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Reseach Article

A Study on the Performance Analysis of a Batch Arrival Queue with Two Stages of Service, Bernoulli Schedule Vacation, Extended Vacation and Service Interruption

by S. Maragathasundari, B. Balamurugan
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 124 - Number 12
Year of Publication: 2015
Authors: S. Maragathasundari, B. Balamurugan
10.5120/ijca2015905695

S. Maragathasundari, B. Balamurugan . A Study on the Performance Analysis of a Batch Arrival Queue with Two Stages of Service, Bernoulli Schedule Vacation, Extended Vacation and Service Interruption. International Journal of Computer Applications. 124, 12 ( August 2015), 33-37. DOI=10.5120/ijca2015905695

@article{ 10.5120/ijca2015905695,
author = { S. Maragathasundari, B. Balamurugan },
title = { A Study on the Performance Analysis of a Batch Arrival Queue with Two Stages of Service, Bernoulli Schedule Vacation, Extended Vacation and Service Interruption },
journal = { International Journal of Computer Applications },
issue_date = { August 2015 },
volume = { 124 },
number = { 12 },
month = { August },
year = { 2015 },
issn = { 0975-8887 },
pages = { 33-37 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume124/number12/22159-2015905695/ },
doi = { 10.5120/ijca2015905695 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T23:14:15.127605+05:30
%A S. Maragathasundari
%A B. Balamurugan
%T A Study on the Performance Analysis of a Batch Arrival Queue with Two Stages of Service, Bernoulli Schedule Vacation, Extended Vacation and Service Interruption
%J International Journal of Computer Applications
%@ 0975-8887
%V 124
%N 12
%P 33-37
%D 2015
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this paper a M[X]/G /1 Queueing model with two stages of service is studied. Service interruption is considered as a major phenomenon. On completion of a service, the server will go for a vacation .An additional aspect of Optional extended vacation is considered in this model . In this model, repair process start immediately. Service time, Vacation time & Repair time follows general distribution. Steady state solution & Performance measures are derived.

References
  1. Chodhury. G and Madan. K.C (2005), “A two stage batch arrival queueing systems with a modified Bernoulli schedule vacation under N-policy”, Mathematical and computer Modelling, Vol.42, pp.71-85.
  2. K.C Madan (1994), “A queueing system with random failures and delayed repairs”, J. Ind Statist. Assoc, Vol.32, pp.39-48.
  3. B.T Doshi (1986), “Queueing systems with Vacation – a Survey”, Queueing Systems, Vol.1, pp.29-66.
  4. Takagi. H (1990), “Time-dependent analysis of M/G/1 vacation with exhaustive service”, Queueing Systems, Vol.6, pp.369-390.
  5. Chodhury. G and Madan. K.C (2004), “A two phase batch arrival queueing system with a vacation time under Bernoulli schedule”, Applied mathematics and Computation, Vol. 149, pp.337-349.
  6. G. Choudhury, L. Tadj and M. Paul(2007), “Steady state analysis of an M[x]/G/1 queue with two phase service and Bernoulli vacation schedule under multiple vacation policy ”, Applied Mathematical Modeling Vol.31, No.3, pp.1079-1091.
  7. Maraghi. F.A, Madan . K.C and Darby-Dowman. K (2009), “Batch Arrival queueing system with Random Breakdowns and Bernoulli Schedule server vacations having General vacation Time Distribution”, International Journal of Information and Management Sciences, Vol.20, pp.55-70.
  8. Takine . T (2001), “Distributional form of Little’s law for FIFO queues with multiple Markovian arrival streams and its application to queues with vacations”, Queueing Systems, Vol.37, pp.31-63.
  9. Chodhury. G (2002), “Some aspects of M/G/1 queue with two different times under multiple vacation policy”, Stochasic Analysis and applications, Vol.20, No.5, pp.901-909.
  10. Madan .K.C and Abu-Dayyeh .W. & Saleh (2002), “ An M/G/1 queue with second optional service and Bernoulli schedule server vacations”, Systems Science, Vol.28, No.3, pp.51-62.
  11. Madan . K.C, Al-Rawi, Z.R & Al-Nasser, A.D (2005), “On Mx/(G1G2)/1/G(BS)/Vs vacation queue with two types of general heterogeneous service”, Journal of Applied mathematics and Decision sciences, Vol.3, pp.123-135.
  12. Madan .K.C and Chodhury. G (2006), “ Steady state analysis of an M^[x] /(G1G2)/1 queue with restricted admissibility and random set up time, International Journal of Information and Management sciences”,Vol.17, No.2,pp.33-56.
  13. K.C Madan.(2001),“On a single server queue with two stage heterogeneous service and deterministic server vacations”, International journal of system sciences, Vol.32, pp.837-844.
  14. K.C Madan and R.F Anabasi (2001), “A single server queue with two types of service, Bernoulli schedule server vacations and a single vacation policy”, Pakistan journal of statistics, Vol.19, pp331-342.
  15. V. Thangaraj and Vanitha (2010), M]/G/1 queue with Two Stage Heterogeneous service Compulsory server vacation and Random breakdowns”, Int Journal of Contemp .Math. Sciences”, Vol.5, pp.307-322.
  16. Maragathasundari. S and Srinivasan. S (2014a), “A Non-Markovian Multistage Batch arrival queue with breakdown and reneging”, Mathematical problems in engineering, Volume 2014/16 pages/ Article ID .519579/ http: // dx. doi. Org / 10.1155/2014/ 519579.
  17. Maragathasundari. S and Srinivasan. S (2014b), “Analysis of Batch arrival queue with two stages of service and phase vacations”, Missouri Journal of Mathematical Sciences, Vol. FALL 2014, No.2, pp.189-205.
Index Terms

Computer Science
Information Sciences

Keywords

Random breakdown Repair process extended vacation Steady state Queue size distribution.