Hostname: page-component-89b8bd64d-z2ts4 Total loading time: 0 Render date: 2026-05-06T12:43:53.974Z Has data issue: false hasContentIssue false
  • English
  • Français

OPTIMAL BERNOULLI ROUTING IN AN UNRELIABLE M/G/1 RETRIAL QUEUE

Published online by Cambridge University Press:  02 November 2010

Nathan P. Sherman  and
Jeffrey P. Kharoufeh
Nathan P. Sherman
Affiliation:
Directorate of Force Management Policy, U.S. Air Force Headquarters, Manpower and Personnel, Washington, DC 20330-1040 E-mail: nathan.sherman@us.af.mil
Jeffrey P. Kharoufeh
Affiliation:
Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, PA 15261 E-mail: jkharouf@pitt.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Recently, Sherman et al. [14] analyzed an M/G/1 retrial queuing model in which customers are forced to retry their service if interrupted by a server failure. Using classical techniques, they provided a stability analysis, queue length distributions, key performance parameters, and stochastic decomposition results. We analyze the system under a static Bernoulli routing policy that routes a proportion of arriving customers directly to the orbit when the server is busy or failed. In addition to providing the key performance parameters, we show that this system exhibits a dual stability structure, and we characterize the optimal Bernoulli routing policy that minimizes the total expected holding costs per unit time.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 25 , Issue 1 , January 2011 , pp. 1 - 20
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1.Aissani, A. & Artalejo, J.R. (1998). On the single server retrial queue subject to breakdowns. Queuing Systems 30(3–4): 309–321.CrossRefGoogle Scholar
2.Artalejo, J.R. & Gómez-Corral, A. (2008). Retrial queuing systems: A computational approach. Berlin: Springer-Verlag.CrossRefGoogle Scholar
3.Atencia, I. & Moreno, P. (2005). A single-server retrial queue with general retrial times and Bernoulli schedule. Applied Mathematics and Computation 162(2): 855–880.CrossRefGoogle Scholar
4.Casetti, C., Cigno, R.L., & Mellia, M. (2000). Load-balancing solutions for static routing schemes in ATM networks. Computer Networks 34: 169–180.CrossRefGoogle Scholar
5.Chang, C.-S., Chao, X., & Pinedo, M. (1990). A note on queues with Bernoulli routing. In Proceedings of the 29th Conference on Decision and Control, Honolulu, pp. 897–902.CrossRefGoogle Scholar
6.Choi, B.D. & Park, K.K. (1990). The M/G/1 retrial queue with Bernoulli schedule. Queuing Systems 7(2): 219–228.CrossRefGoogle Scholar
7.Combé, M.B. & Boxma, O.J. (1994). Optimization of static traffic allocation policies. Theoretical Computer Science 125(1): 17–43.CrossRefGoogle Scholar
8.Falin, G.I. & Templeton, J.G.C. (1997). Retrial queues. London: Chapman & Hall.CrossRefGoogle Scholar
9.Falin, G.I. (2008). The M/M/1 retrial queue with retrials due to failures. Queuing Systems 58: 155–160.CrossRefGoogle Scholar
10.Koole, G. (1996).On the pathwise optimal Bernoulli routing policy for homogeneous parallel servers. Mathematics of Operations Research 21(2): 469–476.CrossRefGoogle Scholar
11.Liang, H.M. & Kulkarni, V.G. (1999). Optimal routing control in retrial queues. In Shanthi-kumar, J.G. & Sumita, U. (eds.). Applied probability and stochastic processes. Dordrecht: Kluwer Academic Publishers, pp. 203–218.CrossRefGoogle Scholar
12.Servi, L. & Humair, S. (1999). Optimizing Bernoulli routing policies for balancing loads on call centers and minimizing transmission costs. Journal of Optimization Theory and Applications 100(3): 623–659.CrossRefGoogle Scholar
13.Sherman, N.P. & Kharoufeh, J.P. (2006). An M/M/1 retrial queue with unreliable server. Operations Research Letters 34(6): 697–705.CrossRefGoogle Scholar
14.Sherman, N.P., Kharoufeh, J.P., & Abramson, M. (2009). An M/G/1 retrial queue with unreliable server for streaming multimedia applications. Probability in the Engineering and Informational Sciences 23(2): 281–304.CrossRefGoogle Scholar