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June 2015 Balanced routing of random calls
Malwina J. Luczak, Colin McDiarmid
Ann. Appl. Probab. 25(3): 1279-1324 (June 2015). DOI: 10.1214/14-AAP1023

Abstract

We consider an online network routing problem in continuous time, where calls have Poisson arrivals and exponential durations. The first-fit dynamic alternative routing algorithm sequentially selects up to $d$ random two-link routes between the two endpoints of a call, via an intermediate node, and assigns the call to the first route with spare capacity on each link, if there is such a route. The balanced dynamic alternative routing algorithm simultaneously selects $d$ random two-link routes, and the call is accepted on a route minimising the maximum of the loads on its two links, provided neither of these two links is saturated.

We determine the capacities needed for these algorithms to route calls successfully and find that the balanced algorithm requires a much smaller capacity. In order to handle such interacting random processes on networks, we develop appropriate tools such as lemmas on biased random walks.

Citation

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Malwina J. Luczak. Colin McDiarmid. "Balanced routing of random calls." Ann. Appl. Probab. 25 (3) 1279 - 1324, June 2015. https://doi.org/10.1214/14-AAP1023

Information

Published: June 2015
First available in Project Euclid: 23 March 2015

zbMATH: 1314.60152
MathSciNet: MR3325274
Digital Object Identifier: 10.1214/14-AAP1023

Subjects:
Primary: 60C05
Secondary: 60K25, 60K30, 68M20, 68R05, 90B22

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.25 • No. 3 • June 2015
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