Performance analysis of variant working vacation queue with balking and reneging (Q1635415)

Summary: This paper studies the effect of balking and reneging in a single server queue under variant working vacation policy. Arriving customers balk (do not join the queue) with a probability and renege (leave the queue after joining) according to exponential distribution. Under the variant vacation policy the server leaves for a working vacation as soon as the system becomes empty. The server takes at most \(J\) working vacations until he finds at least one customer in the queue on return from a working vacation. If customers are not found in the queue by the end of \(J^{\text{th}}\) vacation, the server remains idle in the system. The system length probabilities are derived using matrix form solution. Some performance measures of the model and cost analysis through quadratic fit search method have been discussed. Finally, the sensitivity analysis is carried out through some numerical experiments.