CFP last date
22 April 2024
Reseach Article

Analysis of M^[x]/G/1 Queue with Service Interruption and Extended Server Vacations with Bernoulli Schedule

by G. Ayyappan, K. Sathiya
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 68 - Number 21
Year of Publication: 2013
Authors: G. Ayyappan, K. Sathiya
10.5120/11700-7325

G. Ayyappan, K. Sathiya . Analysis of M^[x]/G/1 Queue with Service Interruption and Extended Server Vacations with Bernoulli Schedule. International Journal of Computer Applications. 68, 21 ( April 2013), 1-7. DOI=10.5120/11700-7325

@article{ 10.5120/11700-7325,
author = { G. Ayyappan, K. Sathiya },
title = { Analysis of M^[x]/G/1 Queue with Service Interruption and Extended Server Vacations with Bernoulli Schedule },
journal = { International Journal of Computer Applications },
issue_date = { April 2013 },
volume = { 68 },
number = { 21 },
month = { April },
year = { 2013 },
issn = { 0975-8887 },
pages = { 1-7 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume68/number21/11700-7325/ },
doi = { 10.5120/11700-7325 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T21:28:28.018827+05:30
%A G. Ayyappan
%A K. Sathiya
%T Analysis of M^[x]/G/1 Queue with Service Interruption and Extended Server Vacations with Bernoulli Schedule
%J International Journal of Computer Applications
%@ 0975-8887
%V 68
%N 21
%P 1-7
%D 2013
%I Foundation of Computer Science (FCS), NY, USA
Abstract

We study a batch arrival queueing system with service interruption and Extended server vacation based on Bernoulli schedule. A single server provides essential service to all arriving customers with service time following general distribution. After every service completion the server has the option to leave for phase one vacation of random length with probability p or to continue staying in the system with probability 1-p. The new assumption in this paper is that the server go on extended vacation, as soon as the completion of phase one vacation, the server undergoes phase two and phase three vacation. On completion of three heterogeneous phase of vacation the server return back to the system. The vacation times are assumed to be general. The server is interrupted at random and the duration of attending interruption follows exponential distribution. Also we assume, the customer whose service is interrupted goes back to the head of the queue where the arrivals are Poisson. Using supplementary variable technique, the Laplace transforms of time dependent probabilities of system state are derived. From this we deduce the steady state results. We also obtain the average queue size and average waiting time.

References
  1. Avi Itzhak, B. and Naor, P. 1963. Some queueing problems with the service station subject to breakdowns, Operations Research , 11, 303 - 319.
  2. Baskar, S. Rajalakshmi Rajagopal and Palaniammal, S. 2011. A Single server M/G/1 queue with service interruption under bernoulli schedule, International Mathematical Forum, 6, 1697 - 1712
  3. Balamani, N. 2012. A single server M/G/1 queue with service interruption and bernoulli schedule server vacation having general vacation time distribution, International Journal of Mathematical Archive, 3(2), 347-353.
  4. Borthakur, A. and Choudhury, G. 1997. On a batch arrival Poisson queue with generalised vacation, Sankhya Ser. B, 59, 369-383.
  5. Doshi, B. 1986. Queueing systems with vacations-a survey, Queueing Systems, 1, 29-66.
  6. Kulkarni, V. G. and Choi, B. D. 1990. Retrial queues with server subject to breakdowns and repairs, Queueing Systems, 7, 191-209.
  7. Madan, K. C. , Abu-Dayyeh, W. Gharaibeh, M. 2003. Steady state analysis of two M[x]=M[a;b]=1 queue models with random breakdowns, International Journal of Information and Management Sciences, 14, 37-51.
  8. 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, 20, 55-70.
  9. Takagi, H. 1991. Queueing Analysis: A Foundation of performance evaluation, Vol. 1: Vacation and priority systems, Part 1, Elsevier Science Publishers, Amsterdam,
  10. Takine, T. and Sengupta, B. 1997. A single server queue with service interruptions, Queueing Systems, 26(3), 285- 300.
  11. Thangaraj, V. and Vanitha, S. 2010. M/G/1 queue with twostage heterogeneous service compulsory server vacation and random breakdowns, Int. J. Contemp. Math. Sciences, 5, 307-322.
  12. Thiruvengadam, K. 1963. Queueing with breakdowns, Operations Research 11, 62-71.
  13. Tian, N. and and Zhang, G. 2006. Vacation queueing models - Theory and Applications, Springer-Verlag, New York.
  14. Tian, N. , Li, Q. and Cao, J. 1999. Conditional stochastic decomposition in M/M/c queue with server vacations, Stochastic Models, 15, 367-377.
  15. Wang, J. , Cao, J. and Li, Q. 2001. Reliability analysis of the retrial queue with server breakdowns and repairs, Queueing Systems, 38, 363-380.
  16. White, H. and Christie, L. 1985. Queueing with preemptive priorities or with breakdowns, Operations Research, 6, 79- 95. 7
Index Terms

Computer Science
Information Sciences

Keywords

Batch arrival Transient state solution Extended vacation time Average queue size Average waiting time