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

Please always quote using this URN: urn:nbn:de:0297-zib-9199
  • 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.

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Metadaten
Author:Andreas Brandt, Manfred Brandt
Document Type:ZIB-Report
Tag:batch arrivals; general input; head of the line processor sharing; many queues; many servers; marked point p; permanent customers; thread pools
MSC-Classification:60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Gxx Stochastic processes / 60G10 Stationary processes
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Gxx Stochastic processes / 60G17 Sample path properties
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Gxx Stochastic processes / 60G55 Point processes
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Kxx Special processes / 60K25 Queueing theory [See also 68M20, 90B22]
68-XX COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area) / 68Mxx Computer system organization / 68M20 Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx]
Date of first Publication:2006/05/22
Series (Serial Number):ZIB-Report (06-25)
ZIB-Reportnumber:06-25
Published in:Appeared in: Queuing Systems 56 (2007) 1-8
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