Instability of the Join-the-Shortest-Queue and FCFS Policies in Queueing Systems and Their Stabilization

Abstract

We demonstrate the instability of the “join-the-shortest-queue” routing policy and the “first-come-first-served” dispatching policy for a multiclass single-station queuing system with multiple nonidentical servers. Although instability is demonstrated in a deterministic setting, we have found strong evidence that it is not limited to this setting. The phenomenon that leads to instability is different from the one reported recently in the literature for nonacyclic systems, namely, servers starvation. The systems considered here are acyclic, and instability is caused by the failure of the policies to assign jobs to servers in an efficient manner. A modification to the investigated policies is proposed to make them stable. The modified policies (called guided policies) provide an oversight control that ensure efficient utilization of the servers and hence stability.