LAUSR

This article deals with single server queue with modified vacation policy. The modified vacation policy captures the operation of a close down period, type 1 vacation period, type 2 vacation period, a start-up period and a dormant period. Here, type 1 vacations takes a short period of random duration and type 2 vacation take a long period of random duration. Explicit expressions have been obtained for steady state queue size distribution at service completion point and steady state system size probabilities. The Laplace-Stieltjes transform of waiting time and its corresponding mean value have been obtained for the system. Finally, some numerical examples have been provided and use the parabolic method to search the optimum value of the control parameter p .