Optimal Workload Allocation in Open Networks of Multiserver Queues

In this paper, we examine the general problem of workload allocation in an open Jackson network of multiserver queues. We show that use of the open network model leads to a separable, convex formulation of the problem with relatively simple optimality conditions. Using these conditions, we prove in general that server groups with the same number of servers should be loaded equally and larger groups should be loaded more heavily than smaller groups. It is also shown that server pooling, combining servers into larger groups, will always reduce congestion and/or increase throughput. We discuss the significance of our results for job shop applications and also for the concept of a production bottleneck. In systems with an unbalanced configuration of servers, traditional, deterministic bottleneck analysis is distinctly nonoptimal; our results provide a simple way to locate production bottlenecks in shops with significant queueing effects.