Multi-layered round robin routing for parallel servers

We study a system of several identical servers in parallel, where a routing decision must be made immediately on a job’s arrival. Jobs arrive according to a Poisson process, with their processing times following a discrete distribution with finite support. The processing time of a job is known on arrival and may be used in the routing decision. We propose a policy consisting of multi-layered round robin routing followed by shortest remaining processing time scheduling at the servers. This policy is shown to have a heavy traffic limit that is identical to one in which there is a single queue (no routing) and optimal scheduling. We then quantify the difference between round robin and multi-layered round robin routing, which in turn yields insights on the relative importance of routing versus (local) scheduling in such systems. Multi-layered Round Robin Routing – D.G. Down and R. Wu 1