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In a recent paper by Fayolle, Mitrani, and Iasnogorodski , 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  does not hold for nonexponential servers. Fayolie et al.  had showed that it did hold for exponential servers.
Date of Publication: July 1983