N-policy for Mx/G/1 Unreliable Retrial G-Queue with Preemptive Resume and Multi-services

Bulk arrival retrial G-queue with impatient customers and multi-services subject to server breakdowns has been analyzed. The system allows the arrival of two types of customers: positive customers and negative customers in the system. The negative customers make the server fail if they find the serv...

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Bibliographic Details
Published in:Journal of the Operations Research Society of China (Internet) 2016-12, Vol.4 (4), p.437-459
Main Authors: Bhagat, Amita, Jain, Madhu
Format: Article
Language:English
Subjects:
Breakdown
Computer viruses
Customer services
Customers
Mathematical analysis
Preempting
Queues
Random variables
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Summary:Bulk arrival retrial G-queue with impatient customers and multi-services subject to server breakdowns has been analyzed. The system allows the arrival of two types of customers: positive customers and negative customers in the system. The negative customers make the server fail if they find the server in busy state, whereas positive customers are served if the server is idle otherwise they join the virtual pool of customers called orbit. The customers from the retrial orbit try their chance again for the service. The customers have the option of obtaining more than one service. Moreover, the customers are impatient and may renege from the system with probability (1-r). The server is sent for repair as soon as it breakdowns; after repair, the service process starts again. Also, the server has the provision to initiate the service when there are N customers accumulated in the system. Using supplementary variables technique and generating functions, various performance measures like reliability indices and long run probabilities have been obtained.
ISSN:2194-668X
2194-6698
DOI:10.1007/s40305-016-0128-0