Path comparisons for a priori and time-adaptive decisions in stochastic, time-varying networks (original) (raw)
Related papers
Least Expected Time Paths in Stochastic, Time-Varying Transportation Networks
Transportation Science, 2000
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.
Adaptive least‐expected time paths in stochastic, time‐varying transportation and data networks
Networks, 2001
In congested transportation and data networks, travel (or transmission) times are time-varying quantities that are at best known a priori with uncertainty. In such stochastic, time-varying (or STV) networks, one can choose to use the a priori least-expected time (LET) path or one can make improved routing decisions en route as traversal times on traveled arcs are experienced and arrival times at intermediate locations are revealed. In this context, for a given origin-destination pair at a specific departure time, a single path may not provide an adequate solution, because the optimal path depends on intermediate information concerning experienced traversal times on traveled arcs. Thus, a set of strategies, referred to as hyperpaths, are generated to provide directions to the destination node conditioned upon arrival times at intermediate locations. In this paper, an efficient label-setting-based algorithm is presented for determining the adaptive LET hyperpaths in STV networks. Such a procedure is useful in making critical routing decisions in Intelligent Transportation Systems (ITS) and data communication networks. A side-by-side comparison of this procedure with a label-correctingbased algorithm for solving the same problem is made. Results of extensive computational tests to assess and compare the performance of both algorithms, as well as to investigate the characteristics of the resulting hyperpaths, are presented. An illustrative example of both procedures is provided.
Expected shortest paths in dynamic and stochastic traffic networks
Transportation Research Part B-methodological, 1998
AbstractÐThe dynamic and stochastic shortest path problem (DSSPP) is de®ned as ®nding the expected shortest path in a trac network where the link travel times are modeled as a continuous-time stochastic process. The objective of this paper is to examine the properties of the problem and to identify a technique that can be used to solve the DSSPP given information that will be available in networks with Intelligent Transportation System (ITS) capabilities. The paper ®rst identi®es a set of relationships between the mean and variance of the travel time of a given path and the mean and variance of the dynamic and stochastic link travel times on these networks. Based on these relationships it is shown that the DSSPP is computationally intractable and traditional shortest path algorithms cannot guarantee an optimal solution. A heuristic algorithm based on the k-shortest path algorithm is subsequently proposed to solve the problem. Lastly, the trade-o between solution quality and computational eciency of the proposed algorithm is demonstrated on a realistic network from Edmonton, Alberta. #
Transportation Research Record, 2005
In this paper, an exact algorithm is proposed for determining adjustable preference path strategies in multicriteria, stochastic, and time-varying (MSTV) networks. In MSTV networks, multiple arc attributes are associated with each arc, each being a time-varying random variable. Solution paths that seek to minimize the expected value of each of multiple criteria are sought from all origins to a specified destination for all departure times in a period of interest. These solution strategies allow a traveler to update a preference for which criterion of multiple criteria is of greatest importance and then adaptively select the best path for the selected criterion at each node in response to knowledge of experienced travel times on the arcs. Such adjustable preference path strategies are particularly useful for providing real-time path-finding assistance.
Transportation Research Record: Journal of the Transportation Research Board, 2016
This paper studies the path finding problem in stochastic networks with known travel time distributions on each link of the network, in the presence of spatial and temporal travel time correlations. As a result of traffic dynamics and the decisions of network users, distributions with different characteristics can be observed for the link travel time at different time intervals. Considering correlations in a dynamic stochastic network and applying simulation-based realistic travel time distributions and correlations in the path finding problem in stochastic networks are the main contributions of this study. Two reliability-based optimal path finding problems were considered: the shortest path problem with on-time arrival probability and the minimum travel time budget path problem. For each problem, user heterogeneity can be considered in the developed approach, as users are allowed to have different preferences for travel time reliability. Solution algorithms for both problems were ...
Transportation Research Record: Journal of the Transportation Research Board, 2014
The aim of this study was to solve the minimum path travel time budget (MPTTB) problem, in which the travel time budget was the reliability index. This index was defined as the sum of the mean path travel time and the scaled standard deviation, which included the covariance matrix to consider correlation. Two existing solution methods in the literature, the outer approximation algorithm and Monte Carlo simulation method, were applied to solve the MPTTB problem. The former method approximated the hard nonlinear constraint of the MPTTB problem by a series of linear cuts generated iteratively and repeatedly solved a mixed integer program. The latter method, which was a simulation-based method, included two stages. The first stage founded a set of candidate paths, and the second stage generated the distribution of travel times for the existing paths in the candidate set. The numerical results for these two solution methods were conducted on the Chicago sketch network, and results showed that the methods found comparable solutions though they have respective advantages and drawbacks. Although the outer approximation algorithm demonstrated promising performance, it still relied on repeatedly solving a mixed integer program (subproblem) with a commercial solver, which could be a challenging task in its own right.
Stochastic Route Planning in Public Transport
Transportation Research Procedia
Journey planning is a key process in public transport, where travelers get informed how to make the best use of a given public transport system for their individual travel needs. A common trait of most available journey planners is that they assume deterministic travel times, but vehicles in public transport often deviate from their schedule. The present paper investigates the problem of finding journey plans in a stochastic environment. To fully exploit the flexibility inherent in multi-service public transport systems, we propose to use the concept of a routing policy instead of a linear journey plan. A policy is a state-dependent routing advice which specifies a set of services at each location from which the traveler is recommended to take the one that arrives first. We consider current time dependent policies, that is, when the routing advice at a given location is based solely on the current time. We propose two heuristic solutions that find routing policies that perform better than deterministic journey plans. A numerical comparison shows the achievable gains when applying the different heuristic policies based on extensive simulations on the public transport network of Budapest. The results show that the probability of arriving on time to a given destination can be significantly improved by following a policy instead of a linear travel plan.
IEEE Transactions on Intelligent Transportation Systems, 2005
Routing vehicles based on real-time traffic information has been shown to significantly reduce travel time, and hence cost, in high-volume traffic situations. However, taking real-time traffic data and transforming them into optimal route decisions is a computational challenge. We model the dynamic route determination problem as a Markov decision process (MDP) and present procedures for identifying traffic data having no decision-making value. Such identification can be used to reduce the state space of the MDP, improving its computational tractability. This reduction can be achieved by a two-step process. The first is an a priori reduction that may be performed using a stationary, deterministic network with upper and lower bounds on the cost functions before the trip begins. The second part of the process dynamically reduces the state space further on the nonstationary stochastic road network as the trip optimally progresses. We demonstrate the significant computational advantages of the introduced methods based on an actual road network in southeast Michigan.