Approximations for periodic load balancing

We consider multiple queues in parallel with unlimited waiting space to which jobs come either in separate independent streams or by assignment (either in random or round robin order) from a single stream. Resource sharing is achieved by periodically redistributing the jobs among the queues. The performance of these systems of queues coupled by periodic load balancing depends on the transient behavior of a single queue. We focus on useful approximations obtained by considering a heavy load and a large number of homogeneous queues. With these approximations, we show how performance depends on the assumed arrival pattern of jobs and the model parameters. We conduct simulation experiments to show the accuracy of the approximations