Volume 53, Number 4, October 2019
|Page(s)||1197 - 1216|
|Published online||29 July 2019|
Analysis of a discrete-time repairable queue with disasters and working breakdowns
School of Mathematics and Statistics, Fuyang Normal College, Fuyang, 236037 Anhui, China
2 Department of Mathematics, Beijing Jiaotong University, 100044 Beijing, China
3 Design and Development of ICT systems (AddICT) Laboratory, Budapest University of Technology and Economics, Magyar tudósok körútja 2, 117 Budapest, Hungary
* Corresponding author: firstname.lastname@example.org
Accepted: 7 July 2018
In this paper, we analyse a discrete-time queue with a primary server of high service capacity and a substitute server of low service capacity. Disasters that only arrive during the busy periods of the primary server remove all customers from the system and make the primary server breakdown. When the primary server fails and is being repaired, the substitute server handles arriving customers. Applying the embedded Markov chain technique and the supplementary variable method, we determine the distribution of the system length at departure epochs and the joint distribution of the queue length and server’s state at an arbitrary instant. Then we derive the sojourn time distribution. We also provide the probability generating function of the time between failures. Some numerical examples are delivered to give an insight into the impact of system parameters on performance measures and a cost function.
Mathematics Subject Classification: 60K25 / 90B22
Key words: Discrete-time queue / disasters / working breakdowns / performance analysis
© EDP Sciences, ROADEF, SMAI 2019
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