Abstract

This paper deals with MX/G/1 retrial queue with unreliable server and multi-optional repair. It is assumed that the server is subject to active breakdowns and the repair of the failed server starts after a random amount of time. Restoration of the failed server is done with two phases, first essential and second multi optional. After completion of the repair the server continues the interrupted service and it is not allowed to accept new customers until the interrupted customer leaves the system. The retrial, service, delay and repair times are arbitrarily distributed. The model is analysed using the supplementary variable technique and the probability generating function of system size at random epoch and stochastic decomposition are obtained. Performance measures and reliability indices to predict the behaviour of the system are derived.

Keyword

Bulk arrival, Retrial queue, Delay, Multi optional repair.

Cite this article

Refference

[1][1]Artalejo JR. A classified bibliography of research on retrial queues: progress in 1990-1999. TOP. 1999;7(2):187-211.

[2][2]Artalejo JR. Accessible bibliography on retrial queues. Mathematical and Computer Modelling. 1999;30(3):1-6.

[3][3]Kulkarni VG, Choi BD. Retrial queues with server subject to breakdowns and repairs. Queueing Systems. 1990;7(2):191-208.

[4][4]Yang T, Li H. The M/G/1 retrial queue with the server subject to starting failures. Queueing Systems. 1994;16(1):83-96.

[5][5]Wang J, Cao J, Li Q. Reliability analysis of the retrial queue with server breakdowns and repairs. Queueing Systems. 2001;38(4):363-80.

[6][6]Jain M, Bhargava C. Unreliable server M/G/1 queueing system with Bernoulli feedback, repeated attempts, modified vacation, phase repair and discouragement. Journal of King Abdulaziz University: Engineering Sciences. 2009; 20(2):45-77.

[7][7]Khalaf RF, Madan KC, Lukas CA. An M [X]/G/1 queue with Bernoulli schedule, general vacation times, random breakdowns, general delay times and general repair times. Applied Mathematical Sciences. 2011;5(1):35-51.

[8][8]Choudhury G, Tadj L, Ke JC. A two-phase service system with Bernoulli vacation schedule, setup time and N-policy for an unreliable server with delaying repair. Quality Technology & Quantitative Management. 2011;8(3):271-84.

[9][9]Choudhury G, Ke JC. A batch arrival retrial queue with general retrial times under Bernoulli vacation schedule for unreliable server and delaying repair. Applied Mathematical Modelling. 2012;36(1):255-69.

[10][10]Jain M, Sharma GC, Sharma R. Working vacation queue with service interruption and multi optional repair. International Journal of Information and Management Sciences. 2011:157-76.

[11][11]Kumar BK, Arivudainambi D, Vijayakumar A. On the M (x)/G/1 retrial queue with Bernoulli schedules and general retrial times. Asia-Pacific Journal of Operational Research. 2002;19(2):177-94.