No abstract

No abstract

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In this paper we get some sufficient conditions for the finiteness or nonfiniteness of the passage-time moments for nonnegative discrete parameter processes. The developed criteria are closely connected with the well-known results of Foster for the ergodicity of Markov chains and are Ž . given in terms of sub super martingales. Then, as an application of the obtained results, we get explicit conditions for the finiteness or nonfiniteness of passage-time moments for reflected random walks in a quadrant with zero drift in the interior.

A single-server processor-sharing system with M job classes is analyzed in the steady state. The scheduling strategy considered divides the total processor capacity in unequal fractions among the different job classes. More precisely, if there are N~jobs of classj in the system, j = 1, 2 ..... M, each class k job receives a fraction gh/(~M.~ giN~) of the processor capacity.Earlier analyses of this system are shown to be incorrect and new expressions for the conditional expected response times Wk(t) of class k jobs with required service time t are obtained (for general required service time distributions). These yield the asymptotic behavior of W~(t) as t ~ oo and rather simple formulas in the exponential case. The unconditional average response times are also obtained.