Persistent-idle load-distribution

A parallel server system is considered in which a dispatcher routes incoming jobs to a fixed number of heterogeneous servers, each with its own queue. Much effort has been previously made to design policies that use limited state information (e.g., the queue lengths in a small subset of the set of servers, or the identity of the idle servers). However, existing policies either do not achieve the stability region or perform poorly in terms of job completion time. We introduce Persistent-Idle (PI), a new, perhaps counterintuitive, loaddistribution policy that is designed to work with limited state information. Roughly speaking, PI always routes to the server that has last been idle. Our main result is that this policy achieves the stability region. Because it operates quite differently from existing policies, our proof method differs from standard arguments in the literature. Specifically, large time properties of reflected random walk, along with a careful choice of a Lyapunov function, are combined to obtain a Lyapunov condition over sufficiently long-time intervals. We also provide simulation results that indicate that job completion times under PI are low for different choices of system parameters, compared with several state-of-the-art load-distribution schemes.