Abstract
The queue Is a closed M/GI/1 queue with a finite number n of customers (sources) which can behave In a different manner. The distributions of busy periods in this queue are derived by connecting Kendall's method of imbedded Markov chains and the method of Laplace-Stieltjes-transformation as usually applied in the study of busy periods, In the case of uniform customers, the distribution of the busy period in the (n/M/GI/1) queue converges monotone decreasing to the distribution of the busy period in the open M/GI/1 queue if the summarized arrival intensity is constant and if n increases to infinity, In the case, the distribution of the busy periods is independent of the service discipline.
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