Analysis of a bulk queueing system with server breakdown and vacation interruption

In this present paper, an M/M/1 retrial queueing model with a waiting server subject to breakdown and repair under working vacation, vacation interruption is considered. Customers are served at a slow rate during the working vacation period, and the server may undergo breakdowns from a normal busy state. The customer has to wait in orbit for the service until the server gets repaired. Steady-state solutions are obtained using the probability generating function technique. Probabilities of different server states and some other performance measures of the system are developed. The variation in mean orbit size, availability of the server, and server state probabilities are plotted for different values of breakdown parameter and repair rate with the help of MATLAB software. Finally, cost optimization of the system is also discussed, and the optimal value of the slow service rate for the model is obtained.

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A DISCRETE-TIME Geo/G/1 RETRIAL QUEUE WITH SERVER BREAKDOWNS

Asia Pacific Journal of Operational Research ◽

10.1142/s0217595906000929 ◽

2006 ◽

Vol 23 (02) ◽

pp. 247-271 ◽

Cited By ~ 27

Author(s):

IVAN ATENCIA ◽

PILAR MORENO

Keyword(s):

Steady State ◽

Performance Measures ◽

Discrete Time ◽

Continuous Time ◽

Queueing System ◽

Retrial Queue ◽

System Size ◽

Stochastic Decomposition ◽

Recursive Procedure ◽

Server Breakdown

This paper discusses a discrete-time Geo/G/1 retrial queue with the server subject to breakdowns and repairs. The customer just being served before server breakdown completes his remaining service when the server is fixed. The server lifetimes are assumed to be geometrical and the server repair times are arbitrarily distributed. We study the Markov chain underlying the considered queueing system and present its stability condition as well as some performance measures of the system in steady-state. Then, we derive a stochastic decomposition law and as an application we give bounds for the proximity between the steady-state distributions of our system and the corresponding system without retrials. Also, we introduce the concept of generalized service time and develop a recursive procedure to obtain the steady-state distributions of the orbit and system size. Finally, we prove the convergence to the continuous-time counterpart and show some numerical results.

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Reliability approximation of a Markov queueing system with server breakdown and repair

Microelectronics Reliability ◽

10.1016/s0026-2714(96)00291-0 ◽

1997 ◽

Vol 37 (8) ◽

pp. 1203-1212 ◽

Cited By ~ 14

Author(s):

Quan-Lin Li ◽

De-Ju Xu ◽

Jinhua Cao

Keyword(s):

Queueing System ◽

Server Breakdown

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Analysis of a queueing system in random environment with an unreliable server and geometric abandonments

RAIRO - Operations Research ◽

10.1051/ro/2018021 ◽

2018 ◽

Vol 52 (3) ◽

pp. 903-922 ◽

Cited By ~ 2

Author(s):

Tao Jiang ◽

Baogui Xin ◽

Baoxian Chang ◽

Liwei Liu

Keyword(s):

Performance Measures ◽

Random Environment ◽

Queueing System ◽

Geometric Approach ◽

Repair Process ◽

Single Server ◽

Steady State Distribution ◽

Server Breakdown ◽

Multi Phase ◽

The Impact

This paper studies a single server queueing model in a multi-phase random environment with server breakdowns and geometric abandonments, where server breakdowns only occur while the server is in operation. At a server breakdown instant (i.e., an abandonment opportunity epoch), all present customers adopt the so-called geometric abandonments, that is, the customers decide sequentially whether they will leave the system or not. In the meantime, the server abandons the service and a repair process starts immediately. After the server is repaired, the server resumes its service, and the system enters into the operative phaseiwith probabilityqi,i= 1, 2, …,d. Using probability generating functions and matrix geometric approach, we obtain the steady state distribution and various performance measures. In addition, some numerical examples are presented to show the impact of parameters on the performance measures.

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