Skip to main content Accessibility help
×
Hostname: page-component-8448b6f56d-tj2md Total loading time: 0 Render date: 2024-04-24T20:12:33.784Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  05 June 2014

Frank Kelly
Affiliation:
University of Cambridge
Elena Yudovina
Affiliation:
University of Michigan, Ann Arbor
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
Stochastic Networks , pp. 217 - 220
Publisher: Cambridge University Press
Print publication year: 2014

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

Aldous, D. 1987. Ultimate instability of exponential back-off protocol for acknowledgement-based transmission control of random access communication channels. IEEE Transactions on Information Theory, 33, 219–223.CrossRefGoogle Scholar
Asmussen, S. 2003. Applied Probability and Queues. 2nd edn. New York, NY: Springer.Google Scholar
Baccelli, F. and Bremaud, P. 2003. Elements of Queueing Theory. Berlin: Springer.CrossRefGoogle Scholar
BenFredj, S., Bonald, T., Proutiere, A., Regnie, G. and Roberts, J. W. 2001. Statistical bandwidth sharing: a study of congestion at flow level. Computer Communication Review, 31, 111–122.Google Scholar
Berry, R. A. and Johari, R. 2013. Economic Modeling: A Primer with Engineering Applications. Foundations and Trends in Networking. Delft: now publishers.Google Scholar
Bonald, T. and Massoulie, L. 2001. Impact of fairness on Internet performance. Performance Evaluation Review, 29, 82–91.CrossRefGoogle Scholar
Boyd, S. and Vandenberghe, L. 2004. Convex Optimization. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Bramson, M. 2006. Stability and Heavy Traffic Limits for Queueing Networks: St. Flour Lecture Notes. Berlin: Springer.Google Scholar
Chang, C.-S. 2000. Performance Guarantees in Communication Networks. London: Springer.CrossRefGoogle Scholar
Chen, M., Liew, S., Shao, Z. and Kai, C. 2013. Markov approximation for combinatorial network optimization. IEEE Transactions on Information Theory. doi: 10.1109/TIT.2013.2268923.Google Scholar
Chiang, M., Low, S. H., Calderbank, A. R. and Doyle, J. C. 2007. Layering as optimization decomposition: a mathematical theory of network architectures. Proceedings of the IEEE, 95, 255–312.CrossRefGoogle Scholar
Courcoubetis, C. and Weber, R. 2003. Pricing Communication Networks: Economics, Technology and Modelling. Chichester: Wiley.CrossRefGoogle Scholar
Crametz, J.-P. and Hunt, P. J. 1991. A limit result respecting graph structure for a fully connected loss network with alternative routing. Annals of Applied Probability, 1, 436–444.CrossRefGoogle Scholar
Crowcroft, J. and Oechslin, P. 1998. Differentiated end-to-end Internet services using a weighted proportionally fair sharing TCP. Computer Communications Review, 28, 53–69.CrossRefGoogle Scholar
Doyle, P. G. and Snell, J. L. 2000. Random Walks and Electric Networks. Carus Mathematical Monographs. Washington D.C.: The Mathematical Association of America.Google Scholar
Erlang, A. K. 1925. A proof of Maxwell's law, the principal proposition in the kinetic theory of gases. In Brockmeyer, E., Halstrom, H. L. and Jensen, A. (eds.), The Life and Works of A. K. Erlang. Copenhagen: Academy of Technical Sciences, 1948, pp. 222–226.Google Scholar
Foster, F. G. 1953. On the stochastic matrices associated with certain queueing processes. Annals of Mathematical Statistics, 24, 355–360.CrossRefGoogle Scholar
Gale, D. 1960. The Theory ofLinear Economic Models. Chicago, IL: The University of Chicago Press.Google Scholar
Gallager, R. G. 1977. A minimum delay routing algorithm using distributed computation. IEEE Transactions on Communications, 25, 73–85.CrossRefGoogle Scholar
Ganesh, A., O'Connell, N. and Wischik, D. 2004. Big Queues. Berlin: Springer.CrossRefGoogle Scholar
Gibbens, R. J., Kelly, F. P. and Key, P. B. 1995. Dynamic alternative routing. In Steen-strup, Martha (ed.), Routing in Communications Networks. Englewood Clifs, NJ: Prentice Hall, pp. 13–47.Google Scholar
Goldberg, L., Jerrum, M., Kannan, S. and Paterson, M. 2004. A bound on the capacity of backoff and acknowledgement-based protocols. SIAM Journal on Computing, 33, 313–331.CrossRefGoogle Scholar
Hajek, B. 2006. Notes for ECE 467: Communication Network Analysis. http://www. ifp.illinois.edu/~hajek/Papers/networkanalysis.html.
