Performance Modelling of a Discrete-Time Retrial Queue with Preferred and Impatient Customers, Bernoulli Vacation and Second Optional Service

2021 ◽  
pp. 331-345
Author(s):  
Geetika Malik ◽  
Shweta Upadhyaya
Keyword(s):  
Discrete Time ◽  
Retrial Queue ◽  
Impatient Customers ◽  
Performance Modelling ◽  
Optional Service ◽  
Second Optional Service ◽  
Bernoulli Vacation

scholarly journals Bernoulli vacation model for MX /G/1 unreliable server retrial queue with Bernoulli feedback, balking and optional service

2020 ◽  
Author(s):  
Dr. Madhu Jain ◽  
Sandeep Kaur
Keyword(s):  
Performance Metrics ◽  
Retrial Queue ◽  
Maximum Entropy Principle ◽  
Approximate Solutions ◽  
Bernoulli Feedback ◽  
Unreliable Server ◽  
Optional Service ◽  
Multi Phase ◽  
Essential Service ◽  
Bernoulli Vacation

The study of unreliable server retrial bulk queue with multiphase optional service is analyzed by incorporating the features of balking, Bernoulli vacation and Bernoulli feedback. On the occasion when the server is occupied with the service of the customers, an arriving customer finding the long queue, can join the retrial orbit and receives its service later on by making re-attempt. The system is reinforced with multi phase optional service along with essential service and joining customer can opt any one of optional services after getting essential service. Furthermore, the essential/ optional service can be aborted due to abrupt failure of the server. There is an immediate support of multi phase repair facility to take care of the failed server, but sometimes repair may be put on hold by virtue of any unexpected cause. If the service is unsatisfactory, the customer can rejoin the queue as feedback customer. Bernoulli vacation is permitted to the server following the respective busy period. For evaluating the queue size distribution and other system performance metrics, supplementary variable technique (SVT) is used. The approximate solutions for the steady state probabilities and waiting time are suggested using maximum entropy principle (MEP). To verify the outcomes of the model, numerical illustrations and cost analysis have been accomplished.

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