This paper develops a new method for calculating the system size distribution on two different M/G/1 queueing system under N-policy with general startup/closedown. Firstly, the stochastic decomposition property is used to derive the p.g.f. of the system size distribution. By the Leibniz formula of derivation, we investigate the additional system size distribution, and then, we get the recursion expression of system sizes distribution. Finally, several examples are given for illustrating the application of the recursion expression and sensitivity analysis is also performed.
KeywordsQueue-LengthN-PolicyStochastic DecompositionRecursion ExpressionLeibniz Formula
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