Approximate expected delay costs for call and contact centre models under light traffic regimes

Bhulai, S. and Brooms, Anthony C. (2008) Approximate expected delay costs for call and contact centre models under light traffic regimes. Working Paper. Birkbeck College, University of London, London, UK.

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.

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