Abstract

This paper considers M1,M2/G1,G2/1 general retrial queueing system with non-pre-emptive priority services. The server serves two type of units subject to modified Bernoulli vacation. After completing the service, if there are no high priority units present in the system then the server may go for a vacation. The high priority unit who find the server busy are queued in the system and the low priority unit finds the server busy, they are routed to a retrial queue that attempts to get the service. The system may become defective at any point of time when it is in operation and does not sent for repair immediately. The remaining service will be given to the unit after that only the server go for repair station. After completing the repair and vacation if there is no high priority unit then the server becomes idle. The low priority unit renege the orbit during server’s busy and unavailable periods. Using the supplementary variable technique, the steady-state distributions of the server state and stability condition are obtained.

Keywords

References

[1] Bo Keun Kim, Doo Ho Lee (2016), The M/G/1 queue with disasters and working breakdowns, Applied Mathematical Modelling, Vol.4,437-459.
[2] Cheng-Dar Liou (2013), Markovian queue optimisation analysis with an unreliable server subject to working breakdowns and impatient customers, International Journal of Systems Science ,Vol. 46(12), 2165-2182. 
[3] Dong-Yuh Yang, Ying-Yi Wu(2017), Analysis of a finite-capacity system with working breakdowns and retention of impatient customers, Journal of Manufacturing Systems, Vol. 44 207-216.
[4] Kailash C. Madan (2011), A Non-Preemptive Priority Queueing System with a Single Server Serving Two Queues M/G/1 and M/D/1 with Optional Server Vacations Based on Exhaustive Service of the Priority Units, Applied Mathematics, Vol. 2, 791-799.
[5] Kalidass K, Kasturi R (2012), A queue with working breakdowns, Computers and Industrial Engineering, Vol. 63, 779-783.
[6] Boutarfa L, Djellab N (2015), On the performance of the M₁,M₂/G₁,G₂/1 retrial queue with pre-emptive resume policy, Yugoslav Journal of Operations Research, Vol. 25(1), 153-164.
[7] Phung-Duc, T. (2019), Retrial Queueing Models: A Survey on Theory and Applications, arXiv 2019, arXiv:1906.09560v1.
[8] Tao Li, Liyuan Zhang (2017), An M/G/1 Retrial G-Queue with General Retrial Times and Working Breakdowns, Math. Comput. Appl. Vol. 22, 15.
[9] Zaiming liu, Yang Song (2014), The M^x/M/1 queue with working breakdown, Rairo operations research, Vol. 48,