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The fluid limit of a heavily loaded processor sharing queue. (English) Zbl 1017.60092
A single server queue with renewal arrivals and i.i.d. service times is considered in which the server operates under a processor sharing service discipline. The authors study a critical fluid model for a heavily loaded processor sharing queue. The fluid model state descriptor is a measure-valued function whose dynamics are governed by a nonlinear integral equation. The critical fluid model can be served as a first order approximation of a heavily loaded processor.

60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
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