Performance Degradation in Parallel-Server Systems

Abstract

We consider a parallel-server system with homogeneous servers where incoming tasks, arriving at rate $\lambda $ , are dispatched by $n$ dispatchers, each of them balancing a fraction $1/n$ of the load to $K/n$ servers. Servers are first-come-first-served (FCFS) queues and dispatchers implement size interval task assignment policy with equal load (SITA-E), a size-based policy such that the servers are equally loaded. We compare the performance of a system with $n>1$ dispatchers and a single dispatcher. We show that the performance of a system with $n$ dispatchers, $K$ servers, and arrival rate $\lambda $ coincides with that of a system with one dispatcher, $K/n$ servers, and arrival rate $\lambda /n$ . We define the degradation factor as the ratio between the performance of a system with $K$ servers and arrival rate $\lambda $ and the performance of a system with $K/n$ servers and arrival rate $\lambda /n$ . We establish a partial monotonicity on $n$ for the degradation factor and, therefore, the degradation factor is lower bounded by one. We then investigate the upper bound of the degradation factor for particular distributions. We consider two continuous service time distributions: uniform and bounded Pareto and a discrete distribution with two values, which is the distribution that maximizes the variance for a given mean. We show that the performance degradation is small for uniformly distributed job sizes but that for Bounded Pareto and two points distributions it can be unbounded. We have investigated the degradation using the distribution obtained from real traces.