📝 SummarXiv

Abstract

We study the steady-state performance of parallel-server systems under an immediate routing architecture with two sources of heterogeneity: servers and job classes, subject to compatibility constraints. We focus on the weighted-workload-task-allocation (WWTA) policy, a load-balancing scheme known to be throughput-optimal for such systems. Under a relaxed complete-resource-pooling (CRP) condition, we prove a "strong form" of state-space collapse in heavy traffic and that the scaled workload of each server converges in distribution to an exponential random variable, whose parameter is explicitly given by system primitives. Our analysis yields three main insights. First, the conventional heavy-traffic requirement of a unique static allocation plan can be dropped; a relaxed CRP condition suffices. Second, the limiting workload distribution is shown to be independent of local scheduling policy on server side, allowing substantial flexibility. Third, the inefficient (non-basic) activities prescribed by static allocation plan is proved to receive an asymptotically negligible fraction of routing and service, even though WWTA has no prior knowledge of which activities are basic, highlighting its robustness to changing arrival rates.