CFP last date
20 January 2025
Reseach Article

Two Heterogeneous Servers Limited Capacity Markovian Queueing System Subjected to Varying Catastrophic

by Gulab Singh Bura
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 87 - Number 2
Year of Publication: 2014
Authors: Gulab Singh Bura
10.5120/15179-3420

Gulab Singh Bura . Two Heterogeneous Servers Limited Capacity Markovian Queueing System Subjected to Varying Catastrophic. International Journal of Computer Applications. 87, 2 ( February 2014), 11-23. DOI=10.5120/15179-3420

@article{ 10.5120/15179-3420,
author = { Gulab Singh Bura },
title = { Two Heterogeneous Servers Limited Capacity Markovian Queueing System Subjected to Varying Catastrophic },
journal = { International Journal of Computer Applications },
issue_date = { February 2014 },
volume = { 87 },
number = { 2 },
month = { February },
year = { 2014 },
issn = { 0975-8887 },
pages = { 11-23 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume87/number2/15179-3420/ },
doi = { 10.5120/15179-3420 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T22:04:52.464976+05:30
%A Gulab Singh Bura
%T Two Heterogeneous Servers Limited Capacity Markovian Queueing System Subjected to Varying Catastrophic
%J International Journal of Computer Applications
%@ 0975-8887
%V 87
%N 2
%P 11-23
%D 2014
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this paper we consider a limited capacity Markovian queueing system with two heterogeneous servers subjected to varying catastrophic intensity. The transient solution of the model has been obtained and various measures of performance have been computed numerically with the help of simulation technique. The steady state solution of the system has also been provided.

References
  1. Bartoszynski, R. Buhler, W. J. , Chan, W. , and Pearl, D. K. (1989), Population processes under the influence of disasters occurring independently of population size, J. Math. Bio. Vol, 27, 179-190.
  2. Brockwell, P. J. , Gani, J. M. and Resnick, S. I. (1982), Birth immigration and catastrophe processes, Adv. Applied Probability, Vol. 14, 709-731.
  3. Brockwell, P. J. (1985), The extinction time of a birth, death and catastrophe process and of a related diffusion model, Advances in Applied Probability,Vol. 17, 42-52.
  4. Chao, X. (1995), A queueing network model with catastrophes and product form solution, Operations Research Letters, Vol. 18, 75-79.
  5. Chao, X. and Zheng, Y. (2003), Transient analysis of immigration birth- death processes with total catastrophes, Prob. Enggn. and Inform. Sciences, Vol. 17, 83-106.
  6. Crescenzo, A. Di, Giorno, V. , Nobile, A. G. and Ricciardi, L. M. (2003), On the M/M/1 queue with catastrophes and its continuous approximation, Queueing Systems,Vol. 43, 329-347.
  7. Economou, A. (2004), The compound Poisson immigration process subject to binomial catastrophes, J. Applied Probability, Vol. 41, No. 2, 508-523.
  8. Gripenberg, G. (1983), A Stationary distribution for the growth of a population subject to random catastrophes, Journal of Mathematical Biology, Vol. 17, 371-379.
  9. Gumbel, H. (1960), Waiting lines with heterogeneous servers, Operations Research, 8, 504-511.
  10. Jain, N. K. and Kanethia, D. K. (2006), Transient analysis of a queue with environmental and Catastrophic effects, International Journal of Information and Management Sciences, Vol. 17, No. 1. 35-45.
  11. Jain, N. K. and Bura Gulab Singh, (2010), A queue with varying catastrophic intensity, International journal of computational and applied mathematics, Vol. 5, 41-46.
  12. Jain, N. K. and Bura Gulab Singh, (2012), two homogeneous servers limited capacity Markovian queueing system subjected to varying catastrophic intensity, International journal of computer applications, Vol. 49, No. 2, 31-41.
  13. Kitamura, K. , Tokunaga, M. , Hikkikoshi, I. A. and Yanagida, T. (1999), A single myosin head moves along an actin filament with regular steps of 5. 3 nanometers, Nature, Vol. 397, 129-134.
  14. Kumar, B. K. and Arivudainambi, D. (2000), Transient solution of an M/M/1 queue with catastrophes, Comp. and Mathematics with Applications, Vol. 40, 1233-1240.
  15. Kumar, B. K. and Madheswari, Pavai S. , (2002), Transient behavior of the M/M/2 queue with catastrophes, Statistica, Vol. 27, 129-136.
  16. Kumar, B. K. , Madheswari, Pavai S. and Venkatakrishnan, K. S. , (2007), Transient solution of an M/M/2 queue with heterogeneous servers subject to catastrophes, International Journal of Information and Management Sciences, Vol. 18, 63-80.
  17. Kyriakidis, E. G. (1994), Stationary probabilities for a simple immigration-birth-death process under the influence of total catastrophes, Stat. and Prob. Letters, Vol. 20, 239-240.
  18. Kyriakidis, E. G. (2001), the transient probabilities of the simple immigration- catastrophe process, Math. Scientist, Vol. 26, 56--58.
  19. Law, M. and Kelton, W. D. , (2003), Simulation modeling and analysis, 3rd edition, McGraw Hill Book Company, New York.
  20. Liu, W. and Kumar, P. , (1984), Optimal control of a queueing system with two heterogeneous servers, IEEE transactions on automatic control, Vol. 29, 696-703.
  21. Miyazaki, Y. and Sibata, S. Mori, (1992), Transient behavior of the M/M/2/ /FIFO queue with starting customers, Journal of information and optimization sciences, Vol. 13, 1-27.
  22. Narsingh Deo, (2007), System simulation with digital computer, Prentice hall of India Privat Ltd.
  23. Rubinovitch, M. ,(1985), The slow server problem, Journal of applied probability, Vol. 22, 205-213.
  24. Saaty, T. L. (1960), Time dependent solution of the many server Poisson queue, Operations Research, Vol. 8, 755-772.
  25. Singh, V. P. ,(1970), Two servers Markovian queues with balking: Heterogeneous vs. homogeneous servers, Operations Research, Vol. 19, 145-159.
Index Terms

Computer Science
Information Sciences

Keywords

Transient Solution Varying Catastrophic Intensity Simulation Markovian Queueing System Steady State Solution