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40
Path Planning under TimeDependent Uncertainty
 In Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence
, 1995
"... Standard algorithms for finding the shortest path in a graph require that the cost of a path be additive in edge costs, and typically assume that costs are deterministic. We consider the problem of uncertain edge costs, with potential probabilistic dependencies among the costs. Although these depend ..."
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Cited by 30 (3 self)
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Standard algorithms for finding the shortest path in a graph require that the cost of a path be additive in edge costs, and typically assume that costs are deterministic. We consider the problem of uncertain edge costs, with potential probabilistic dependencies among the costs. Although these dependencies violate the standard dynamicprogramming decomposition, we identify a weaker stochastic consistency condition that justifies a generalized dynamicprogramming approach based on stochastic dominance. We present a revised pathplanning algorithm and prove that it produces optimal paths under timedependent uncertain costs. We illustrate the algorithm by applying it to a model of stochastic bus networks, and present sample performance results comparing it to some alternatives. For the case where all or some of the uncertainty is resolved during path traversal, we extend the algorithm to produce optimal policies. This report is based on a paper presented at the Eleventh Conference on Unc...
Adaptive leastexpected time paths in stochastic, timevarying transportation and data networks
 Networks
"... In congested transportation and data networks, travel (or transmission) times are timevarying quantities that are at best known a priori with uncertainty. In such stochastic, timevarying (or STV) networks, one can choose to use the a priori leastexpected time (LET) path or one can make improved r ..."
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Cited by 28 (0 self)
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In congested transportation and data networks, travel (or transmission) times are timevarying quantities that are at best known a priori with uncertainty. In such stochastic, timevarying (or STV) networks, one can choose to use the a priori leastexpected 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 labelsettingbased 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 sidebyside comparison of this procedure with a labelcorrectingbased 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. © 2001 John Wiley & Sons, Inc.
Minimum delay routing in stochastic networks
 IEEE/ACM Transactions on Networking
, 1993
"... We consider the problem of trave ling with least expec ted dela y in networ ks whose link delays change probabilistically acc ording to Markov cha ins. This is a typical routing problem in dynamic computer communication networ ks. We formulate sever al optimization problems, posed on infinite and fi ..."
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Cited by 17 (2 self)
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We consider the problem of trave ling with least expec ted dela y in networ ks whose link delays change probabilistically acc ording to Markov cha ins. This is a typical routing problem in dynamic computer communication networ ks. We formulate sever al optimization problems, posed on infinite and finite horizons, and consider them with and without using memory in the decision making proc ess. We prove that all these problems ar e, in genera l, intrac table. Howe ver, for networks with nodal stochastic delays, a simple polynomial optimal solution is prese nted. This is typical of highspee d networks, in which the dominant delays are incurre d by the nodes. For more gene ral networks, a tracta ble εoptimal solution is pre sented.
Finding the k shortest hyperpaths
"... The K shortest paths problem has been extensively studied for many years. Efficient methods have been devised, and many practical applications are known. Shortest hyperpath models have been proposed for several problems in different areas, for example in relation with routing in dynamic networks. Ho ..."
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Cited by 17 (4 self)
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The K shortest paths problem has been extensively studied for many years. Efficient methods have been devised, and many practical applications are known. Shortest hyperpath models have been proposed for several problems in different areas, for example in relation with routing in dynamic networks. However, the K shortest hyperpaths problem has not yet been investigated. In this paper we present procedures for finding the K shortest hyperpaths in a directed hypergraph. This is done by extending existing algorithms for K shortest loopless paths. Computational experiments on the proposed procedures are performed, and applications in transportation, planning and combinatorial optimization are discussed.
Optimal route planning under uncertainty
 In Proc. of International Conference on Automated Planning and Scheduling
, 2006
"... We present new complexity results and efficient algorithms for optimal route planning in the presence of uncertainty. We employ a decision theoretic framework for defining the optimal route: for a given source S and destination T in the graph, we seek an STpath of lowest expected cost where the edg ..."
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Cited by 13 (6 self)
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We present new complexity results and efficient algorithms for optimal route planning in the presence of uncertainty. We employ a decision theoretic framework for defining the optimal route: for a given source S and destination T in the graph, we seek an STpath of lowest expected cost where the edge travel trimes are eandom variable and the cost is a nonlinear function of total travel time. Although this is a natural model for routeplanning on realworld road networks, results are sparse due to the analytic difficulty of finding closed form expressions for the exptected cost (Fan, Kalaba and Moore), as well as the computational/combinatorial difficulty of efficiently finding an optimal path which minimizes the exptected cost. We identify a family of appropriate cost models and travel time distributions that are closed under convolution and physically valid. We obtain hardness results for routing problems with a given start time and cost functions with a global minimum, in a variety of deterministic and stochastic settings. In general the global cost is not separable into edge costs, precluding classic shortestpath approaches. However, using partial minimization techniques, we exhibit an efficient solution via dynamic programming with low polynomial complexity.
