when modelling delay. Occupy-based delay is modelled with mean waiting time in Queueing theory. Transfer block-based delay and block-based delay are modelled based on standard deviation of waiting time and the probabilities of their occurrences. Two stops in Vancouver, Canada are selected for parameter estimation and model validation. The unknown parameter is estimated as 0.4230 using Ordinary Least Squares (OLS), which indicates that 42.3% of waiting time variation can be attributed to buses being blocked by the buses in front and red light for the selected stops. Model validation shows the average accuracy rate of the proposed model is 75.07% for the selected stops. Bus delay at stop evidently increases when arrival rate is more than 85 buses per hour for the given service time (50 s), ratio of red time to cycle length (0.65) and berth number (2). We also figure out that bus delay at stop evidently increases when service time is more than 60 s for the given arrival rate (54 buses per hour), ratio of red time to cycle length (0.65) and berth number (2). The proposed model can provide a tool for bus stop design and offer the foundation for service quality evaluation of transit.