Aggregation approaches for incorporating e-mail processing history in queueing models of customer contact centers

Scope and method of study. The operation of a customer contact center where the interface between the agents' and the customer happens through e-mail was modeled using a multi-class open queueing network model. A novel approach to model the dependence of processing times and routing on e-mail history called the history-based aggregation method was developed. This aggregation method extends the popular parametric decomposition (PD) method for solving multi-class open queueing networks to more general situations. A discrete-time Markov chain (DTMC) with an expanded state space was developed to model the non-Markovian routing of a new e-mail through the contact center until its eventual resolution. The analysis of this absorbing Markov chain led to the computation of the proportion of e-mails in an agent's in-box that are new, previously processed by the same agent, or previously processed by another agent. Using these proportions, a new "history-based" aggregation step for each customer class in the PD method was introduced. This step precedes the existing class-based aggregation step in the PD method. The resulting queueing network model was solved using the RAQS software package. (Abstract shortened by UMI.)...