NDLI: Interacting queues in heavy traffic

Content Provider	Springer Nature Link
Author	Morrison, J. A. Borst, S. C.
Copyright Year	2010
Abstract	We consider a system of parallel queues with Poisson arrivals and exponentially distributed service requirements. The various queues are coupled through their service rates, causing a complex dynamic interaction. Specifically, the system consists of one primary queue and several secondary queues whose service rates depend on whether the primary queue is empty or not. Conversely, the service rate of the primary queue depends on which of the secondary queues are empty.An important special case arises when the service rates satisfy a specific relationship so that the various queues form a work-conserving system. This case is, in fact, equivalent to a so-called Generalized Processor Sharing (GPS) system. GPS-based scheduling algorithms have emerged as popular mechanisms for achieving service differentiation while providing statistical multiplexing gains.We consider a heavy-traffic scenario, and assume that each of the secondary queues is underloaded when the primary queue is busy. Using a perturbation procedure, we derive the lowest-order asymptotic approximation to the joint stationary distribution of the queue lengths, in terms of a small positive parameter measuring the closeness of the system to instability. Heuristic derivations of these results are presented.We also pursue two extensions: (i) the more general work-conserving case where the service rate of a secondary queue may depend on its own length, and is a slowly varying function of the length of the primary queue; and (ii) the non-work-conserving case where the service rate of a secondary queue may depend on its own length, but not on the length of the primary queue.
Ending Page	156
Page Count	22
Starting Page	135
File Format	PDF
ISSN	02570130
e-ISSN	15729443
Journal	Queueing Systems
Issue Number	2
Volume Number	65
Language	English
Publisher	Springer US
Publisher Date	2010-04-21
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Queues and service Systems Theory, Control Time scale decomposition State-dependent service rates Probability Theory and Stochastic Processes Generalized processor sharing Perturbation Bandwidth sharing First-order approximation Asymptotic expansion Heavy traffic Operations Research/Decision Theory Production/Logistics Coupled processors Computer Communication Networks Applications (congestion, allocation, storage, traffic, etc.)
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Management Science and Operations Research Computational Theory and Mathematics Computer Science Applications

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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