M/G/1/N vacation model with varying E-limited service discipline

Abstract

We define and analyze an M/G/1/N vacation model that uses a service discipline that we call the E-limited with limit variation discipline. According to this discipline, the server provides service until either the system is emptied (i.e. exhausted) or a randomly chosen limit of l customers has been served. The server then goes on a vacation before returning to service the queue again. The queue length distribution and the Laplace-Stieltjes transforms of the waiting time, busy period and cycle time distributions are found. Further, an expression for the mean waiting time is developed. Several previously analyzed service disciplines, including Bernoulli scheduling, nonexhaustive service and limited service, are special cases of the general varying limit discipline that is analyzed in this paper. © 1992 J.C. Baltzer AG, Scientific Publishing Company.