232,130 research outputs found

    Reliable network design under supply uncertainty with probabilistic guarantees

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    This paper proposes a bi-level risk-averse network design model for transportation networks with heterogeneous link travel time distributions. The objective of the network design is to minimise the total system travel time (TSTT) budget (TSTTB), which consists of the mean TSTT and a safety margin. The design is achieved by selecting optimal link capacity expansions subject to a fixed expansion budget. Users’ selfish behaviour and risk attitude are captured in the lower level traffic assignment constraints, in which travellers select routes to minimise their own path travel time budget. The properties of the design problem are analysed analytically and numerically. The analysis shows that despite the lack of knowledge of travel time distributions, the probabilities that the actual TSTT and the actual path travel time are, respectively, within the optimal TSTTB and the minimum path travel time budget under optimal design have lower bounds. The lower bounds are related to the system manager's and travellers’ risk aversion. The optimal TSTTB is proven to be bounded below even when the link expansion budget is unlimited.postprin

    A Reach and Bound algorithm for acyclic dynamic-programming networks

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    Node pruning is a commonly used technique for solution acceleration in a dynamic-programming network. In pruning, nodes are adaptively removed from the dynamic programming network when they are determined not to lie on an optimal path. We introduce an [epsiv]-pruning condition that extends pruning to include a possible error in the pruning step. This results in a greater reduction of the computation time; however, as a result of the inclusion of this error, the solution can be suboptimal or possibly infeasible. This condition requires the ability to compare the costs of an optimal path from a node to a terminal node. Therefore, we focus on the class of acyclic dynamic programming networks with monotonically decreasing optimal costs-to-go. We provide an easily implementable algorithm, Reach and Bound, which maintains feasibility and bounds the solution's error. We conclude by illustrating the applicability of Reach and Bound on a problem of single location capacity expansion. © 2007 Wiley Periodicals, Inc. NETWORKS, 2008Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/60450/1/20219_ftp.pd

    A continuous network design model in stochastic user equilibrium based on sensitivity analysis

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    The continuous network design problem (CNDP) is known to be difficult to solve due to the intrinsic properties of non-convexity and nonlinearity. Such kinds of CNDP can be formulated as a bi-level programme, in which the upper level represents the designer's decisions and the lower level the travellers' responses. Formulations of this kind can be classified as either Stackelberg approaches or Nash ones according to the relationship between the upper level and the lower level parts. This paper formulates the CNDP for road expansion based on Stackelberg game where leader and follower exist, and allows for variety of travellers' behaviour in choosing their routes. In order to solve the problem by the Stackelberg approach, we need a relation between link flows and design parameters. For this purpose, we use a logit route choice model, which provides this in an explicit closed-form function. This model is applied to two example road networks to test and briefly compare the results between the Stackelberg and Nash approaches to explore the differences between them
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