Volume 54, Number 3, May-June 2020
|Page(s)||675 - 691|
|Published online||10 March 2020|
The analysis of a discrete time finite-buffer queue with working vacations under Markovian arrival process and PH-service time
School of Science, Nanjing University of Information Science and Technology, Nanjing, P.R. China
2 School of Science, Nanjing University of Science and Technology, Nanjing, P.R. China
3 College of Economics and Management, Shandong University of Science and Technology, Qingdao, P.R. China
4 School of Mathematical and Physical Sciences, Nanjing Tech University, Nanjing P.R. China
* Corresponding author: firstname.lastname@example.org
Accepted: 5 February 2019
In this paper, we study the discrete-time MAP/PH/1 queue with multiple working vacations and finite buffer N. Using the Matrix-Geometric Combination method, we obtain the stationary probability vectors of this model, which can be expressed as a linear combination of two matrix-geometric vectors. Furthermore, we obtain some performance measures including the loss probability and give the limit of loss probability as finite buffer N goes to infinite. Waiting time distribution is derived by using the absorbing Markov chain. Moreover, we obtain the number of customers served in the busy period. At last, some numerical examples are presented to verify the results we obtained and show the impact of parameter N on performance measures.
Mathematics Subject Classification: 60K25 / 68M20
Key words: Working vacation / finite buffer / matrix-geometric combination method / Sojourn time / busy period
© EDP Sciences, ROADEF, SMAI 2020
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