Buffer and server allocation in general multi-server queueing networks

This paper deals with the joint optimization of the number of buffers and servers, an important issue since buffers and servers represent a significant amount of investment for many companies. The joint buffer and server optimization problem (BCAP) is a non-linear optimization problem with integer decision variables. The performance of the BCAP is evaluated by a combination of a two-moment approximation (developed for the performance analysis of finite general-service queues) and the generalized expansion method (a well-known method for performance analysis of acyclic networks of finite queues). A standard non-linear optimization package is used to optimize the BCAP for a large number of experiments. A comprehensive set of numerical results is presented. The results show that the methodology is capable of handling the trade-off between the number of servers and buffers, yielding better throughputs than previously published studies. Also, the importance of the squared coefficient of variation of the service time is stressed, since it strongly influences the approximate optimal allocation.