On the Optimal Allocation of Servers and Workloads in Closed Queueing Networks

In this paper, properties are derived that are useful for characterizing optimal allocations of servers and workloads in single-class, multiserver closed queueing networks (CQNs). The problem is as follows: Suppose a particular workload is allocated to a set of servers within a subnetwork of a CQN. This set of servers is to be partitioned into several multiserver stations. The number of stations, the number of servers, and the workload allocation to each station define a configuration of this subnetwork. Thus, the problem is to determine the best configuration of each subnetwork to maximize the throughput in the original CQN. Decomposition is used to address this problem. Results are obtained for subnetworks in isolation. These results are used to solve the optimal-configuration problem. Applications of the results to design and planning problems of flexible manufacturing are also described.