On the modeling of passenger mobility for stochastic bi-modal urban corridors

This paper proposes a methodology to estimate the passenger macroscopic fundamental diagram for bi-modal urban corridors while accounting for the stochastic nature of bus operations. The proposed framework extends the existing variational theory (VT) approaches by: (i) introducing a probabilistic VT graph, where the costs are computed using an efficient stochastic shortest path algorithm; (ii) capturing the effects of stochastic moving bus bottlenecks and the correlation of bus arrival times; (iii) incorporating a macroscopic passenger model that reflects the passenger dynamics for the different modes; and (iv) accounting for the effects that the traffic conditions might have on bus operations. Using a Monte-Carlo simulation and empirical data from a bi-modal corridor in Zurich, Switzerland, we not only successfully validate the results yielded by our stochastic VT approach, but also show its applicability on a real corridor. A comparison with a deterministic VT approach reveals the value of the proposed framework, especially for corridors with a high bus frequency and considerable stochasticity. The results demonstrate that incorporating stochasticity and the traffic conditions is essential if buses run with relatively short and variable headways. Moreover, we introduce an innovative application example for the evaluation of different bus lane layouts, aiming to maximize the passenger throughput along a bi-modal urban corridor. The application example shows that the proposed framework can be used as an efficient modeling tool for practitioners. In particular, it can be used to identify a proper lane allocation strategy by computing the critical density of cars when a mixed lane should be switched to a dedicated bus lane or vice versa. It is important to note that such application would not have been possible without our proposed VT extensions, which account for both passenger dynamics and the impact of traffic conditions. Finally, given that the proposed methodology is generic, it can be easily extended to various traffic problems involving stochasticity.