Mathematical Problems in Engineering
Volume 3 (1997), Issue 3, Pages 243-253

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

Alexander V. Babitsky

Department of Applied Mathematics, Belarusian State University, Minsk, Belarus

Received 1 April 1994; Revised 1 February 1996

Copyright © 1997 Alexander V. Babitsky. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.