EURO Working Group on Stochastic Modelling

FIRST MEETING: 19-21 APRIL 2006, AMSTERDAM

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Abstracts

Oualid Jouini, Moments of State-Dependent Queueing Delays in Call Centers with Reneging

Motivated by practices in call centers, we consider a non-preemptive markovian queueing system that offers information about anticipated delays to customers. The system consists of a pool of full-flexible agents, and two classes of impatient customers type A and B. Times before reneging are mutually independent but not necessarily identically distributed. We investigate the prediction of the waiting time of a new arrival customer, assuming that the arrival does not himself renege. It is known that analyzing such systems is too complex due to the impact of announcing waiting times on the customers' behavior. In this paper, we first investigate the impact of the announcement on the customers' abandonment experience. Next, we derive closed-form expressions for any moment of order k, k>=1, of the state-dependent waiting time distribution for each customer type. To the best of our knowledge, this analysis has not been done before in an exact manner. Here, we reduce the problem to the computation of the moments of first passage times in Markov chains. For customers type A, we employ a birth-death process to derive the results. As for customers type B, we model the problem with a two-dimension Markov chain that has special structure allowing analytical solutions.