Sufficient conditions for stability of longest-queue-first scheduling: second-order properties using fluid limits

Sufficient Conditions for Stability of Longest Queue First Scheduling: Second Order Properties Using Fluid Limits

We consider the stability of Longest Queue First (LQF), a natural and low complexity scheduling policy, for a generalized switch model [1]. Contrary to common scheduling policies, the stability of LQF depends on the variance of the arrival processes in addition to their average intensities. We identify new sufficient conditions for LQF to be throughput optimal for i.i.d. arrival processes. Dete...

Stability of Lu-Kumar Networks under Longest-Queue and Longest-Dominating-Queue Scheduling

We consider the stability of robust scheduling policies for Lu-Kumar networks. These are open networks with arbitrary routing matrix and several disjoint groups of queues in which at most one queue can be served at a time in each group. The arrival and potential service processes and routing decisions at the queues are independent, stationary and ergodic. A scheduling policy is called robust if...

Stability of multiclass queueing networks under longest-queue and longest-dominating-queue scheduling

We consider the stability of robust scheduling policies for multiclass queueing networks. These are open networks with arbitrary routing matrix and several disjoint groups of queues in which at most one queue can be served at a time. The arrival and potential service processes and routing decisions at the queues are independent, stationary and ergodic. A scheduling policy is called robust if it...

Stability analysis of parallel server systems under longest queue first

We consider the stability of parallel server systems under the longest queue first (LQF) rule. We show that when the underlying graph of a parallel server system is a tree, the standard nominal traffic condition is sufficient for the stability of that system under LQF when interarrival and service times have general distributions. Then we consider a special parallel server system, which is know...

Necessary and sufficient conditions for absolute stability: the case of second-order systems