Abstract:

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 areN 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.

Key words: Retrial queue ·, N-policy vacation ·, Negative customers ·, Reneging ·, Bulk
arrival ·, Breakdowns ·, Preemptive resume ·, Multi-services