Optimal server allocation in general, finite, multi-server queueing networks

Queueing networks with finite buffers, multiple servers, arbitrary acyclic, series-parallel topologies, and general service time distributions are considered in this paper. An approach to optimally allocate servers to series, merge, and split topologies and their combinations is demonstrated. The methodology builds on two-moment approximations to the service time distribution embedded in the generalized expansion method for computing the performance measures in complex finite queueing networks and Powell's algorithm for optimally allocating servers to the network topology. Convexity of the objective function along with results from computational experiments is presented for showing the efficacy of the methodology.