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. Deterministic fluid analogs, proved to be powerful in the analysis of stability in queueing networks, do not adequately characterize the stability of LQF. We combine properties of diffusion-scaled sample path functionals and local fluid limits into a sharper characterization of stability.