Call center data modeling: a queueing science approach based on Markovian arrival process

In this paper we analyze the well-known ‘Anonymous bank’ call center dataset from a queueing science viewpoint. For this purpose, fitted distributions for both the inter-arrival and service times as well as for customers patiences are integrated in a simulator to infer quantities of interest related to call centers managerial decisions as waiting times, abandonment rates and queue lengths. In particular, it is shown how a type of Markov renewal process, the Markovian arrival process (<i>MAP</i>), is able to capture some of the characterizing properties of arrivals in a modern call center as overdispersion and positive correlation between arrival counts. The work provides a new inference approach for the <i>MAP</i> based on the count process descriptors and presents new properties concerning the dependence structure of the cumulated number of arrivals in a <i>MAP</i>.