The topological network design of general service, finite waiting room, multi-server queueing networks is a complex optimization problem. Series, merge, and split topologies are examined using an approximation method to estimate the performance of these queueing networks and an iterative search methodology to find the optimal buffer allocation within the network. The coefficient of variation is shown to be a significant factor in the buffer allocation for multiple servers in uniform and bottleneck server networks. Extensive computational results are included to illustrate the symmetries and asymmetries in the buffer patterns which emerge from the series, merge, and splitting topologies.
MacGregor Smith, J., Cruz, F. R. B., & Woensel, van, T. (2010). Topological network design of general, finite, multi-server queueing networks. European Journal of Operational Research, 201(2), 427-441. https://doi.org/10.1016/j.ejor.2009.03.012