Transient Waiting Time Distributions in Small Call Centres with Skills-Based Routing

Many call centres are subject to service level agreements that stipulate that they must achieve targets in terms of the proportion of calls that are answered within a specified time. In order to manage a centre so that targets like these are met, we need to have a method of calculating the waiting time distributions experienced by customers. In this paper, we provide such a method for small call centres that employ skills-based routing. We first build the methodology for the single-skill case and then extend it to a multi-skill case. We model the call centre system as a continuous-time Markov chain and then make use of the Laplace transform to calculate the relevant quantities. We later demonstrate the use of this method to find the optimal routing policy in a certain class of policies.