Skip to main content Accessibility help
×
Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-26T04:38:44.426Z Has data issue: false hasContentIssue false

11 - Continuous-Time Markov Chain: Queuing Systems

from Part III - State-Space Models with Exponential Distributions

Published online by Cambridge University Press:  30 August 2017

Kishor S. Trivedi
Affiliation:
Duke University, North Carolina
Andrea Bobbio
Affiliation:
Università degli Studi del Piemonte Orientale, Italy
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Reliability and Availability Engineering
Modeling, Analysis, and Applications
, pp. 423 - 452
Publisher: Cambridge University Press
Print publication year: 2017

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.)

References

[1] L., Kleinrock, Queuing Systems, Volume 1: Theory. Wiley Interscience, 1975.
[2] G., Bolch, S., Greiner, H. de, Meer, and K. S., Trivedi, Queueing Networks and Markov Chains: Modeling and Performance Evaluation with Computer Science Applications, 2nd edn. Wiley Interscience, 2006.
[3] L., Lakatos, L., Szeid, and M., Telek, Introduction to Queueing Systems with Telecommunication Applications. Springer, 2013.
[4] D., Kendall, “Stochastic processes occurring in the theory of queues and their analysis by the method of the imbedded Markov chain,The Annals of Mathematical Statistics, vol. 24, no. 3, pp. 338–354, 1953.Google Scholar
[5] K., Trivedi, Probability and Statistics with Reliability, Queueing and Computer Science Applications, 2nd edn. John Wiley & Sons, 2001.
[6] J., Little, “A proof of the queueing formula Operations Research, vol. 9, pp. 383–387, 1961.
[7] P., Leguesdron, J., Pellaumail, G., Rubino, and B., Sericola, “Transient analysis of the M/M/1 queue,Advances in Applied Probability, vol. 25, no. 3, pp. 702–713, 1993.Google Scholar
[8] R., Wolff, “Poisson arrivals see time averages,Operations Research, vol. 30, no. 2, pp. 223–231, 1982.Google Scholar
[9] A., Avritzer, A., Bondi, M., Grottke, K., Trivedi, and E., Weyuker, “Performance assurance via software rejuvenation: Monitoring, statistics and algorithms,” in Proc. Int. Conf. on Dependable Systems and Networks, DSN 2006, Jun. 2006, pp. 435–444.
[10] Y., Liu and K., Trivedi, “Survivability quantification: The analytical modeling approach,” International Journal of Performability Engineering, vol. 2, no. 1, p. 29, 2006.Google Scholar
[11] S., Dharmaraja, K. S., Trivedi, and D., Logothetis, “Performance modelling of wireless networks with generally distributed hand-off interarrival times,Computer Communications, vol. 26, pp. 1747–1755, 2003.Google Scholar
[12] D., Gaver, “A waiting line with interrupted service, including priorities,” Journal of the Royal Statistical Society, vol. B24, pp. 73–90, 1962.Google Scholar
[13] B., Avi-Itzhak and P., Naor, “Some queuing problems with the service station subject to breakdown,Operations Research, vol. 11, no. 3, pp. 303–320, 1963.Google Scholar
[14] M., Malhotra, J. K., Muppala, and K. S., Trivedi, “Stiffness-tolerant methods for transient analysis of stiff Markov chains,Journal of Microelectronics and Reliability, vol. 34, pp. 1825–1841, 1994.Google Scholar
[15] A., Bobbio and K. S., Trivedi, “An aggregation technique for the transient analysis of stiff Markov chains,IEEE Transactions on Computers, vol. C-35, pp. 803–814, 1986.Google Scholar
[16] J., Meyer, “On evaluating the performability of degradable systems,IEEE Transactions on Computers, vol. C-29, pp. 720–731, 1980.Google Scholar
[17] S. C., Liew and K. W., Lu, “A framework for characterizing disaster-based network survivability,IEEE Journal on Selected Areas in Communications, vol. 12, no. 1, pp. 52–58, Jan. 1994.Google Scholar
[18] D., Heimann, N., Mittal, and K., Trivedi, “Availability and reliability modeling for computer systems,” in Advances in Computers, ed. M., Yovits, vol. 31. Academic Press, 1990, pp. 176–231.
[19] R., Huslende,A combined evaluation of performance and reliability for degradable systems,” in Proc. ACM/SIGMETRICS Conf., 1981, pp. 157–164.Google Scholar
[20] V., Nicola, V., Kulkarni, and K., Trivedi, “Queueing analysis of fault-tolerant computer systems,” IEEE Transactions on Software Engineering, vol. SE-13, pp. 363–375, 1987.Google Scholar
[21] P., Chimento and K., Trivedi, “The performance of block structured programs on processors subject to failure and repair,” in High Performance Computer Systems, ed. E., Gelenbe. North Holland, 1988, pp. 269–280.

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×