An algorithm for optimal load balancing in a multiple GI/G/1 queueing system

The issue of optimal load balancing has been raised in several important engineering fields such as the file management in a data base, the job control in a multiple processor system or the flow assignment in a packet switched data network. By modeling the subsystems as multiple GI/G/1 queues and applying known approximations and decomposition methods, the system mean response time is expressed as a function of the load allocation. To find the optimal load balancing, the convexity property is first studied with respect to the type of the arrival process of the system. We give then an efficient algorithm which finds for the convex case the global and for the non-convex case a local minimum. Some important properties of the multiple Gl/G/1 queueing system are revealed with several numerical examples.