Fluid approximations for a processor-sharing queue

Authors:
Hong Chen;Offer Kella;Gideon Weiss
Affiliations:
Department of Industrial Engineering and Engineering Management, Hong Kong University of Science and Technology, Hong Kong E-mail: hongchen@uxmail.ust.hk;Department of Statistics, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem 91905, Israel E-mail: mskella@olive.mscc.huji.ac.il;Department of Statistics, The University of Haifa, Haifa 31905, Israel E-mail: gweiss@stat.haifa.ac.il
Venue:
Queueing Systems: Theory and Applications
Year:
1997

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Abstract

In this paper a fluid approximation, also known as a functional strong law of large numbers (FSLLN) for a GI/G/1 queue under a processor-sharing service discipline is established and its properties are analysed. The fluid limit depends on the arrival rate, the service time distribution of the initial customers, and the service time distribution of the arriving customers. This is in contrast to the known result for the GI/G/1 queue under a FIFO service discipline, where the fluid limit is piecewise linear and depends on the service time distribution only through its mean. The piecewise linear form of the limit can be recovered by an equilibrium type choice of the initial service distribution.