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

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.