M/G/1 vacation model with limited service discipline and hybrid switching-on policy (Q679411)

Summary: The author studies an M/G/1 queueing system with multiple vacations. The server is turned off in accordance with the K-limited discipline, and is turned on in accordance with the T-N-hybrid policy. This is to say that the server will begin a vacation from the system if either the queue is empty or \(K\) customers were served during a busy period. The server idles until it finds at least \(N\) waiting units upon return from a vacation. Formulas for the distribution generating function and some characteristics of the queueing process are derived. An optimization problem is discussed.