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Moments of the conditioned waiting time in a large closed processor- sharing system. (English)
Commun. Stat., Stochastic Models 2, 293-321 (1986).
An interactive computer system consists of N terminals in series and a CPU, which feeds back to terminals. A quantity of interest is conditional waiting (response) time of an arriving job in such a system, conditioned on its required service time. The waiting time has been extensively investigated by {\it D. Mitra} [see, e.g., "Waiting time distribution from closed queueing network of shared-processor systems", PERFORMANCE ’81, 113-131 (1981)], however, the moments of waiting time have been expressed in terms of the solution of $N\times N$ system of linear equations. For large N, the solution of the matrix equation becomes troublesome, hence the author of this paper derives asymptotic approximation of the conditional moments. In particular, the conditional means and the conditional variance are considered in detail. Three cases are investigated: normal usage $(ρ<1)$, heavy-usage $(ρ- 1=O(N\sp{-1/2}))$, and very heavy-usage $(ρ>1)$. Finally, the approximations are numerically compared with exact results showing good accuracy.
Reviewer: W.Szpankowski