Unreliable M^X/(G1,G2)/1 Retrial Queue with Bernoulli Feedback Under Modified Vacation Policy

10.6186/IJIMS.2012.23.4.6

Madhu Jain；G. C. Sharma；Richa Sharma

Retrial queue ； bulk arrival ； balking ； modified vacation ； unreliable server

International Journal of Information and Management Sciences

23:4（2012 / 12 / 01）

425 - 448

英文

In this paper, a batch arrival retrial queueing system with Bernoulli feedback and balking under modified vacation policy is considered wherein the server provides two phases of essential service to all arriving customers. In addition, the server may breakdown during the busy state at any time. After the completion of two phases of heterogeneous service, the server may go for 'j^th' (1 ≤ j ≤ J) vacation on finding the orbit empty until at least one customer is accumulated in the system. The inter-retrial times, service times, repair times and vacation times are assumed to be governed by the general distribution. By introducing the supplementary variables and using generating function, the expressions for the expected number of the customers in the orbit as well as in the system are derived. Finally, the numerical results are provided.

1. Almási, B.,Roszik, J.,Sztrik, J.(2005).Homogeneous finite-source retrial queues with server subject to breakdowns and repairs.Mathematical and Computer Modelling,42,673-682.
2. Artalejo, J. R.(1997).Analysis of an M/G/1 queue with constant repeated attempts and server vacations.Computers and Operations Research,24,493-504.
3. Artalejo, J. R.,Lopez-Herrero, M. J.(2000).On the single server retrial queue with balking.INFOR,38,33-50.
4. Atencia, I.,Fortes, I.,Sánchez, S.(2009).A discrete-time retrial queueing systems with starting failures, Bernoulli feedback and general retrial times.Computers and Industrial Engineering,57,1291-1299.
5. Choudhury, G.(2005).Some aspects of an Mx/G/1 queue with two different vacation periods under multiple vacation policy.Soochow Journal of Mathematics,31,21-29.
6. Choudhury, G.(2009).An M/G/1 retrial queue with an additional phase of second service and general retrial times.International Journal of Information and Management Sciences,20,1-14.
7. Choudhury, G.(2007).A two phase batch arrival retrial queueing system with Bernoulli vacation schedule.Applied Mathematics and Computation,188,1455-1466.
8. Choudhury, G.,Madan, K. C.(2005).A two-stage batch arrival retrial queueing system with a modified bernoulli schedule vacation under N-policy.Mathematical and Computer Modelling,42,71-85.
9. Choudhury, G.,Tadj, L.(2011).The optimal control of an Mx/G/1 unreliable server queue with two phases of service and Bernoulli vacation schedule.Mathematical and Computer Modelling,54,673-688.
10. Choudhury, G.,Tadj, L.,Deka, K.(2010).A batch arrival retrial queue with two phases of service and service interruption.Computers and Mathematics with Applications,59,437-450.
11. Cox, D. R.(1955).The analysis of non-Markovian stochastic processes by the inclusion of supple-mentary variables.Proc. Cambridge Philoso. Soc.,51,433-441.
12. Economou, A.,Kapodistria, S.(2010).Synchronized abandonments in a single server unreliable queue.European Journal of Operational Research,203,143-155.
13. Fuhrmann, S. W.,Cooper, R. B.(1985).Stochastic decompositions in an M/G/1 queue with generalized vacations.Operations Research,33,1117-1129.
14. Gommes Corral, A.(1999).Stochastic analysis of a single server retrial queue with general retrial times.Naval Research Logistic,46,561-581.
15. Ke, J. C.(2007).Operating characteristic analysis on the M[x]/G/1 system with a variant vacation policy and balking.Applied Mathematical Modelling,31,1321-1337.
16. Ke, J. C.,Chang, F. M.(2009).Modified vacation policy for M/G/1 retrial queue with balking and feedback.Computers and Industrial Engineering,57,433-443.
17. Ke, J. C.,Huang, H. I.,Chu, Y. K.(2010).Batch arrival queue with N-policy and at most J vacations.Applied Mathematical Modelling,34,451-466.
18. Kim, J.,Kim, B.,Kim, J.(2010).Moments of the queue size distribution in the MAP/G/1 retrial queue.Computers and Operations Research,37,1212-1219.
19. Kumar, K. B.,Arivudainambi, D.(2002).An M/G/1 retrial queue with Bernoulli schedule and general retrial times.Computers and Mathematics with Applications,43,15-30.
20. Kumar, K. B.,Arivudainambi, D.,Vijayakumar, A.(2002).On the Mx/G/1 retrial queue with Bernoulli schedules and general retrial times.Asia Pacific Journal of Operations Research,19,177-194.
21. Kumar, K. B.,Madheshwari, P. S.,Vijayakumar, A.(2002).The M/G/1 retrial queue with feedback and starting failures.Applied Mathematical Modelling,26,1057-1075.
22. Liu, Z.,Wu, J.,Yang, G.(2009).An M/G/1 retrial G-queue with preemptive resume and feedback under N-policy subject to the server breakdowns and repairs.Computers and Mathematics with Applications,58,1792-1807.
23. Madan, K. C.,Al-Rawwash, M.(2005).On the Mx/G/1 queue with feedback and optional server vacations based on a single vacation policy.Applied Mathematics and Computation,160,909-919.
24. Maraghi, F. A.,Madan, K. C.,Dowman, K. D.(2009).Batch arrival queueing system with random breakdowns and Bernoulli schedule sever vacations having general vacation time distribution.International Journal of Information and Management Sciences,20,55-70.
25. Takagi, H.(1991).A Foundation of Performance Evaluation, Vol.I, Vacation and Priority Systems.North-Holland:Amsterdam.
26. Thangaraj, V.,Vanitha, S.(2010).A single server M/G/1 feedback queue with two types of service having general distribution.International Mathematical Forum,5,15-33.
27. Wang, J.(2004).An M/G/1 queue with second optional service and server breakdowns.Computers and Mathematics with Applications,47,1713-1723.
28. Wu, J.,Liu, Z.,Yang, G.(2011).Analysis of the finite source MAP/PH/N retrial G-queues operating in a random environment.Applied Mathematical Modelling,35,1184-1193.
29. Zadeh, A. B.,Shahkar(2008).G. H., A two phases queue system with Bernoulli feedback and Bernoulli schedule server vacation.Information Management Science,19,329-338.