Advances and Applications in Statistics
Volume 35, Issue 2, Pages 111 - 126
(August 2013)
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BATCH ARRIVAL QUEUE WITH THREE STAGES OF SERVICE HAVING SERVER VACATIONS AND SERVICE INTERRUPTIONS
G. Ayyappan and K. Sathiya
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Abstract: We consider a batch arrival queueing system with three stages of heterogeneous service provided by a single server with different general (arbitrary) service time distribution subject to random interruption. Each customer undergoes three stages of heterogeneous service. However, at the completion of each third stage of service, the server will take compulsory vacation. After compulsory vacation, the server may take optional vacation with probability p or stay in the system with probability (1-p) for next service. The server is interrupted at random and the duration of attending interruption follows exponential distribution. Also, we assume the customer whose service is interrupted goes back to the head of the queue where the arrivals are Poisson. The vacation times are assumed to be general. The time dependent probability generating functions have been obtained in terms of their Laplace transforms. |
Keywords and phrases: batch arrival, compulsory vacation, optional vacation, three stage heterogeneous service, service interruption. |
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