Performance Analysis of a Single Server Retrial Queueing System with Bernoulli and Phase Type Vacations

International Journal of Computer Applications
© 2012 by IJCA Journal
Volume 54 - Number 7
Year of Publication: 2012
J. Ebenesar Anna Bagyam
K. Udaya Chandrika

Ebenesar Anna J Bagyam and Udaya K Chandrika. Article: Performance Analysis of a Single Server Retrial Queueing System with Bernoulli and Phase Type Vacations. International Journal of Computer Applications 54(7):30-35, September 2012. Full text available. BibTeX

	author = {J. Ebenesar Anna Bagyam and K. Udaya Chandrika},
	title = {Article: Performance Analysis of a Single Server Retrial Queueing System with Bernoulli and Phase Type Vacations},
	journal = {International Journal of Computer Applications},
	year = {2012},
	volume = {54},
	number = {7},
	pages = {30-35},
	month = {September},
	note = {Full text available}


This paper analyses the steady state behavior of an M/G/1 retrial queueing system with Bernoulli and phase type vacations. Customers arrive one by one at the system in a Poisson stream. At the arrival epoch, if the server is busy then the arriving customer joins the orbit. If the server is free, then the arriving customer starts its service immediately. The service time of a customer is assumed to be general. At each service completion epoch, the server may opt to take a phase 1 vacation with probability p or else with probability 1- p stay in the system for the next service. After the completion of phase 1 vacation the server may take phase 2 vacation with probability q or return back to the system with probability 1-q. The vacation times are assumed to be general. The service times and vacation times are independent of each other. Generating function technique is applied to obtain the system size and orbit size. Numerical examples are provided to illustrate the sensitivity of the performance measures for changes in the parametric of the system.


  • Amar Aissani. 2011. An Mx/G/1 Energetic Retrial Queue with Vacations and Control. IMA Journal of Management Mathematics. 22:13-32.
  • Arivudainambi, D. and Godhandaraman, P. 2012. A Batch Arrival Retrial Queue with Two Phase of Service, Feedback and K Optional Vacations. Applied Mathematical Sciences. 6; 22;1071-1087.
  • Badamchi Zadeh, A. 2012. A Batch Arrival Queue System with Coxian -2 Server Vacations and Admissibility Restricted. American Journal of Industrial and Business Management. 2;47-54.
  • Choudhury, G. and Jau- ChuanKe. 2012. A batch Arrival Retrial Queue with General Retrial Times Under Bernoulli Vacation Schedule for Unreliable Server and Delaying Repair. Applied Mathematical Modelling. 36;255-269.
  • Ebenesar Anna Bagyam, J. and Udaya Chandrika, K. 2010. Single server Retrial Queueing System with Two Different Vacation Policies. International Journal of Contemporary Mathematical Sciences. 5; ;32;1591-1598.
  • Jehad Al-Jararha and Madan K. 2002. Steady State Analysis of an M/D/1 Queue with Coxian–2 Server Vacations and a Single Vacation Policy. Information and Management Sciences. 13;4; 69-81.
  • Jia, S. , Chen,Y. and Liu, J. 2011. Steady State Analysis of Bernoulli Feedback on Geom X/g/1 Queue with Multiple Vacation and Setup Times. International Journal of Applied Physics and Mathematics. 1;1.
  • Maragatha Sundari, S. and Srinivasan, S. 2012. Analysis of Transient Behaviour of M/G/1 Queue with Single Vacation. International Journal of Pure and Applied Mathematics. 76;1;149-156.
  • Muthu Ganapathi, Ayyappan, and Gopal Sekar. 2011. Study of Multi Server retrial Queueing System Under Vacation Policies By Direct Truncation Method. QTNA. 23-26.
  • Purohit, G. N. , Madhu Jain and Shinu Rani. 2012. M/M/1 Retrial Queue with Constant Retrial Policy, Unreliable Sever, Threshold based Recovery and State dependent Arrival Rates. Applied Mathematical Sciences. 6;37;1837 – 1846.
  • Tuan PhungDuc and Kenichi Kawanishi. 2011. Multi Server Retrial Queue with After Call Work. Numerical Algebra, Control and Optimization. 1;4; 639-656.
  • Wang, W. and Xu, X. 2011. Performance Analysis of GI/Geom/1 with Single Working Vacation and Setup Times. Journal of Information and Computational Science. 8;14; 3083, 3090.