Modeling

A first step in capacity planning at a contact center is to model the contact center as a queueing model. In modeling a contact center, it is desirable that (i) the queueing model well captures the behavior of the contact center, (ii) the queueing model can be analyzed efficiently, and (iii) the modeling can be done easily and quickly. Property (i) is important, since a more precise queueing model provides a more accurate number of agents to be assigned. This can significantly reduce the necessary iterations of simulation. Properties (ii)-(iii) are important so that modeling and analysis does not become a bottleneck in capacity planning. An efficient analysis also helps in designing good routing policies, as we will see in Section 8.3.3.

A popular approach in modeling a contact center is to map the forecasted interarrival time, service time, and time a customer is willing to wait to phase type (PH) distributions (as defined in Section 2.2), so that the resulting queueing model can be analyzed as a Markov chain. The moment matching algorithms developed in Chapter 2 can be used exactly for this purpose. Recall the four desired properties that our moment matching algorithm has. Each of the four properties is desirable specifically in contact center modeling. Specifically, our moment matching algorithm can match the first three moments of the input distribution (and is defined for a broadest possible class of input distributions). This allows the queueing model to better capture the behavior of the contact center, as compared to existing moment matching algorithms that match only two moments. Also, the matching PH distribution provided by our moment matching algorithm has at most ${\rm OPT}(G)+1$ phases. This makes the state space of the queueing model (and the corresponding Markov chain) small, which in turn allows an efficient evaluation of the Markov chain. Further, our moment matching algorithm has short running time (closed form solutions are provided), which allows easy and quick modeling.