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On Queueing Network Models of Service Systems |
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Chinnaswamy,
M. and M. Kamath,
In service systems, the service time and the subsequent routing of a customer after service with an agent could depend on the processing history of the customer. An example is the processing time of a customer’s e-mail and its subsequent routing within a customer contact center, both of which could depend on the e-mail’s processing history. Motivated by the analysis of contact center operations, we present a novel aggregation approach to model processing history. This aggregation approach extends the popular parametric decomposition technique for solving open queueing networks. We illustrate our approach by modeling an e-mail customer contact center as an open queueing network. We develop a discrete-time Markov chain to model the routing of a new e-mail through the contact center until its eventual resolution. We use the fundamental matrix of this absorbing Markov chain to obtain the average number of visits an e-mail makes to each node before getting resolved. Based on the average number of visits, weights needed for aggregation are obtained. These weights represent the proportion of new and previously processed e-mails in an agent’s inbox. The resulting queueing network model is solved using the RAQS software package. The analytical results are compared with simulation estimates to evaluate the accuracy of the aggregation approach.
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Center for Computer integrated Manufacturing enterprises
School of Industrial
Engineering and Management |