Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-19T16:44:47.582Z Has data issue: false hasContentIssue false

An M/G/l queueing system with fixed feedback policy

Published online by Cambridge University Press:  17 February 2009

Bong Dae Choi
Affiliation:
Department of Mathematics and Telecommunication Mathematics Research Center, Korea University, 1, Anam-dong, Sungbuk-ku, Seoul, 136-701, Korea; e-mail: [email protected].
Bara Kim
Affiliation:
School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta GA 30332-0205, USA; e-mail: [email protected].
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We consider a single server queueing system where each customer visits the queue a fixed number of times before departure. A customer on his j th visit to the queue is defined to be a class-j -customer. We obtain the joint probability generating function for the number of class-j-customers and also obtain the Laplace-Stieltjes transform for the total response time of a customer.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Adve, V. S. and Nelson, R., “The relationship between Bernoulli and fixed feedback policies for the M/G/l queue”, Oper. Res. 42 (1994) 380385.CrossRefGoogle Scholar
[2]Baskett, F., Chandy, K. M., Muntz, R. R. and Palacios, F. G., “Open, closed and mixed networks of queues with different classes of customers”, J. ACM 22 (1975) 248260.CrossRefGoogle Scholar
[3]Boxma, O. J. and Yechiali, U., “An M/G/l queue with multiple types of feedback and gated vacations”, J. Appl. Prob. 34 (1997) 773784.CrossRefGoogle Scholar
[4]Choi, B. D., Choi, S. H., Park, C. G. and Sung, D. K., “Analysis of a leaky bucket control scheme in the signaling system no. 7 network”, IEE Proceeding Communications 145 (1998) 2532.CrossRefGoogle Scholar
[5]Choi, B. D., Kim, B. and Choi, S. H., “An M/G/l queue with multiple types of feedback, gated vacations and FCFS policy”, Comput. Open Res. 44 (22) (2002) to appear.Google Scholar
[6]Choi, B. D., Kim, B. and Choi, S. H., “On the M/G/l Bernoulli feedback queue with multi-class customers”, Comput. Oper. Res. 27 (3) (2000) 269286.CrossRefGoogle Scholar
[7]Choi, B. D. and Kulkarni, V. G., “Feedback retrial queueing system”, in Queueing and related models, (Oxford Univ. Press, New York, 1992) 93105.Google Scholar
[8]Rege, K., “On the M/G/l queue with Bernoulli feedback”, Oper. Res. Lett. 14 (1993) 163170.Google Scholar
[9]Simon, B., “Priority queues with feedback”, J. ACM 31 (1984) 134149.Google Scholar
[10]Takacs, L., “A single-server queue with feedback”, Bell System Technical J. 42 (1963) 509519.CrossRefGoogle Scholar
[11]Takagi, H. (ed.), Queueing Analysis: A Foundation of Performance Evaluation, Vol. 1, Vacation and Priority Systems, Part I (Elsevier Science Publishers, North-Holland, Amsterdam, 1991).Google Scholar
[12]Willmann, G. and Kühn, P. J., “Performance modeling of signaling no. 7”, IEEE Communications Magazine 28 (1990) 4456.CrossRefGoogle Scholar
[13]Wortman, M. A. and Disney, R., “The M/GI/l Bernoulli feedback queue with vacations”, Queueing Systems Theory Appl. 9 (1991) 353364.CrossRefGoogle Scholar