3 research outputs found
Qualitative Properties of alpha-Weighted Scheduling Policies
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 -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 , a
property that was known only for . Finally, we analyze the
excursions of the maximum backlog over a finite time horizon for . As a consequence, for , we establish the full state space
collapse property.Comment: 13 page
Qualitative properties of -fair policies in bandwidth-sharing networks
We consider a flow-level model of a network operating under an -fair
bandwidth sharing policy (with ) proposed by Roberts and
Massouli\'{e} [Telecomunication Systems 15 (2000) 185-201]. This is a
probabilistic model that captures the long-term aspects of bandwidth sharing
between users or flows in a communication network. We study the transient
properties as well as the steady-state distribution of the model. In
particular, for , we obtain bounds on the maximum number of flows
in the network over a given time horizon, by means of a maximal inequality
derived from the standard Lyapunov drift condition. As a corollary, we
establish the full state space collapse property for all . For the
steady-state distribution, we obtain explicit exponential tail bounds on the
number of flows, for any , by relying on a norm-like Lyapunov
function. As a corollary, we establish the validity of the diffusion
approximation developed by Kang et al. [Ann. Appl. Probab. 19 (2009)
1719-1780], in steady state, for the case where and under a local
traffic condition.Comment: Published in at http://dx.doi.org/10.1214/12-AAP915 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Quantifying the Cost of Learning in Queueing Systems
Queueing systems are widely applicable stochastic models with use cases in
communication networks, healthcare, service systems, etc. Although their
optimal control has been extensively studied, most existing approaches assume
perfect knowledge of system parameters. Of course, this assumption rarely holds
in practice where there is parameter uncertainty, thus motivating a recent line
of work on bandit learning for queueing systems. This nascent stream of
research focuses on the asymptotic performance of the proposed algorithms.
In this paper, we argue that an asymptotic metric, which focuses on
late-stage performance, is insufficient to capture the intrinsic statistical
complexity of learning in queueing systems which typically occurs in the early
stage. Instead, we propose the Cost of Learning in Queueing (CLQ), a new metric
that quantifies the maximum increase in time-averaged queue length caused by
parameter uncertainty. We characterize the CLQ of a single-queue multi-server
system, and then extend these results to multi-queue multi-server systems and
networks of queues. In establishing our results, we propose a unified analysis
framework for CLQ that bridges Lyapunov and bandit analysis, which could be of
independent interest