IJSRP, Volume 7, Issue 4, April 2017 Edition [ISSN 2250-3153]
S. Uma, P. Manikandan
The concept of this paper studies with the customers arriving in bulk or group, in a single server queueing system, in Poisson distribution which provides three types of general services in bulk of fixed size M (≥1) in first come first served basis. After first two stage service, the server must provide the third stage service. After the completion of third stage service, the server takes compulsory vacation under exponential distribution. If the required bulk of customers are not available on the return of the server, the server again goes for vacation or remains in the system till bulk is reached. The arriving batch balks during the period when the server is busy or when the server is on vacation or other constraints. This may result in the impatient behavior of the customers. From the above concept, we compute the time dependent probability generating functions and from it the corresponding steady state results are obtained. The average queue size and the system size are derived.