Power series for stationary distributions of coupled processor models
SIAM Journal on Applied Mathematics
Queueing Systems: Theory and Applications
Diffusion approximation for head-of-the-line processor sharing for two parallel queues
SIAM Journal on Applied Mathematics
Waiting Time Distributions for Processor-Sharing Systems
Journal of the ACM (JACM)
Queueing Systems: Theory and Applications
Sojourn times in a processor sharing queue with service interruptions
Queueing Systems: Theory and Applications
A Reduced-Load Equivalence for Generalised Processor Sharing Networks with Long-Tailed Input Flows
Queueing Systems: Theory and Applications
Sojourn Times in the M/PH/1 Processor Sharing Queue
Queueing Systems: Theory and Applications
A sample path relation for the sojourn times in G/G/1-PS systems and its applications
Queueing Systems: Theory and Applications
Waiting times for M/M systems under state-dependent processor sharing
Queueing Systems: Theory and Applications
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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.