Queueing Systems

, Volume 6, Issue 1, pp 369–389

Time-dependent analysis of M/G/1 vacation models with exhaustive service

  • Hideaki Takagi
Short Communication

DOI: 10.1007/BF02411484

Cite this article as:
Takagi, H. Queueing Syst (1990) 6: 369. doi:10.1007/BF02411484

Abstract

We analyze the time-dependent process in severalM/G/1 vacation models, and explicitly obtain the Laplace transform (with respect to an arbitrary point in time) of the joint distribution of server state, queue size, and elapsed time in that state. Exhaustive-serviceM/G/1 systems with multiple vacations, single vacations, an exceptional service time for the first customer in each busy period, and a combination ofN-policy and setup times are considered. The decomposition property in the steady-state joint distribution of the queue size and the remaining service time is demonstrated.

Keywords

Time-dependent queuesvacation modelsexhaustive servicemultiple vacationssingle vacationssetup timesN-policy

Copyright information

© J.C. Baltzer A.G. Scientific Publishing Company 1990

Authors and Affiliations

  • Hideaki Takagi
    • 1
  1. 1.IBM Research, Tokyo Research LaboratoryTokyoJapan