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Waiting times for M/M systems under state-dependent processor sharing

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Abstract

We consider a system where the arrivals form a Poisson process and the required service times of the requests are exponentially distributed. The requests are served according to the state-dependent (Cohen’s generalized) processor sharing discipline, where each request in the system receives a service capacity which depends on the actual number of requests in the system. For this system we derive systems of ordinary differential equations for the LST and for the moments of the conditional waiting time of a request with given required service time as well as a stable and fast recursive algorithm for the LST of the second moment of the conditional waiting time, which in particular yields the second moment of the unconditional waiting time. Moreover, asymptotically tight upper bounds for the moments of the conditional waiting time are given. The presented numerical results for the first two moments of the sojourn times in M/M/m−PS systems show that the proposed algorithms work well.

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Authors and Affiliations

  1. Institut für Operations Research, Humboldt-Universität zu Berlin, Spandauer Str. 1, 10178, Berlin, Germany

    Andreas Brandt

  2. Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB), Takustr. 7, 14195, Berlin, Germany

    Manfred Brandt

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  1. Andreas Brandt
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  2. Manfred Brandt
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Correspondence to Andreas Brandt.

Additional information

This work was supported by a grant from the Siemens AG.

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Brandt, A., Brandt, M. Waiting times for M/M systems under state-dependent processor sharing. Queueing Syst 59, 297–319 (2008). https://doi.org/10.1007/s11134-008-9086-5

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  • DOI: https://doi.org/10.1007/s11134-008-9086-5

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