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Approximating Wardrop equilibria with finitely many agents

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Abstract

We present efficient algorithms for computing approximate Wardrop equilibria in a distributed and concurrent fashion. Our algorithms are exexuted by a finite number of agents each of which controls the flow of one commodity striving to balance the induced latency over all utilised paths. The set of allowed paths is represented by a DAG. Our algorithms are based on previous work on policies for infinite populations of agents. These policies achieve a convergence time which is independent of the underlying network and depends mildly on the latency functions. These policies can neither be applied to a finite set of agents nor can they be simulated directly due to the exponential number of paths. Our algorithms circumvent these problems by computing a randomised path decomposition in every communication round. Based on this decomposition, flow is shifted from overloaded to underloaded paths. This way, our algorithm can handle exponentially large path collections in polynomial time. Our algorithms are stateless, and the number of communication rounds depends polynomially on the approximation quality and is independent of the topology and size of the network.

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Authors and Affiliations

  1. RWTH Aachen, Aachen, Germany

    Simon Fischer, Lars Olbrich & Berthold Vöcking

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  1. Simon Fischer
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  2. Lars Olbrich
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  3. Berthold Vöcking
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Correspondence to Simon Fischer.

Additional information

Supported by DFG grant Vo889/1–3 and by DFG through German excellence cluster UMIC at RWTH Aachen.

Supported by the DFG GK/1298 “AlgoSyn”.

Supported in part by the the EU within the 6th Framework Programme under contract 001907 (DELIS) and by DFG through German excellence cluster UMIC at RWTH Aachen.

A preliminary version of this work has appeared in [14].

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Fischer, S., Olbrich, L. & Vöcking, B. Approximating Wardrop equilibria with finitely many agents. Distrib. Comput. 21, 129–139 (2008). https://doi.org/10.1007/s00446-008-0057-1

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  • DOI: https://doi.org/10.1007/s00446-008-0057-1

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