Processor-sharing queues: some progress in analysis
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
On the stability of the multi-queue multi-server processor sharing with limited service
Queueing Systems: Theory and Applications
Waiting times for M/M systems under state-dependent processor sharing
Queueing Systems: Theory and Applications
Power series approximations for two-class generalized processor sharing systems
Queueing Systems: Theory and Applications
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We consider a single server system consisting of n queues with different types of customers and k permanent customers. The permanent customers and those at the head of the queues are served in processor-sharing by the service facility (head-of-the-line processor-sharing). By means of Loynes’ monotonicity method a stationary work load process is constructed and using sample path analysis general stability conditions are derived. They allow to decide which queues are stable and, moreover, to compute the fraction of processor capacity devoted to the permanent customers. In case of a stable system the constructed stationary state process is the only one and for any initial state the system converges pathwise to the steady state.