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Approximate Expected Delay Costs for Call and Contact Centre models under Light Traffic Regimes


  • S. Bhulai
  • A.C. Brooms

    (Department of Economics, Mathematics & Statistics, Birkbeck)


This paper studies the form of certain expected delay costs as a function of the arrival rate for customers who pass through a service facility that allows for reneging and retrials. We show that, under certain light traffic conditions, these costs are continuously increasing and convex functions of the arrival rate (within a finite interval). This result is first explored for the processor sharing system, in which a penalty cost is incurred for reneging from the service facility for good without ever receiving service, and then we consider a system with a more general structure governing the output processes and costs incurred per unit time, but without the penalty cost. A suggested application for these results, in which game theoretic considerations are utilized for gauging customer behaviour within a decentralized context, is briefly discussed.

Suggested Citation

  • S. Bhulai & A.C. Brooms, 2008. "Approximate Expected Delay Costs for Call and Contact Centre models under Light Traffic Regimes," Birkbeck Working Papers in Economics and Finance 0805, Birkbeck, Department of Economics, Mathematics & Statistics.
  • Handle: RePEc:bbk:bbkefp:0805

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    References listed on IDEAS

    1. Sanjeev Dewan & Haim Mendelson, 1990. "User Delay Costs and Internal Pricing for a Service Facility," Management Science, INFORMS, vol. 36(12), pages 1502-1517, December.
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