Expected Time Paths Research Articles

Corrigendum to “Least Expected Time Paths in Stochastic Schedule-Based Transit Networks”

Corrigendum to “Least Expected Time Paths in Stochastic Schedule-Based Transit Networks”

Least Expected Time Paths in Stochastic Schedule-Based Transit Networks

We consider the problem of determining a least expected time (LET) path that minimizes the number of transfers and the expected total travel time in a stochastic schedule-based transit network. A time-dependent model is proposed to represent the stochastic transit network where vehicle arrival times are fully stochastically correlated. An exact label-correcting algorithm is developed, based on a proposed dominance condition by which Bellman’s principle of optimality is valid. Experimental results, which are conducted on the Ho Chi Minh City bus network, show that the running time of the proposed algorithm is suitable for real-time operation, and the resulting LET paths are robust against uncertainty, such as unknown traffic scenarios.

A priori least expected time paths in fuzzy, time-variant transportation networks

Dynamics and fuzziness are two significant characteristics of real-world transportation networks. To capture these two features theoretically, this article proposes the concept of a fuzzy, time-variant network characterized by a series of time-dependent fuzzy link travel times. To find an effective route guidance for travelers, the expected travel time is specifically adopted as an evaluation criterion to assess the route generation process. Then the shortest path problem is formulated as a multi-objective 0–1 optimization model for finding the least expected time path over the considered time horizon. Different from the shortest path problem in dynamic and random networks, an efficient method is proposed in this article to calculate the fuzzy expected travel time for each given path. A tabu search algorithm is designed for the problem to generate the best solution under the framework of linear weighted methods. Finally, two numerical experiments are performed to verify the effectiveness and efficiency of the model and algorithm.

Shortest Path Finding Problem in Stochastic Time-Dependent Road Networks With Stochastic First-In-First-Out Property

As travel times in road networks are dynamic and uncertain, it is difficult and time-consuming to search for the least expected time path in large-scale networks. This paper addresses the problem of finding the least expected time path in stochastic time-dependent (STD) road networks. A stochastic travel speed model is proposed to represent STD link travel times. It is proved that the link travel times in STD networks satisfy the stochastic first-in-first-out (S-FIFO) property. Based on this S-FIFO property, an efficient multicriteria A* algorithm is proposed to exactly determine the least expected time path in STD networks. Computational results using several large-scale road networks show that the proposed algorithm has a significant computational advantage over existing solution algorithms without the S-FIFO property.

Constraint reformulation and a Lagrangian relaxation-based solution algorithm for a least expected time path problem

Using a sample-based representation scheme to capture spatial and temporal travel time correlations, this article constructs an integer programming model for finding the a priori least expected time paths. We explicitly consider the non-anticipativity constraint associated with the a priori path in a time-dependent and stochastic network, and propose a number of reformulations to establish linear inequalities that can be easily dualized by a Lagrangian relaxation solution approach. The relaxed model is further decomposed into two sub-problems, which can be solved directly by using a modified label-correcting algorithm and a simple single-value linear programming method. Several solution algorithms, including a sub-gradient method, a branch and bound method, and heuristics with additional constraints on Lagrangian multipliers, are proposed to improve solution quality and find approximate optimal solutions. The numerical experiments investigate the quality and computational efficiency of the proposed solution approach.

Algorithm for Determining Most Reliable Travel Time Path on Network with Normally Distributed and Correlated Link Travel Times

Transportation networks are subject to significant travel time uncertainty as a result of traveler behavior, recurring congestion, capacity variability (construction zones, traffic incidents), variation in demand, and so on. Therefore, interest is growing in modeling and optimizing travel time reliability in such networks. This paper proposes an efficient algorithm to compute the path of maximum travel time reliability on a network with normally distributed and correlated link travel times. For this optimal reliability path (ORP) problem, it is shown that the subpath optimality condition for the deterministic shortest path problem does not hold, and consequently, a new bounds-based optimality criterion is proposed using the K shortest expected time paths and the minimum path variance on the network. An algorithm is developed to solve the ORP problem on the basis of the proposed optimality criterion and an efficient path generation procedure. Computational experiments on various test networks show the proposed algorithm to be efficient, requiring limited path enumeration. With as few as five shortest paths and 50 Monte Carlo draws, the proposed algorithm is able to find the most reliable path for realistic network sizes. Empirical investigations highlight the unreliability of the least expected time path and suboptimality of the independence assumption. The study also underscores the role of risk attitudes (reflected by reliability threshold) on the benefits of the ORP. The algorithm and empirical results have important applications for developing reliability-based routing applications for congestion mitigation and intelligent transportation systems.

Least Expected Time Paths in Stochastic, Time-Varying Transportation Networks

We consider stochastic, time-varying transportation networks, where the arc weights (arc travel times) are random variables with probability distribution functions that vary with time. Efficient procedures are widely available for determining least time paths in deterministic networks. In stochastic but time-invariant networks, least expected time paths can be determined by setting each random arc weight to its expected value and solving an equivalent deterministic problem. This paper addresses the problem of determining least expected time paths in stochastic, time-varying networks. Two procedures are presented. The first procedure determines the a priori least expected time paths from all origins to a single destination for each departure time in the peak period. The second procedure determines lower bounds on the expected times of these a priori least expected time paths. This procedure determines an exact solution for the problem where the driver is permitted to react to revealed travel times on traveled links en route, i.e., in a time-adaptive route choice framework. Modifications to each of these procedures for determining least expected cost (where cost is not necessarily travel time) paths and lower bounds on the expected costs of these paths are given. Extensive numerical tests are conducted to illustrate the algorithms' computational performance as well as the properties of the solution.

The Role of Trade Flows in Exchange Rate Determination: A Rational Expectations Approach

The purpose of this paper is to examine the interaction between the exchange rate and the trade balance within the framework of the portfolio approach to exchange rates and rational expectations. In a simplified linear version, it is shown that the difference between the spot exchange rate and its long-run equilibrium value is proportional to the current level of the trade-balance surplus normalized by the current stock of foreign-asset holdings. Therefore, the analysis provides some evidence in favor of the presumption that surplus country should have an undervalued currency (relative to its long-run level). The basic idea behind the analysis is that, in a world of high capital mobility,current flow payments disequilibria can be accommodated by capital flows without need, in principle, for exchange rate movements. Only if the public expects lasting change in the required rate of capital flows will exchange rates adjust, since in this case the expected time path of net foreign assets will be significantly affected.