Tarun Rambha

Modeling Parking Search on a Network by Using Stochastic Shortest Paths with History Dependence

A substantial amount of urban traffic is related to drivers searching for parking. This study developed an online stochastic shortest path model to represent the parking search process in which drivers must choose whether to park at an available space or continue searching for a space closer to their destination. Existing online shortest path algorithms had been formulated for the full-reset or no-reset assumptions on revisiting links. As described in this paper, neither assumption was fully suitable for the parking search process. Accordingly, this paper proposes an asymptotic reset model that generalizes the full-reset and no-reset cases and uses the concept of reset rate to characterize the temporal dependence of parking probabilities on earlier observations. In this model, drivers try to minimize their expected travel cost, which includes the driving cost and the cost of walking from a parking spot to the actual destination conditioned on the parking availability on m most recently traversed links. The problem was formulated as a Markov decision process and was demonstrated with a network representing the neighborhood of the University of Wyoming campus in Laramie. The case study successfully shows the extra time used by drivers to cruise for an acceptable parking space and illustrates the impact of m on the computation effort required to compute an optimal policy.

Adaptive Transit Routing in Stochastic Time-Dependent Networks

We define an adaptive routing problem in a stochastic time-dependent transit network in which transit arc travel times are discrete random variables with known probability distributions. We formulate it as a finite horizon Markov decision process. Routing strategies are conditioned on the arrival time of the traveler at intermediate nodes and real-time information on arrival times of buses at stops along their routes. The objective is to find a strategy that minimizes the expected travel time, subject to a constraint that guarantees that the destination is reached within a certain threshold. Although this framework proves to be advantageous over a priori routing, it inherits the curse of dimensionality, and state space reduction through preprocessing is achieved by solving variants of the time-dependent shortest path problem. Numerical results on a network representing a part of the Austin, Texas, transit system indicate a promising reduction in the state space size and improved tractability of the dynamic program.

A note on detecting unbounded instances of the online shortest path problem

The online shortest path problem is a type of stochastic shortest path problem in which certain arc costs are revealed en route, and the path is updated accordingly to minimize expected cost. This note addresses the open problem of determining whether a problem instance admits a finite optimal solution in the presence of negative arc costs. We formulate the problem as a Markov decision process and show ways to detect such instances in the course of solving the problem using standard algorithms such as value and policy iteration.

Equilibrium Analysis of Low-Conflict Network Designs

Low-conflict network designs aim to reduce intersection delay by restricting or eliminating crossing conflicts. These designs range from alternating one-way street grids in central business districts to more radical designs that eliminate crossing conflicts altogether. However, travel distances in such networks are generally higher than in traditional networks. This paper proposes an equilibrium approach for evaluating the trade-off between increased distance and reduced intersection delay in networks of varying topology and demand patterns. To accomplish this objective, suitable link performance functions are developed to reflect different types of intersection control. Three control strategies are compared: two-way grids, one-way grids, and a vortex design with priority merges. These strategies are compared in grid networks, with analysis of sensitivity to demand levels and other parameters. The vortex-based design generally leads to lower average travel times and higher trip distances. However, at high demand levels the use of gap-acceptance formulas for priority merges with route choice; this union results in unstable, chaotic conditions.