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This paper studies the problem of finding a priori shortest paths to guarantee a given likelihood of arriving on-time in a stochastic network. Such reliable paths help travelers better plan their trips to prepare for the risk of running late in the face of stochastic travel times. Optimal solutions to the problem can be obtained from local-reliable paths, which are a set of non-dominated paths under first-order stochastic dominance. We show that Bellman's principle of optimality can be applied to construct local-reliable paths. Acyclicity of local-reliable paths is established and used for proving finite convergence of solution procedures. The connection between the a priori path problem and the corresponding adaptive routing problem is also revealed. A label-correcting algorithm is proposed and its complexity is analyzed. A pseudo-polynomial approximation is proposed based on extreme-dominance. An extension that allows travel time distribution functions to vary over time is also discussed. We show that the time-dependent problem is decomposable with respect to arrival times and therefore can be solved as easily as its static counterpart. Numerical results are provided using typical transportation networks. (C) 2009 Elsevier Ltd. All rights reserved.
Keyword:
Arriving on-time
A priori shortest path
First-order stochastic dominance
Bellman's principle of optimality
Label-correcting
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An adaptive routing algorithm for in-vehicle route guidance systems with real-time information具有实时信息的车载路径引导系统的自适应路由算法.png)
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