Jacobson, V. 1988. Congestion avoidance and control. Computer Communication Review, 18, 314–329.CrossRefGoogle Scholar
Jiang, L. and Walrand, J. 2010. A distributed CSMA algorithm for throughput and utility maximization in wireless networks. IEEE/ACM Transactions on Networking, 18, 960–972.Google Scholar
Jiang, L. and Walrand, J. 2012. Stability and delay of distributed scheduling algorithms for networks of conflicting queues. Queueing Systems, 72, 161–187.CrossRefGoogle Scholar
Johari, R. and Tsitsiklis, J. N. 2004. Efficiency loss in a network resource allocation game. Mathematics of Operations Research, 29, 407–435.CrossRefGoogle Scholar
Kang, W. N., Kelly, F. P., Lee, N. H. and Williams, R. J. 2009. State space collapse and difusion approximation for a network operating under a fair bandwidth-sharing policy. Annals of Applied Probability, 19, 1719–1780.CrossRefGoogle Scholar
Kelly, F. P. 1991. Loss networks. Annals of Applied Probability, 1, 319–378.CrossRefGoogle Scholar
Kelly, F. P. 1996. Notes on efective bandwidths. In Kelly, F. P., Zachary, S. and Ziedins, I. B. (eds.), Stochastic Networks: Theory and Applications. Oxford: Oxford University Press, pp. 141–168.Google Scholar
Kelly, F. P. 2003a. Fairness and stability of end-to-end congestion control. European Journal ofControl, 9, 159–176.Google Scholar
Kelly, F. P. 2011. Reversibility and Stochastic Networks. Cambridge: Cambridge University Press.Google Scholar
Kelly, F. P. and MacPhee, I. M. 1987. The number of packets transmitted by collision detect random access schemes. Annals of Probability, 15, 1557–1668.CrossRefGoogle Scholar
Kelly, F. P. and Raina, G. 2011. Explicit congestion control: charging, fairness and admission management. In Ramamurthy, B., Rouskas, G. and Sivalingam, K. (eds.), Next-Generation Internet Architectures and Protocols. Cambridge: Cambridge University Press, pp. 257–274.Google Scholar
Kelly, T. 2003b. Scalable TCP: improving performance in highspeed wide area networks. Computer Communication Review, 33, 83–91.CrossRefGoogle Scholar
Kendall, D. G. 1953. Stochastic processes occurring in the theory of queues and their analysis by the method of the imbedded Markov chain. Annals of Mathematical Statistics, 24, 338–354.CrossRefGoogle Scholar
Kendall, D. G. 1975. Some problems in mathematical genealogy. In Gani, J. (ed.), Perspectives in Probability and Statistics: Papers in Honour of M.S. Bartlett. London: Applied Probability Trust/Academic Press, pp. 325–345.Google Scholar
Key, P. B. 1988. Implied cost methodology and software tools for a fully connected network with DAR and trunk reservation. British Telecom Technology Journal, 6, 52–65.Google Scholar
Kind, J., Niessen, T. and Mathar, R. 1998. Theory of maximum packing and related channel assignment strategies for cellular radio networks. Mathematical Methods of Operations Research, 48, 1–16.CrossRefGoogle Scholar
Kingman, J. F. C. 1993. Poisson Processes. Oxford: Oxford University Press.Google Scholar
Kleinrock, L. 1964. Communication Nets: Stochastic Message Flow and Delay. New York, NY: McGraw Hill.Google Scholar
Kleinrock, L. 1976. Queueing Systems, vol II: Computer Applications. NewYork,NY: Wiley.Google Scholar
Lu, S. H. and Kumar, P. R. 1991. Distributed scheduling based on due dates and buffer priorities. IEEE Transactions on Automatic Control, 36, 1406–1416.CrossRefGoogle Scholar
Marbach, P., Eryilmaz, A. and Ozdaglar, A. 2011. Asynchronous CSMA policies in multihop wireless networks with primary interference constraints. IEEE Transactions on Information Theory, 57, 3644–3676.CrossRefGoogle Scholar
Mazumdar, R. 2010. Performance Modeling, Loss Networks, and Statistical Multiplexing. San Rafael, CA: Morgan and Claypool.Google Scholar
Meyn, S. P. and Tweedie, R. L. 1993. Markov Chains and Stochastic Stability. London: Springer.CrossRefGoogle Scholar
