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Math. Comput. Appl. 2015, 20(1), 39-49; doi:10.3390/mca20010049

Analysis of an M (λ1,λ2) / M /1 / WV Queue with Controlled Vacation Interruption and Variable Arrival Rate

1,2,* and 1,2,*
1
Visual Computing and Virtual Reality Key Laboratory of Sichuan Province, Sichuan Normal University, 610068, Chengdu, Sichuan, China
2
School of Mathematics & Software Science, Sichuan Normal University, 610068, Chengdu, Sichuan, China
*
Authors to whom correspondence should be addressed.
Published: 1 April 2015
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Abstract

This paper studies a Markovian queue with multiple working vacations and controlled vacation interruption. If there are at least N customers waiting upon completion of a service at a lower rate, the vacation is interrupted and the server returns to the system to resume the normal working level. Otherwise, the server continues the vacation until the system is non-empty after a vacation ends or there are at least N customers after a service ends. Moreover, the variable arrival rate of the customers is taken into account. Under such assumptions, by using the quasi-birth-and-death process, the matrix- geometric method and the difference equation theory, the steady-state queue length distribution along with various performance measures are derived. Additionally, under a certain cost structure, the optimal threshold N* that minimizes the long-run expected cost function per unit time is numerically determined.
Keywords: Markovian queue; working vacation; vacation interruption; cost function Markovian queue; working vacation; vacation interruption; cost function
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Wu, W.; Tang, Y. Analysis of an M (λ1,λ2) / M /1 / WV Queue with Controlled Vacation Interruption and Variable Arrival Rate. Math. Comput. Appl. 2015, 20, 39-49.

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