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Queueing and scheduling in random environments

Part of: Special processes Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Nicholas Bambos  and
George Michailidis
Nicholas Bambos*
Affiliation:
Stanford University
George Michailidis*
Affiliation:
University of Michigan
*
∗ Postal address: Department of Management Science and Engineering and Department of Electrical Engineering, Stanford University, Stanford, CA 94305, USA.
∗∗ Postal address: Department of Statistics, University of Michigan, Ann Arbor, MI 48109-1092, USA. Email address: gmichail@umich.edu
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Abstract

We consider a processing system, composed of several parallel queues and a processor, which operates in a time-varying environment that fluctuates between various states or modes. The service rate at each queue depends on the processor bandwidth allocated to it, as well as the environment mode. Each queue is driven by a job traffic flow, which may also depend on the environment mode. Dynamic processor scheduling policies are investigated for maximizing the system throughput, by adapting to queue backlogs and the environment mode. We show that allocating the processor bandwidth to the queues, so as to maximize the projection of the service rate vector onto a linear function of the workload vector, can keep the system stable under the maximum possible traffic load. The analysis of the system dynamics is first done under very general assumptions, addressing rate stability and flow conservation on individual traffic and environment evolution traces. The connection with stochastic stability is later discussed for stationary and ergodic traffic and environment processes. Various extensions to feed-forward networks of such nodes, the multi-processor case, etc., are also discussed. The approach advances the methodology of trace-based modelling of queueing structures. Applications of the model include bandwidth allocation in wireless channels with fluctuating interference and allocation of switching bandwidth to traffic flows in communication networks with fluctuating congestion levels.

Keywords

Stability of queuesprocessing networkdynamic schedulingbandwidth allocationcomputer networkwireless network

MSC classification

Primary: 60K25: Queueing theory 60K30: Applications (congestion, allocation, storage, traffic, etc.) 60K37: Processes in random environments
Secondary: 60G55: Point processes
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 36 , Issue 1 , March 2004 , pp. 293 - 317
Copyright
Copyright © Applied Probability Trust 2004 

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