Contents

A call center is a popular term for a service operation that caters to customers ’ needs via the telephone. A call center typically consists of agents that serve customers, telephone lines, an Interactive Voice Response (IVR) unit, and a switch that routes calls to agents. In this paper we study a Markovian model for a call center with an IVR. We calculate operational performance measures, such as the probability for a busy signal and the average wait time for an agent. Exact calculations of these measures are cumbersome and they lack insight. We thus approximate the measures in an asymptotic regime known as QED (Quality & Efficiency Driven) or the Halfin-Whitt regime, which accomodates moderate to large call centers. The approximations are both insightful and easy to apply (for up to 1000’s of agents). They yield, as special cases, known and novel approximations for the M/M/N/N (Erlang-B), M/M/S (Erlang-C) and M/M/S/N queue.