Gromoll, H. Christian; Puha, Amber L.; Williams, Ruth J. The fluid limit of a heavily loaded processor sharing queue. (English) Zbl 1017.60092 Ann. Appl. Probab. 12, No. 3, 797-859 (2002). 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. Reviewer: Anatolij Dvurečenskij (Bratislava) Cited in 3 ReviewsCited in 32 Documents MSC: 60K25 Queueing theory (aspects of probability theory) 90B22 Queues and service in operations research Keywords:processor sharing queue; heavy traffic; fluid model; renewal equation; measure valued process PDFBibTeX XMLCite \textit{H. C. Gromoll} et al., Ann. Appl. Probab. 12, No. 3, 797--859 (2002; Zbl 1017.60092) Full Text: DOI