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 q$$ ≥ 0 to phase i. In this study, the distribution of the buffer content is determined using the probability generating function. In addition, some numerical results are provided to illustrate the effect of various parameters on the distribution of the buffer content.
Keywords: $$/$$/1 queue, disasters, random environment, stationary probabilities, buffer content distribution
@article{RO_2021__55_S1_S2677_0,
author = {Ammar, Sherif I.},
title = {Fluid $M / M / 1$ catastrophic queue in a random environment},
journal = {RAIRO. Operations Research},
pages = {S2677--S2690},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
doi = {10.1051/ro/2020100},
mrnumber = {4223169},
zbl = {1469.90054},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2020100/}
}
TY - JOUR AU - Ammar, Sherif I. TI - Fluid $M / M / 1$ catastrophic queue in a random environment JO - RAIRO. Operations Research PY - 2021 SP - S2677 EP - S2690 VL - 55 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2020100/ DO - 10.1051/ro/2020100 LA - en ID - RO_2021__55_S1_S2677_0 ER -
Ammar, Sherif I. Fluid $M / M / 1$ catastrophic queue in a random environment. RAIRO. Operations Research, Tome 55 (2021), pp. S2677-S2690. doi: 10.1051/ro/2020100
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