期刊
APPLIED MATHEMATICAL MODELLING
卷 37, 期 3, 页码 1564-1579出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2012.04.045
关键词
Working vacation; Vacation interruption; Matrix-geometric approach; Supplementary variable technique
资金
- National Natural Science Foundation of China [11171179]
- Humanities and Social Sciences Key Project of Anhui Provincial Education Department [2010sk327zd]
This paper treats an M/G/1 queue with single working vacation and vacation interruption under Bernoulli schedule. Whenever the system becomes empty at a service completion instant, the server goes for a single working vacation. In the working vacation, a customer is served at a lower speed, and if there are customers in the queue at the instant of a service completion, the server is resumed to a regular busy period with probability p (i.e., the vacation is interrupted) or continues the vacation with probability 1 - p. Using the matrix analytic method, we obtain the distribution for the stationary queue length at departure epochs. The joint distribution for the stationary queue length and service status at the arbitrary epoch is also obtained by using supplementary variable technique. We also develop a variety of stationary performance measures for this system and give a conditional stochastic decomposition result. Finally, several numerical examples are presented. (C) 2012 Elsevier Inc. All rights reserved.
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