Consider a GI M 1 queue with set up period and working vacations. During the working vacation period, customers can be served at a lower rate, if there are customers at a service completion instant, the vacation can be interrupted and the server will come back to a set up period with probability or continue the working vacation with probability , and when the set up period ends, the server will switch to the normal working level. Using the matrix analytic method, we obtain the steady state distributions for the queue length at arrival epochs. Li Tao "The Queue Length of a GI/M/1 Queue with Set-Up Period and Bernoulli Working Vacation Interruption" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-5 , August 2021, URL: https://www.ijtsrd.com/papers/ijtsrd43743.pdf Paper URL: https://www.ijtsrd.com/mathemetics/other/43743/the-queue-length-of-a-gim1-queue-with-setup-period-and-bernoulli-working-vacation-interruption/li-tao
International Journal of Trend in Scientific Research and Development (IJTSRD)
Volume 5 Issue 5, July-August 2021 Available Online: www.ijtsrd.com e-ISSN: 2456 – 6470
@ IJTSRD | Unique Paper ID – IJTSRD43743 | Volume – 5 | Issue – 5 | Jul-Aug 2021
Page 72
The Queue Length of a GI/M/1 Queue with Set-Up
Period and Bernoulli Working Vacation Interruption
Li Tao
School of Mathematics and Statistics, Shandong University of Technology, Zibo, China
ABSTRACT
Consider a GI/M/1 queue with set-up period and working vacations.
During the working vacation period, customers can be served at a
lower rate, if there are customers at a service completion instant, the
vacation can be interrupted and the server will come back to a set-up
period with probability
(0
1)
p
p
≤ ≤ or continue the working vacation
with probability1 p
−
, and when the set-up period ends, the server will
switch to the normal working level. Using the matrix analytic
method, we obtain the steady-state distributions for the queue length
at arrival epochs.
KEYWORDS: GI/M/1; set-up period; working vacation; vacation
interruption; Bernoulli
How to cite this paper: Li Tao "The
Queue Length of a GI/M/1 Queue with
Set-Up Period and Bernoulli Working
Vacation
Interruption"
Published
in
International Journal
of
Trend
in
Scientific Research
and Development
(ijtsrd), ISSN: 2456-
6470, Volume-5 | Issue-5, August 2021,
pp.72-76,
URL:
www.ijtsrd.com/papers/ijtsrd43743.pdf
Copyright © 2021 by author (s) and
International Journal of Trend in
Scientific Research and Development
Journal. This is an
Open Access article
distributed under the
terms of
the Creative Commons
Attribution License (CC BY 4.0)
(http://creativecommons.org/licenses/by/4.0)
1. INTRODUCTION
Servi and Finn [1] first introduced the working
vacation models and studied an M/M/1 queue, the
server commits a lower service rate rather than
completely stopping the service during a vacation.
Baba [2] considere