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Insensitive bounds for the moments of the sojourn time distribution in the M/G/1 processor-sharing queue

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Abstract

This paper studies the M/G/1 processor-sharing (PS) queue, in particular the sojourn time distribution conditioned on the initial job size. Although several expressions for the Laplace-Stieltjes transform (LST) are known, these expressions are not suitable for computational purposes. This paper derives readily applicable insensitive bounds for all moments of the conditional sojourn time distribution. The instantaneous sojourn time, i.e., the sojourn time of an infinitesimally small job, leads to insensitive upper bounds requiring only knowledge of the traffic intensity and the initial job size. Interestingly, the upper bounds involve polynomials with so-called Eulerian numbers as coefficients. In addition, stochastic ordering and moment ordering results for the sojourn time distribution are obtained.

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Authors and Affiliations

  1. Department of Applied Mathematics, Stochastic Operations Research Group, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    Sing-Kong Cheung & Richard J. Boucherie

  2. TNO Information and Communication Technology, P.O. Box 5050, 2600 GB, Delft, The Netherlands

    Hans van den Berg

  3. Department of Computer Science, Design and Analysis of Communication Systems, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    Hans van den Berg

Authors
  1. Sing-Kong Cheung
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  2. Hans van den Berg
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  3. Richard J. Boucherie
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Correspondence to Sing-Kong Cheung.

Additional information

AMS Subject Classification: 60K25, 60E15

This work has been partially funded by the Dutch Ministry of Economic Affairs under the program ‘Technologische Samenwerking ICT-doorbraakprojecten’, project TSIT1025 BEYOND 3G.

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Cheung, SK., van den Berg, H. & Boucherie, R.J. Insensitive bounds for the moments of the sojourn time distribution in the M/G/1 processor-sharing queue. Queueing Syst 53, 7–18 (2006). https://doi.org/10.1007/s11134-006-7583-y

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  • DOI: https://doi.org/10.1007/s11134-006-7583-y

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