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Sojourn times in (discrete) time shared systems and their continuous time limits

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Abstract

We study the mean sojourn times in two M/G/1 weighted round-robin systems: the weight of a customer at any given point in time in the first system is a function of its age (imparted service), while in the second system the weight is a function of the customer’s remaining processing time (RPT). We provide a sufficient condition under which the sojourn time of a customer with large service requirement (say, x) and that arrives in the steady state is close to that of a customer which starts a busy period and has the same service requirement. A sufficient condition is then provided for continuity of the performance metric (the mean sojourn time) as the quanta size in the discrete time system converges to 0. We then consider a multi-class system and provide relative ordering of the mean sojourn times among the various classes.

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Authors and Affiliations

  1. General Motors India Science Laboratory, Bangalore, India

    Arzad A. Kherani

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  1. Arzad A. Kherani
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Correspondence to Arzad A. Kherani.

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A preliminary version of this work appeared in the Valuetools 2006 conference. This work was done when the author was with the department of Computer Science and Engineering, Indian Institute of Technology Delhi, New Delhi, India.

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Kherani, A.A. Sojourn times in (discrete) time shared systems and their continuous time limits. Queueing Syst 60, 171–191 (2008). https://doi.org/10.1007/s11134-008-9092-7

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  • DOI: https://doi.org/10.1007/s11134-008-9092-7

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