Transient behavior of / /1 [ ] M G X Queueing Model With State Dependent Arrival, Balking and Bernoulli Vacation

Abstract

This paper analyzes single server queueing system wherein the arrival units are in batches following compound Poisson process with varying arrival rates for different states. The arrival rates differ for different 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 ï‚£ p ï‚£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 time dependent solution followed by the steady state analysis with some performance measures of our model.