Combining Size-Based Load Balancing with Round-Robin for Scalable Low Latency

When dispatching jobs to parallel servers, or queues, the highly scalable round-robin (RR) scheme reduces the variance of interarrival times at all queues to a great extent but has no impact on the variances of service processes. Contrariwise, size-interval task assignment (SITA) routing has little impact on the variances of interarrival times but makes the service processes as deterministic as possible. In this paper, we unify both `static' approaches to design a scalable load balancing framework able to control the variances of the arrival and service processes jointly. It turns out that the resulting combination significantly improves performance and is able to drive the mean job delay to zero in the large-system limit; it is known that this property is not achieved when both approaches are considered separately. Within realistic parameters, we show that the optimal number of size intervals that partition the support of the job size distribution is small with respect to the system size. This enhances the applicability of the proposed load balancing scheme at a large scale. In fact, we find that adding a little bit of information about job sizes to a dispatcher operating under RR improves performance a lot. Under the optimal scaling of size intervals and assuming highly variable job sizes, numerical simulations indicate that the proposed algorithm is competitive with the (less scalable) join-the-shortest-workload algorithm even when the system size grows large.