Journal of Applied Science and Engineering

Published by Tamkang University Press


Impact Factor



M. Senthil Kumar This email address is being protected from spambots. You need JavaScript enabled to view it.1 and R. Arumuganathan1

1Department of Mathematics & Computer Applications, PSG College of Technology, Coimbatore, 641 004, India


Received: October 3, 2008
Accepted: September 7, 2009
Publication Date: June 1, 2010

Download Citation: ||  


This paper analyses the steady state behaviour of an M/G/1 retrial queue with impatient subscribers, two phases of essential service, general retrial time and general vacation time.  If the primary call, on arrival finds the server busy, becomes impatient and leaves the system with probability (1-) and with probability, it enters into an orbit.  The server provides preliminary first essential service (FES) and second essential service (SES) to the primary arriving calls or calls from the retrial group.  As soon as the SES of a call is completed, the server may terminate call connection (vacation of random length of time) with probability ‘p’(0< p < 1) or may remain in the system to serve the next call, if any, with probability ‘q’ (=1-p).  The steady state queue size distribution of number of customers in retrial group, expected number of customers in retrial group and expected waiting time of the customers in the orbit are obtained.  The application of the proposed model is also discussed to analyze a communication protocol with the numerical illustration.

Keywords: Retrial Queues, Steady State Distribution, Essential Service, Vacation Time, Impatient Subscribers, SMTP Protocol


  1. [1]Falin, G.I. and Templeton, J.G.C. (1997) Retrial Queues. Chapman and Hall, London.
  2. [2]J.R. (1999). Accessible bibliography on retrial queues. Mathematical and Computer Modeling, 30, 1-6.
  3. [3]Artalejo J.R. (1999). A classified bibliography of research on retrial queues: progress in 1990 – 1999, Top 7, 187 – 211
  4. [4]Choi B.D. and Park. K.K.(1990), The M/G/1 retrial queue with Bernoulli schedule, Queueing Systems 7, 219 – 227
  5. [5]Choi B.D., Choi K.B. and Lee Y.W. (1995), M/G/1 retrial queueing system with two types of calls and finite capacity, Queueing Systems, 19,215 – 229.
  6. [6]Choi B.D. and Chang. Y. (1999), Single server retrial queues with priority calls. Mathematical and Computer Modeling. 30, 7 – 32.
  7. [7]Lopez – Herrero. M.J. (2002). Distribution of number of customers served in an M/G/1 retrial queue. Journal of Applied Probability, 39, 2, 407 – 413.
  8. [8]B., Pavai Madheswari. S. and Vijayakumar, A. (2002). The M/G/1 retrial queue with feedback and starting failures, Applied Mathematical Modeling.  Vol. 26, 11,  1057 – 1076.
  9. [9]Choudhury, G. and Kandarpa Deka (2008). An M/G/1 retrial queue with two phases of service subject to the server breakdowns and repair. Performance Evaluation, 65, 10,714 – 724
  10. [10]Senthil Kumar M and Arumuganathan R (2008). On the single server Batch Arrival Retrial Queue with General vacation Time under Bernoulli schedule and two phases of Heterogeneous service, Quality Technology and Quantitative Management, 5, No.2, 145 – 160.
  11. [11]Madan, K. C. (2000). An M/G/1 queue with second optional service.  Queueing systems, 34, 37 – 46.
  12. [12]Medhi, J. (2002). A single server Poisson input queue with a second optional channel. Queueing systems, 42, 239 – 242.
  13. [13]Choudhury, G. (2003). Some aspects of an M/ G /1 queueing system with optional second service.  Top, 11, 141 – 150.
  14. [14]B., Vijayakumar, A. and Arivudainambi, D. (2002). An M/G/1 retrial queueing system with two – phase service and preemptive resume. Annals of Operations Research, 113, 61 – 79.
  15. [15]Artalejo J.R. (2004). Steady state analysis of an M/G/1 queue with repeated attempts and two phase service. Quality Technology and Quantitative Management, Vol.1, No. 2, 189 – 199.
  16. [16]Cohen, J.W.(1957). Basis problems for telephone traffic theory and the influence of repeated calls. Philips Telecommunication Review 18(2):49–100.
  17. [17]Yang, T., M.J.M. Posner and J.G.C.Templeton. (1990). The M/G/1 retrial queue with non-persistent customers.  Queueing Systems 7 (2): 209 – 218.
  18. [18]Krishnamoorthy A., Deepak. T.G. and Joshua V.C. (2005). An M/G/1 Retrial queue with Non- persistent Customers and Orbital search.  Stochastic Analysis and Applications, 23, 975- 997.