Adaptive least‐expected time paths in stochastic, time‐varying transportation and data networks (original) (raw)
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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.
A framework for efficient dynamic routing under stochastically varying conditions
Transportation Research Part B: Methodological
Despite measures to reduce congestion, occurrences of both recurrent and non-recurrent congestion cause large delays in road networks with important economic implications. Educated use of Intelligent Transportation Systems (ITS) can significantly reduce travel times. We focus on a dynamic stochastic shortest path problem: our objective is to minimize the expected travel time of a vehicle, assuming the vehicle may adapt the chosen route while driving. We introduce a new stochastic process that incorporates ITS information to model the uncertainties affecting congestion in road networks. A Markov-modulated background process tracks traffic events that affect the speed of travelers. The resulting continuous-time routing model allows for correlation between velocities on the arcs and incorporates both recurrent and non-recurrent congestion. Obtaining the optimal routing policy in the resulting semi-Markov decision process using dynamic programming is computationally intractable for realistic network sizes. To overcome this, we present the edsger algorithm, a Dijkstra-like shortest path algorithm that can be used dynamically with real-time response. We develop additional speed-up techniques that reduce the size of the network model. We quantify the performance of the algorithms by providing numerical examples that use road network detector data for The Netherlands.
Fast Shortest Path Routing in Transportation Networks with Time-Dependent Road Speeds
2015
The current paper deals with the subject of shortest path routing in transportation networks (in terms of travelling time), where the speed in several of the network's roads is a function of the time interval. The main contribution of the paper is a procedure that is faster compared to the conventional approaches, that derives the road's traversal time according to the time instant of departure, for the case where the road's speed has a constant value inside each time interval (in general, different value for each time interval). Furthermore, the case where the road's speed is a linear function of time inside each time interval (in general, different linear function for each time interval) is investigated. A procedure that derives the road's traversal time according to the time instant of departure is proposed for this case as well. The proposed procedures are combined with Dijkstra's algorithm and the resulting algorithms, that are practically applicable and...
Algorithms for routing problems in stochastic time-dependent networks
2002
This thesis considers routing problems in stochastic time-dependent networks where link travel times are modeled as time-dependent discrete random variables. Among various routing problems that arise in stochastic time-dependent networks, we focus on the following three problem classes: the minimum possible travel time path problem, the minimum expected travel time next-arc hyperpath problem, and the minimum expected travel time path problem. In the first problem class, we study the all-to-one minimum possible travel time paths problem, the all-to-one minimum possible travel cost paths problem, the all-to-one k-minimum path travel time realizations problem, and the all-to-one k-dynamic shortest paths problem. As routing problems in the second problem class, we discuss the all-to-one minimum expected travel time next-arc hyperpaths problem, the all-to-one minimum expected travel cost next-arc hyperpaths problem, the all-to-one minimum expected travel time nextarc hyperpaths problem i...
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. #
European Journal of Operational Research
We propose in this article an adaptive algorithm for optimal and robust guidance for the users of the road networks. The algorithm is based on the Stochastic On Time Arrival (SOTA) family of routing algorithms, which is appropriate for taking into account the variability of travel times through the road networks. The SOTA approach permits the derivation of the maximum cumulative probability distribution of the time arrival toward a given destination in the network. Those distributions allow the selection of the most reliable origin-destination paths under given travel time budgets. We investigate here the introduction of robustness against link and path failures in the criterion of the guidance strategy selection. Our algorithm takes into account the reliability of itinerary travel times, since it is based on a SOTA approach. In addition, the algorithm takes into account itinerary robustness, by favoring itineraries with possible and reliable alternative diversions, in case of link failures, with respect to itineraries without or with less reliable alternatives. We first analyze the algorithm in its static version, without considering the traffic dynamics, and show some interesting properties. We then combine the robust guidance algorithm with a dynamic traffic model by using the traffic simulator SUMO (Simulation of Urban Mobility), and illustrate its effectiveness in some dynamic scenarios.
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.
Online Stochastic Routing Incorporating Real-Time Traffic Information
Transportation Research Record: Journal of the Transportation Research Board, 2013
This study develops on-line stochastic routing policies which identify the optimal next (path choice) action at the current decision node (intersection) for travelers, based on their preferring future paths with the shortest travel time, the lowest travel time variability, or a combination thereof, given the current network conditions. A modified label-correcting algorithm is provided to solve for the shortest path resulting from the proposed routing policies. Its running time is bounded by O( mn 2 ) , where m and n are the number of arcs and nodes, respectively, in the network. Considering that real-time traffic information is usually available with a certain level of accuracy, the proposed on-line routing policy integrates an existing information fusion model by the authors (1), which provides real-time short-term arc travel time distributions by considering information accuracy. Numerical experiments are used to demonstrate the performance of the proposed routing policies/algorithms as well as the impacts of real-time information accuracy on the online stochastic routing.