Issue No. 04 - July (1983 vol. 9)
M.J. Ferguson , Bell-Northern Research Ltd., Ottawa, Ont., Canada and INRS-T?l?communications
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.
M.J. Ferguson, "Weighted Processor Sharing-Results for Hyperexponential Servers", IEEE Transactions on Software Engineering, vol. 9, no. , pp. 531-535, July 1983, doi:10.1109/TSE.1983.234962