Qualitative properties of α-weighted scheduling policies

Authors:
Devavrat Shah;John N. Tsitsiklis;Yuan Zhong
Affiliations:
Massachusetts Institute of Technology, Cambridge, MA, USA;Massachusetts Institute of Technology, Cambridge, MA, USA;Massachusetts Institute of Technology, Cambridge, MA, USA
Venue:
Proceedings of the ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Year:
2010

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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 α-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 α Finally, we analyze the excursions of the maximum backlog over a finite time horizon for α ≥ 1. As a consequence, for α ≥ 1, we establish the full state space collapse property.