Qualitative Properties of alpha-Weighted Scheduling Policies

TL;DR

This paper investigates the qualitative performance of alpha-weighted scheduling policies in constrained queueing networks, establishing stability, tail bounds, and state space collapse properties for various alpha values.

Contribution

It provides new insights into the stability and tail behavior of alpha-weighted policies, including finiteness of expected backlog for alpha<1 and state space collapse for alpha≥1.

Findings

Established exponential tail bounds on backlog distribution.

Proved finiteness of expected steady-state backlog for alpha<1.

Demonstrated state space collapse for alpha≥1.

Abstract

We consider a switched network, a fairly general constrained queueing network model that has been used successfully to model the detailed packet-level dynamics in communication networks, such as input-queued switches and wireless networks. The main operational issue in this model is that of deciding which queues to serve, subject to certain constraints. In this paper, we study qualitative performance properties of the well known $\alpha$-weighted scheduling policies. The stability, in the sense of positive recurrence, of these policies has been well understood. We establish exponential upper bounds on the tail of the steady-state distribution of the backlog. Along the way, we prove finiteness of the expected steady-state backlog when $\alpha<1$, a property that was known only for $\alpha\geq 1$. Finally, we analyze the excursions of the maximum backlog over a finite time horizon for $\alpha \geq 1$. As a consequence, for $\alpha \geq 1$, we establish the full state space collapse property.