Abstract
This thesis analyzes an M/M/R queue with multiple working vacations which the server works with different service rates rather than completely terminates service during the vacation period. We assume that the server begins a working vacation when the system is empty. We show that this is a generalization of an M/M/1 queue with working vacations considered in the literature. Service times during vacation period, service times during service period and vacation times are all exponentially distributed. We obtain the useful formula for the rate matrix through matrix-geometric method. We further develop the explicit formulae for system performance measures. A cost model is derived to determine the optimal values of the number of servers and the working vacation rate simultaneously at the minimal total expected cost per unit time. Under the optimal operating conditions, numerical results are provided in which several system performance measures are calculated based on assumed numerical values of the system parameters. Sensitivity investigation is also presented.
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