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

Author

Listed:
  • S. Bhulai
  • A.C. Brooms

    (Department of Economics, Mathematics & Statistics, Birkbeck)

Abstract

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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    File URL: https://eprints.bbk.ac.uk/id/eprint/7591
    File Function: First version, 2008
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    References listed on IDEAS

    as
    1. D. J. Daley & T. Rolski, 1991. "Light Traffic Approximations in Queues," Mathematics of Operations Research, INFORMS, vol. 16(1), pages 57-71, February.
    2. Kristin Fridgeirsdottir & Sam Chiu, 2005. "A Note on Convexity of the Expected Delay Cost in Single-Server Queues," Operations Research, INFORMS, vol. 53(3), pages 568-570, June.
    3. 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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