Mathematical Problems in Engineering 
Volume 3 (1997), Issue 3, Pages 243-253
doi:10.1155/S1024123X97000550

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

Abstract

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.