M[X]/G/1 Retrial Queueing System with Second Optional Service , Random Break down ,Set Up Time and Bernoulli Vacation

2014 ◽  
Vol 7 (1) ◽  
pp. 23-39 ◽  
Author(s):  
G. Ayyappan ◽  
S. Shyamala
Keyword(s):  
Queueing System ◽  
Retrial Queueing System ◽  
Retrial Queueing ◽  
Optional Service ◽  
Second Optional Service ◽  
Set Up ◽  
Bernoulli Vacation

scholarly journals A Discrete-Time UnreliableGeo/G/1Retrial Queue with Balking Customers, Second Optional Service, and General Retrial Times

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Feng Zhang ◽  
Zhifeng Zhu
Keyword(s):  
Performance Measures ◽  
Discrete Time ◽  
Queueing System ◽  
System Size ◽  
Stochastic Decomposition ◽  
State Behavior ◽  
Retrial Queueing System ◽  
Retrial Queueing ◽  
Optional Service ◽  
Second Optional Service

This paper deals with the steady-state behavior of a discrete-time unreliableGeo/G/1retrial queueing system with balking customers and second optional service. The server may break down randomly while serving the customers. If the server breaks down, the server is sent to be repaired immediately. We analyze the Markov chain underlying the considered system and its ergodicity condition. Then, we obtain some performance measures based on the generating functions. Moreover, a stochastic decomposition result of the system size is investigated. Finally, some numerical examples are provided to illustrate the effect of some parameters on main performance measures of the system.

scholarly journals Transient Analysis of M[X1],M[X2]/G1,G2/1 retrial queueing system with priority services, working breakdown, start up/close down time, Bernoulli vacation, reneging and balking

2020 ◽  
pp. 203-216
Author(s):  
Govindhan Ayyappan ◽  
Udayageetha J
Keyword(s):  
Transient Analysis ◽  
Queueing System ◽  
Variable Technique ◽  
Retrial Queueing System ◽  
System A ◽  
Retrial Queueing ◽  
Start Up ◽  
Set Up ◽  
Number Of Customers ◽  
Bernoulli Vacation

This paper considers  M[X1],M[X2]/G1,G2/1 general retrial queueing system with priority services. Two types of customers from different classes arrive at the system in different independent compound Poisson processes. The server follows the pre-emptive priority rule subject to working breakdown, startup/closedown time and Bernoulli vacation with general (arbitrary) vacation periods. After completing the service, if there are no priority customers present in the system the server may go for a vacation or close down the system. On completion of the close down, the server needs some time to set up the system. The priority customers who find the server busy are queued in the system. A low-priority customer who find the server busy are routed to a retrial (orbit) queue that attempts to get the service. The system may breakdown at any point of time when it is in operation. However, when the system fails, instead of stopping service completely, the service is continued only to the high priority customers at a slower rate. We consider balking to occur to the low priority customer while the server is busy or idle, and reneging to occur at the high priority customers during server’s vacation, start up/close down time. Using the supplementary variable technique, we derive the joint distribution of the server state and the number of customers in the system. Finally, some performance measures and numerical examples are presented.

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