The effects of changing system parameters on job scheduling policies are studied for load balancing of multi-class jobs in a distributed computer system that consists of heterogeneous host computers connected by a single-channel communications network. A job scheduling policy decides which host should process the arriving jobs. We consider two job scheduling policies. The one is the overall optimal policy whereby jobs are scheduled so as to minimize the overall mean job response time. Tantawi and Towsley obtained the algorithm that gives the solution of the policy in the single class job environment and Kim and Kameda extended it to the multiple job class environment. The other is the individually optimal policy whereby jobs are scheduled so that every job may feel that its own expected response time is minimized. We can consider three important system parameters in a distributed computer system: the communication time of the network, the processing capacity of each node, and the job arrival rate of each node. We examine the effects of these three parameters on the two load balancing policies by numerical experiment.

Optimal static load balancing problems in open BCMP queueing networks with state-independent arrival and service rates are studied. Their examples include optimal static load balancing in distributed computer systems and static routing in communication networks. We refer to the load balancing policy of minimizing the overall mean response (or sojourn) time of a job as the overall optimal policy. We show the conditions that the solutions of the overall optimal policy satisfy and show that the policy uniquely determines the utilization of each service center, the mean delay for each class and each path class, etc., although the solution, the utilization for each class, the mean delay for all classes at each service center, etc., may not be unique. Then we give tha linear relations that characterize the set whose elements are the optimal solutions, and discuss the condition wherein the overall optimal policy has a unique solution. In parametric analysis and numerical calculation of optimal values of performance variables we must ensure whether they can be uniquely determined.