Volume 55, 2021Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
|S2677 - S2690
|02 March 2021
Fluid M/M/1 catastrophic queue in a random environment
Mathematics and Computer Science Department, Faculty of Science, Menoufia University, Shebin El Kom, Egypt
2 Department of Mathematics, Faculty of Science, Taibah University, Medinah, Saudi Arabia
* Corresponding author: firstname.lastname@example.org
Accepted: 8 September 2020
Our main objective in this study is to investigate the stationary behavior of a fluid catastrophic queue of M/M/1 in a random multi-phase environment. Occasionally, a queueing system experiences a catastrophic failure causing a loss of all current jobs. The system then goes into a process of repair. As soon as the system is repaired, it moves with probability qi ≥ 0 to phase i. In this study, the distribution of the buffer content is determined using the probability generating function. In addition, some numerical results are provided to illustrate the effect of various parameters on the distribution of the buffer content.
Mathematics Subject Classification: 90B22 / 60K25 / 68M20
Key words: M/M/1 queue / disasters / random environment / stationary probabilities / buffer content distribution
© EDP Sciences, ROADEF, SMAI 2021
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