Economic application in a BernoulliF-policy queueing system with server breakdown

2013 ◽  
Vol 52 (3) ◽  
pp. 743-756 ◽  
Author(s):  
Chia-Jung Chang ◽  
Fu-Min Chang ◽  
Jau-Chuan Ke
Keyword(s):  
Queueing System ◽  
Economic Application ◽  
Server Breakdown

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

2006 ◽  
Vol 23 (02) ◽  
pp. 247-271 ◽  
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.

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

1997 ◽  
Vol 37 (8) ◽  
pp. 1203-1212 ◽  
Author(s):  
Quan-Lin Li ◽  
De-Ju Xu ◽  
Jinhua Cao
Keyword(s):  
Queueing System ◽  
Server Breakdown

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

2018 ◽  
Vol 52 (3) ◽  
pp. 903-922 ◽  
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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