  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.
