Journal ArticleDOI
A Tractable Class of Algorithms for Reliable Routing in Stochastic Networks
TLDR
The goal of this article is to provide the theoretical basis for enabling tractable solutions to the "arriving on time" problem and enabling its use in real-time mobile phone applications and to present an efficient algorithm for finding an optimal routing policy with a well bounded computational complexity.Abstract:
The goal of this article is to provide the theoretical basis for enabling tractable solutions to the "arriving on time" problem and enabling its use in real-time mobile phone applications. Optimal routing in transportation networks with highly varying traffic conditions is a challenging problem due to the stochastic nature of travel-times on links of the network. The definition of optimality criteria and the design of solution methods must account for the random nature of the travel-time on each link. Most common routing algorithms consider the expected value of link travel-time as a sufficient statistic for the problem and produce least expected travel-time paths without consideration of travel-time variability. However, in numerous practical settings the reliability of the route is also an important decision factor. In this article, the authors consider the following optimality criterion: maximizing the probability of arriving on time at a destination given a departure time and a time budget. The authors present an efficient algorithm for finding an optimal routing policy with a well bounded computational complexity, improving on an existing solution that takes an unbounded number of iterations to converge to the optimal solution. A routing policy is an adaptive algorithm that determines the optimal solution based on en route travel-times and therefore provides better reliability guarantees than an a-priori solution. Novel speed-up techniques to efficiently compute the adaptive optimal strategy and methods to prune the search space of the problem are also investigated. Finally, an extension of this algorithm which allows for both time varying traffic conditions and spatio-temporal correlations of link travel-time distributions is presented. The dramatic runtime improvements provided by the algorithm are demonstrated for practical scenarios in California.read more
Citations
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Journal ArticleDOI
Constraint reformulation and a Lagrangian relaxation-based solution algorithm for a least expected time path problem
Lixing Yang,Xuesong Zhou +1 more
TL;DR: In this paper, an integer programming model for finding the a priori least expected time paths in a time-dependent and stochastic network is presented, and a number of reformulations to establish linear inequalities that can be easily dualized by a Lagrangian relaxation solution approach.
Journal ArticleDOI
Predicting travel time reliability using mobile phone GPS data
TL;DR: TRIP is the first method to provide accurate predictions of travel time reliability for complete, large-scale road networks, using GPS data from mobile phones or other probe vehicles.
ReportDOI
Least expected time paths in stochastic, time-varying transportation networks
TL;DR: In this paper, the authors consider stochastic, time-varying transportation networks, where the arc weights (arc travel times) are random variables with probability distribution functions that vary with time.
Journal ArticleDOI
Optimizing on-time arrival probability and percentile travel time for elementary path finding in time-dependent transportation networks: Linear mixed integer programming reformulations
Lixing Yang,Xuesong Zhou +1 more
TL;DR: In this paper, a generic modeling framework for finding reliable paths in dynamic and stochastic transportation networks is proposed to address a class of two-stage routing models through reformulation of two commonly used travel time reliability measures, namely on-time arrival probability and percentile travel time, which are much more complex to model in comparison to expected utility criteria.
Journal ArticleDOI
Application of Lagrangian relaxation approach to α-reliable path finding in stochastic networks with correlated link travel times
TL;DR: In this article, the authors investigated the important problem of determining a reliable path in a stochastic network with correlated link travel times, and the Lagrangian relaxation based framework was used to handle the α-reliable path problem, by which the intractable problem with a non-linear and non-additive structure can be decomposed into several easy-to-solve problems.
References
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TL;DR: A tree is a graph with one and only one path between every two nodes, where at least one path exists between any two nodes and the length of each branch is given.
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Dynamic Programming and Optimal Control
TL;DR: The leading and most up-to-date textbook on the far-ranging algorithmic methododogy of Dynamic Programming, which can be used for optimal control, Markovian decision problems, planning and sequential decision making under uncertainty, and discrete/combinatorial optimization.
Neuro-Dynamic Programming.
TL;DR: In this article, the authors present the first textbook that fully explains the neuro-dynamic programming/reinforcement learning methodology, which is a recent breakthrough in the practical application of neural networks and dynamic programming to complex problems of planning, optimal decision making, and intelligent control.
Book
Neuro-dynamic programming
TL;DR: This is the first textbook that fully explains the neuro-dynamic programming/reinforcement learning methodology, which is a recent breakthrough in the practical application of neural networks and dynamic programming to complex problems of planning, optimal decision making, and intelligent control.