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Weighted Processor Sharing-Results for Hyperexponential Servers

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1 Author(s)
Ferguson, M.J. ; Bell-Northern Research Ltd., Ottawa, Ont., Canada and INRS-Télécommunications

In a recent paper by Fayolle, Mitrani, and Iasnogorodski [2], some general multidimensional integral equations were derived in order to solve for the mean response time of each of several classes in a queue whose service discipline was weighted processor sharing. The arrival processes were Poisson. The weighting means that each job within a class k is given an amount of processing proportional to the priority weight gk associated with that class. For exponential service times, the general equations were solved. In this note, a simple observation allows use of the exponential solution directly for the case of hyperexponential servers. As a result, it is possible to state the following. •Characterization of a server in terms of its mean and coefficient of variation is not sufficient to predict even the mean response time for a class using weighted processor sharing. In unweighted or egalitarian processor sharing, only the mean is sufficient. •The Kleinrock conservation law [4] does not hold for nonexponential servers. Fayolie et al. [2] had showed that it did hold for exponential servers.

Published in:

Software Engineering, IEEE Transactions on  (Volume:SE-9 ,  Issue: 4 )