Abstract
This paper analyzes single server queueing system wherein the arrival units are in batches following compound Poisson process with varying arrival rates for dierent states. The arrival rates dier for dierent states like idle state, busy state and vacation period. The server provides service one by one and after completion of a service, the server either takes a vacation of random length with probability p (0 p 1) or continue to serve the next customer with probability 1-p, if any. Both service time and vacation time follow general distribution. In addition to this one of the customer impatience, balking is also discussed. We have obtained state dependent solution for the model the steady state analysis.
Published Version
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