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

S. Bhulai and A.C. Brooms
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A.C. Brooms: Department of Economics, Mathematics & Statistics, Birkbeck

No 805, Birkbeck Working Papers in Economics and Finance from Birkbeck, Department of Economics, Mathematics & Statistics

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.

Date: 2008-08
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https://eprints.bbk.ac.uk/id/eprint/7591 First version, 2008 (application/pdf)

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