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《Mathematics in Practice and Theory》 2018-06
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A Fluid Model Driven by an M/M/1 Vacations Queue with Optional Service

XU Xiu-li;WANG Xian-ying;XU Biao;School of Science, Yanshan University;  
Introducing second optional service into the M/M/1 multiple vocations queue,this paper considers a fluid model driven by an M/M/1 queue model with multiple vocations and second optional service. The net input rate structure is established, and using QBD method we get the stationary distribution of the driving system. By Laplace Transform(LT) method, we get the Laplace-Stieltjes(LST) of the buffer content, the probability of the empty buffer and the average buffer content in the steady state. Finally, we present the numerical example to describe the change tendency of performance indices with parameters.
【Fund】: 国家自然科学基金(11201408);; 河北省自然科学基金(A2013203148)
【CateGory Index】: O226
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