The M=M=1 Queue with Single Working Vacation Serving at a Slower Rate during the Start-up Period

Chun Xiu, Naishuo Tian, Yazhen Liu


We consider the M/M/1 queue with single working vacation serving at a slower rate during the start-up period. In order
to save energy and reduce waste, the server works at a slower rate rather than completely stops during a vacation and
start-up period. Using quasi birth and death process and matrix-geometric solution method, we obtain the distribution of
the nember of customers in the system, the average nember of the customers and the average sojourn time of a customer
in the stationary state.

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Journal of Mathematics Research   ISSN 1916-9795 (Print)   ISSN 1916-9809 (Online)

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