Partitioning Customers into Service Groups

We explore the issue of when and how to partition arriving customers into service groups that will be served separately, in a first-come first-served manner, by multi-server service systems having a provision for waiting, and how to assign an appropriate number of servers to each group. We assume that customers can be classified upon arrival, so that different service groups can have different service-time distributions. We provide methodology for quantifying the tradeoff between economies of scale associated with larger systems and the benefit of having customers with shorter service times separated from other customers with longer service times, as is done in service systems with express lines. To properly quantify this tradeoff, it is important to characterize service-time distributions beyond their means. In particular, it is important to also determine the variance of the service-time distribution of each service group. Assuming Poisson arrival processes, we then can model the congestion experienced by each server group as an M/G/s queue with unlimited waiting room. We use previously developed approximations for M/G/s performance measures to quickly evaluate alternative partitions.