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Studies of transit dwell times suggest that the delay caused by passengers boarding and alighting rises with the number of passengers on each vehicle. This paper incorporates such a “friction effect” into an isotropic model of a transit route with elastic demand. We derive a strongly unimodal “Network Alighting Function” giving the steady-state rate of passenger flows in terms of the accumulation of passengers on vehicles. Like the Network Exit Function developed for isotropic models of vehicle traffic, the system may exhibit hypercongestion. Since ridership depends on travel times, wait times and the level of crowding, the physical model is used to solve for (possibly multiple) equilibria as well as the social optimum. Using replicator dynamics to describe the evolution of demand, we also investigate the asymptotic local stability of different kinds of equilibria.
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Operations Design of Modular Vehicles on an Oversaturated Corridor with First-in, First-out Passenger Queueing
Although urban transit systems (UTS) often have fixed vehicle capacity and relatively constant departure headways, they may need to accommodate dramatically fluctuating passenger demands over space and time, resulting in either excessive passenger waiting or vehicle capacity and energy waste. Therefore, on the one hand, optimal operations of UTS rely on accurate modeling of passenger queuing dynamics, which is particularly complex on a multistop transit corridor. On the other hand, capacities of transit vehicles can be made variable and adaptive to time-variant passenger demand so as to minimize energy waste, especially with the emergence of modular vehicle technologies. This paper investigates operations of a multistop transit corridor in which vehicles may have different capacities across dispatches. We specify skewed time coordinates to simplify the problem structure while incorporating traffic congestion. Then, we propose a mixed integer linear programming model that determines the optimal dynamic headways and vehicle capacities over the study time horizon to minimize the overall system cost for the transit corridor. In particular, the proposed model considers a realistic multistop first-in, first-out (MSFIFO) rule that gives the same boarding priority to passengers arriving at a station in the same time interval yet with different destinations. A customized dynamic programming (DP) algorithm is proposed to solve this model efficiently. To circumvent the rapid increase of the state space of a typical DP algorithm, we analyze the theoretical properties of the investigated problem and identify upper and lower bounds to a feasible solution. The bounds largely reduce the state space during the DP iterations and greatly improve the efficiency of the proposed DP algorithm. The state dimensions are also reduced with the MSFIFO rule such that all queues with different destinations at the same origin can be tracked with a single boarding position state variable at each stage. A hypothetical example and a real-world case study show that the proposed DP algorithm greatly outperforms a state-of-the-art commercial solver (Gurobi) in both solution quality and time.
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- PAR ID:
- 10291911
- Date Published:
- Journal Name:
- Transportation Science
- ISSN:
- 0041-1655
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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null (Ed.)Public transit agencies struggle to maintain transit accessibility with reduced resources, unreliable ridership data, reduced vehicle capacities due to social distancing, and reduced services due to driver unavailability. In collaboration with transit agencies from two large metropolitan areas in the USA, we are designing novel approaches for addressing the afore-mentioned challenges by collecting accurate real-time ridership data, providing guidance to commuters, and performing operational optimization for public transit. We estimate rider-ship data using historical automated passenger counting data, conditional on a set of relevant determinants. Accurate ridership forecasting is essential to optimize the public transit schedule, which is necessary to improve current fixed lines with on-demand transit. Also, passenger crowding has been a problem for public transportation since it deteriorates passengers’ wellbeing and satisfaction. During the COVID-19 pandemic, passenger crowding has gained importance since it represents a risk for social distancing violations. Therefore, we are creating optimization models to ensure that social distancing norms can be adequately followed while ensuring that the total demand for transit is met. We will then use accurate forecasts for operational optimization that includes \textit(a) proactive fixed-line schedule optimization based on predicted demand, \textit(b) dispatch of on-demand micro-transit, prioritizing at-risk populations, and \textit(c) allocation of vehicles to transit and cargo trips, considering exigent vehicle maintenance requirements (\textiti.e., disinfection). Finally, this paper presents some initial results from our project regarding the estimation of ridership in public transit.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1287/trsc.2021.1074
