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On-line routing of random calls in networks
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  • Published: April 2003

On-line routing of random calls in networks

  • Malwina J. Luczak1,
  • Colin McDiarmid2 &
  • Eli Upfal3 

Probability Theory and Related Fields volume 125, pages 457–482 (2003)Cite this article

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  • 7 Citations

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Abstract.

 We consider a random sequence of calls between nodes in a complete network with link capacities. Each call first tries the direct link. If that link is saturated, then the `first-fit dynamic alternative routing algorithm' sequentially selects up to d random two-link alternative routes, 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 alternative 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 second `balanced' algorithm requires a much smaller capacity. Our results strengthen and extend the discrete-time results presented in [10].

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Authors and Affiliations

  1. Statistical Laboratory, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0DS, UK. e-mail: M.J.Luczak@statslab.cam.ac.uk, , , , , , GB

    Malwina J. Luczak

  2. Department of Statistics, 1 South Parks Road, Oxford OX1 3TG, UK. e-mail: cmcd@stats.ox.ac.uk, , , , , , GB

    Colin McDiarmid

  3. Computer Science Department, Brown University, Box 1910, Providence, RI 02912-1910, USA. e-mail: eli@cs.brown.edu, , , , , , US

    Eli Upfal

Authors
  1. Malwina J. Luczak
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  2. Colin McDiarmid
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  3. Eli Upfal
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Additional information

Received: 10 January 2002 / Revised version: 7 July 2002 / Published online: 28 March 2003

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Luczak, M., McDiarmid, C. & Upfal, E. On-line routing of random calls in networks. Probab. Theory Relat. Fields 125, 457–482 (2003). https://doi.org/10.1007/s00440-002-0242-2

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  • Issue Date: April 2003

  • DOI: https://doi.org/10.1007/s00440-002-0242-2

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Keywords

  • Direct Link
  • Random Sequence
  • Alternative Route
  • Balance Dynamic
  • Link Capacity
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