Analysis of bathtub congestion with continuous scheduling preference

Abstract

The bathtub model provides a vital analysis tool to capture the features of traffic jam, especially that of hypercongested traffic. For reducing the complication of analysis, previous studies adopted the constant α-β-γ preferences for travel time, arrival early and late penalties. This treatment not only destroys the continuity of user equilibrium (UE) departure rate, but also leaves out of considering the influences of continuity of schedule preference. In this paper, we investigate a specific bathtub model with continuous schedule preference (CSP) and explore the UE and social optimum (SO) solutions. Analytical and numerical results show that the introduction of CSP lets departure rate continuous. In the UE state, it results in traffic congestion being more costly and duration of hypercongestion being longer than existing bathtub models. In the SO state, the system cost becomes lower. Our study extends the knowledge about bathtub models and provides more insight into downtown traffic congestion.