A Directed Hypergraph Model for Random Time Dependent Shortest Paths
 EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
, 1998
"... We consider routing problems in dynamic networks where arc travel times are both random and time dependent. The problem of finding the best route to a fixed destination is formulated in terms of shortest hyperpaths on a suitable timeexpanded directed hypergraph. The latter problem can be solved in ..."
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Cited by 12 (5 self)
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We consider routing problems in dynamic networks where arc travel times are both random and time dependent. The problem of finding the best route to a fixed destination is formulated in terms of shortest hyperpaths on a suitable timeexpanded directed hypergraph. The latter problem can be solved in linear time, with respect to the size of the hypergraph, for several definitions of hyperpath length. Different criteria for ranking routes can be modeled by suitable definitions of hyperpath length. We also show that the problem becomes intractable if a constraint on the route structure is imposed.
Optimal Vehicle Routing with RealTime Traffic Information
 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS
, 2002
"... This paper examines the value of realtime traffic information to optimal vehicle routing in a nonstationary stochastic network. We present a systematic approach to aid in the implementation of transportation systems integrated with real time information technology. We develop decisionmaking procedu ..."
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Cited by 11 (1 self)
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This paper examines the value of realtime traffic information to optimal vehicle routing in a nonstationary stochastic network. We present a systematic approach to aid in the implementation of transportation systems integrated with real time information technology. We develop decisionmaking procedures for determining the optimal driver attendance time, optimal departure times, and optimal routing policies under stochastically changing traffic flows based on a Markov decision process formulation. With a numerical study carried out on an urban road network in Southeast Michigan, we demonstrate significant advantages when using this information in terms of total costs savings and vehicle usage reduction while satisfying or improving service levels for justintime delivery.
A Concept of Communication Distance And Its Application to Six Situations in Mobile Environments
 IEEE Transactions on Mobile Computing
, 2005
"... Wireless networks combined with location technology create new problems and call for new decision aids. As a precursor to the development of these decision aids, a concept of communication distance is developed and applied to six situations. This concept allows travel time and bandwidth to be combin ..."
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Cited by 8 (3 self)
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Wireless networks combined with location technology create new problems and call for new decision aids. As a precursor to the development of these decision aids, a concept of communication distance is developed and applied to six situations. This concept allows travel time and bandwidth to be combined in a single measure so that many problems can be mapped onto a weighted graph and solved through shortest path algorithms. The paper looks at the problem of intercepting an outofcommunication team member and describes ways of using planning to reduce communication distance in anticipation of a break in connection. The concept is also applied to ad hoc radio networks. A way of performing route planning using a bandwidth map is developed and analyzed. The general implications of the work to transportation planning are discussed.
A polynomialtime algorithm to find shortest paths with recourse
 Networks
, 2003
"... The Shortest Path with Recourse Problem involves finding the shortest expectedlength paths in a directed network each of whose arcs have stochastic traversal lengths (or delays) that become known only upon arrival at the tail of that arc. The traveler starts at a given source node, and makes routin ..."
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Cited by 8 (0 self)
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The Shortest Path with Recourse Problem involves finding the shortest expectedlength paths in a directed network each of whose arcs have stochastic traversal lengths (or delays) that become known only upon arrival at the tail of that arc. The traveler starts at a given source node, and makes routing decisions at each node in such a way that the expected distance to a given sink node is minimized. We develop an extension of Dijkstra’s algorithm to solve the version of the problem where arclengths are nonnegative and reset after each arc traversal. All known noreset versions of the problem are NPhard. We make a partial extension to the case where negative arclengths are present.
Using StochasticDominance Relationships for Bounding Travel Times in Stochastic Networks
, 1999
"... We consider stochastic networks' in which link travel times are dependent, discrete random variables. We present methods' for computing bounds' on path travel times using stochastic dominance relationships among link travel times, and discuss techniques for controlling tightness of the bounds'. We a ..."
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Cited by 7 (5 self)
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We consider stochastic networks' in which link travel times are dependent, discrete random variables. We present methods' for computing bounds' on path travel times using stochastic dominance relationships among link travel times, and discuss techniques for controlling tightness of the bounds'. We apply these methods' to shortestpath problems, show that the proposed algorithm can provide bounds' on the recommended path, and elaborate on extensions of the algorithm for demonstrating the anytime property.