Asia Mathematika

An International Journal. ISSN: 2457-0834 (online)

Volume 1, Issue 2, December 2017, pp 22-48

A Comparative Study of Various Vacation Policies in an M/G/1 Retrial Queue with Customer Balking

S. Pavai Madheswari, P. Suganthi

Department of Mathematics, R. M. K. Engineering College, Tamil Nadu- 601206, India


It is very important in many real life systems to decide when the server should go for a vacation and what type of vacation policy to be adopted for a better performance of the system. In this paper, an M/G/1 retrial queue, where the customer being informed of the system state is permitted to balk, is considered. This system is studied under various vacation polices such as single vacation with exhaustive service, 1¬-limited service, Bernoulli Scheme and modified Bernoulli Scheme. The system under multiple Bernoulli vacation policy is also discussed. The performance measures P_0, the probability of the system being empty, P_EO, the probability of the orbit being empty, L_s, the mean number of customers in the system and server utilization are found and some interesting results are derived. Stochastic decomposition law is established when there is no balking permitted. Extensive numerical analysis has been carried out to exhibit the effect of the system parameters and compared for the various vacation schedules on the performance measures.


M/G/1 Queue; Retrial; Balking; Bernoulli Vacation; Modified Bernoulli Vacation; Multiple Vacation; Supplementary Variables.



1. Artalejo, T.R., Analysis of an M/G/1 queue with constant repeated attempts and server vacations, Computers and Operations Research, 24, (1997), 493-504.

2. Artalejo, T.R. and Lopez Herrero, M.J., on the single server retrial queue with balking, IN FOR, 38, (2000), 33-50.

3. Artalejo, J.R., Accessible bibliography on retrial queue, Mathematical and Computer Modeling, 30, (1999), 1-6.

4. Choudhury, G. and Ke, J.C., An un retrial queue with delaying repair and general retrial times under Bernoulli vacation schedule, Applied Mathematics and Computation, 230, (2014), 436-450.

5. Choudhury, G., An M/G/1 retrial queue with an additional phase of second service and general retrial time, Int. J. Inform. Manage. Sci., 20, (2009), 1-14.

6. Choi, B.D., Rhee, K.H. and Park, K.K., The M/G/1 retrial queue with retrial rate control policy, Prob. In the Engg. and Info. Sci., 7, (1993), 26-46.

7. Doshi, B.T., Queueing systems with vacations ¬A survey, Queueing systems, 1, (1986), 29-66.

8. Foyolle, G., A simple telephone exchange with delayed feedback, In: Boxma, O.J., Cohen, J.W. and Tijms, H.C., (eds.), Teletrafic Analysis and Computer Performance Evaluation, Elsevier Science, Amsterdam, (1986).

9. Falin, G.I., A survey of retrial queues, Queueing systems, 7, (1990), 127-168.

10. Falin, G.I. and Templeton, J.G.C., Retrial Queues, Chapman and Hall, London, (1997).

11. Gomez-Corral, A., Stochastic analysis of a single server retrial queue with general retrial times, Naval Research Logistics, 46, (1999), 561-581.

12. Haight, F.A., Queueing and Balking, Bio metrika, 44, (1957), 360-369.

13. Krishna Kumar, B., Pavai Madheswari, S. and Vijayakumar, A., the M/G/1 retrial queue with feedback and starting failure, Applied Mathematical modeling, 26, (2002), 1057-1075.

14. Krishna Kumar, B., Vijayakumar, A. and Arivudainambi, D., A M/G/1 retrial queueing system with two ¬phase service and preemptive resume, Annals of operations Research, 113, (2002, 2002a), 61-79.

15. Ke, J.C. and Chang, F.M., Modified vacation policy for M/G/1 retrial queue with balking and feedback, Computer and Industrial Engineering, 57, (2009), 433-443.

16. Ke, J.C., Operating characteristic analysis on the MX/G/1 system with a variant vacation policy and balking, Applied Mathematical modeling, 31, (2007), 1321-1337.

17. Keilson, J., and Servi, L.D., Oscillating random walk models for M/G/1 vacation systems with Bernoulli schedules, Journal of Applied probability, 23, (1986), 790-802.

18. Madan, K.C., Balking phenomenon in the MX/G/1 vacation queue, J. Korea statist soc, 31, (2002), 491-507.

19. Shawky, A.I., The single server machine interference model with balking, reneging and an additional server for longer queues, Microelectronics Reliability, 37, (1997), 355-357.

20. Takagi, H., Vacation and priority systems, Part 1. Queueing analysis: A foundation of performance evaluation (Vol.1). Amsterdam: North Holland, (1991).

21. Wang, K.H. and Ke, J.C., Probabilistic analysis of a repairable system with warm stand by plus balking and reneging, Appl. Math. Model, 27, (2003), 327-336.

22. Wang, J. and Li, J., A repairable M/G/1 retrial queue with Bernoulli vacation and two ¬phase service, Quality Technology and Quantitative Management, 5, (2008), 179-192.

23. Yang, T. and Templeton, J.G.C., A survey on retrial queue, Queueing systems, 2, (1987), 201-233.

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