This book envisages to present a detailed analysis of two-phase N-policy Queueing systems with adequate illustrated data. Chapters I and II deals with necessary preliminaries and a preamble to the main topic. Chapter III presents optimal control of Mx/Ej/1(j being a random variable) with N-Policy. In chapters IV, V, VI and VII a comprehensive account of the optimal control of N-Policy two-phase M/M/1, M/Ek/1, Mx/M/1 and Mx/Ek/1 queueing systems under exhaustive gated and non-gated services is presented. The distribution of the system size has been derived through probability generating functions and further obtained therefrom various system performance measures. From the results thus obtained the total expected cost function per unit time that includes customer holding cost, system set up cost, server start up cost, server running cost and the extra revenue earned through the server working during vacation is formulated. Next the optimal threshold N to minimize the total expected cost has been determined. Finally, the entire sensitivity analysis is highlighted through numerical illustrations.

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