Static load balancing among heterogenous parallel servers

In this paper, we present a model for balancing the workload among several heterogeneous queues so that the mean and variation of system response time can be jointly minimized. This problem is of particular relevance in the design of distributed or parallel computer systems where the queues represent processing nodes, each with its own stream of jobs to process. The resulting nonlinear programming problem is proved to have a unique optimum. By illustrating a numerical example, we show that further improvement in performance can be achieved by simultaneously optimizing the mean and variation of response time.