Analysis of a queueing model for a call center with impatient customers and after-call work

Abstract

Two essential features needed for queueing models of call centers are "impatient customers" and "after-call work" (ACW) of operators. Their effects on the performance are comparable to those of service times. We propose and analyze a queueing model of a call center with impatient customers and ACW. We consider a two-dimensional birth-and-death process for the state combining the number of calls waiting or being served in the system and the number of operators working on ACW. The steady-state distribution is obtained numerically, from which we compute a variety of performance measures, including the blocking probability, the probability of wait, the mean waiting time, the ratio of getting service and abandonment, and the fraction of operators who are serving customers, working on ACW, or being idle at an arbitrary time. Furthermore, we show a method of finding the mean waiting time for those customers who get served and for those who abandon while waiting. Our analysis is validated by numerical examples for a call center model of realistic size, namely 40 operators and 30 incoming telephone lines.