NDLI: On the stability of the multi-queue multi-server processor sharing with limited service

Content Provider	Springer Nature Link
Author	Brandt, Andreas Brandt, Manfred
Copyright Year	2007
Abstract	We consider a multi-queue multi-server system with n servers (processors) and m queues. At the system there arrives a stationary and ergodic stream of m different types of requests with service requirements which are served according to the following k-limited head of the line processor sharing discipline: The first k requests at the head of the m queues are served in processor sharing by the n processors, where each request may receive at most the capacity of one processor. By means of sample path analysis and Loynes’ monotonicity method, a stationary and ergodic state process is constructed, and a necessary as well as a sufficient condition for the stability of the m separate queues are given, which are tight within the class of all stationary ergodic inputs. These conditions lead to tight necessary and sufficient conditions for the whole system, also in case of permanent customers, generalizing an earlier result by the authors for the case of n=k=1.
Ending Page	8
Page Count	8
Starting Page	1
File Format	PDF
ISSN	02570130
e-ISSN	15729443
Journal	Queueing Systems
Issue Number	1
Volume Number	56
Language	English
Publisher	Kluwer Academic Publishers-Plenum Publishers
Publisher Date	2007-05-17
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Thread pools Permanent customers Systems Theory, Control Batch arrivals Stationary processes Many servers Stationarity Ergodicity Probability Theory and Stochastic Processes Stability condition Many queues Point processes Head of the line processor sharing Marked point process Performance evaluation; queueing; scheduling Operations Research/Decision Theory Production/Logistics General input Queueing theory Sample path properties Computer Communication Networks Loynes’ construction
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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