Moallemi, C. and Shah, D. 2010. On the flow-level dynamics of a packet-switched network. Performance Evaluation Review, 38, 83–94.CrossRefGoogle Scholar
Modiano, E., Shah, D. and Zussman, G. 2006. Maximizing throughput in wireless networks via gossiping. Performance Evaluation Review, 34, 27–38.CrossRefGoogle Scholar
Nash, J. F. 1950. The bargaining problem. Econometrica, 18, 155–162.CrossRefGoogle Scholar
Norris, J. R. 1998. Markov Chains. Cambridge: Cambridge University Press.Google Scholar
Ott, T. J. 2006. Rate of convergence for the ‘square root formula’ in the Internet transmission control protocol. Advances in Applied Probability, 38, 1132–1154.Google Scholar
Pallant, D. L. and Taylor, P. G. 1995. Modeling handovers in cellular mobile networks with dynamic channel allocation. Operations Research, 43, 33–42.CrossRefGoogle Scholar
Pitman, J. 2006. Combinatorial Stochastic Processes. Berlin: Springer.Google Scholar
Rawls, J. 1971. A Theory of Justice. Cambridge, MA: Harvard University Press.Google Scholar
Ross, K. W. 1995. Multiservice Loss Models for Broadband Communication Networks. London: Springer.CrossRefGoogle Scholar
Shah, D. and Shin, J. 2012. Randomized scheduling algorithm for queueing networks. Annals of Applied Probability, 22, 128–171.CrossRefGoogle Scholar
Shah, D. and Wischik, D. 2012. Switched networks with maximum weight policies: fluid approximation and multiplicative state space collapse. Annals of Applied Probability, 22, 70–127.CrossRefGoogle Scholar
Shah, D., Walton, N. S. and Zhong, Y. 2012. Optimal queue-size scaling in switched networks. Performance Evaluation Review, 40, 17–28.CrossRefGoogle Scholar
Shakkottai, S. and Srikant, R. 2007. Network Optimization and Control. Foundations and Trends in Networking. Hanover, MA: now publishers.Google Scholar
Songhurst, D. J. 1999. Charging Communication Networks: From Theory to Practice. Amsterdam: Elsevier.Google Scholar
Srikant, R. 2004. The Mathematics of Internet Congestion Control. Boston, MA: BirkhausenCrossRefGoogle Scholar
Tassiulas, L. and Ephremides, A. 1992. Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks. IEEE Transactions on Automatic Control, 37, 1936–1948.CrossRefGoogle Scholar
Tian, Y.-P. 2012. Frequency-Domain Analysis and Design of Distributed Control Systems. Singapore: Wiley.CrossRefGoogle Scholar
Vinnicombe, G. 2002. On the stability of networks operating TCP-like congestion control. Proc. 15th Int. Fed. Automatic Control World Congress, Barcelona, Spain, 217–222.Google Scholar
Walrand, J. 1988. An Introduction to Queueing Networks. Englewood Clifs, NJ: Prentice Hall.Google Scholar
Walton, N. S. 2009. Proportional fairness and its relationship with multi-class queueing networks. Annals of Applied Probability, 19, 2301–2333.CrossRefGoogle Scholar
Whittle, P. 1971. Optimization Under Constraints. New York, NY: Wiley.Google Scholar
Whittle, P. 1986. Systems in Stochastic Equilibrium. New York, NY: Wiley.Google Scholar
Whittle, P. 2007. Networks: Optimisation and Evolution. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Wischik, D. 1999. The output of a switch, or, effective bandwidths for networks. Queue-ing Systems, 32, 383–396.Google Scholar
Wischik, D., Raiciu, C., Greenhalgh, A. and Handley, M. 2011. Design, implementation and evaluation of congestion control for multipath TCP. Proc. 8th USENIX Conference on Networked Systems Design and Implementation, Boston, MA, 99–112.Google Scholar
Zachary, S. and Ziedins, I. 2011. Loss networks. In Boucherie, R. J. and van Dijk, N. M. (eds.), Queueing Networks: A Fundamental Approach. New York, NY: Springer, pp. 701–728.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org 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.

  • References
  • Frank Kelly, University of Cambridge, Elena Yudovina, University of Michigan, Ann Arbor
  • Book: Stochastic Networks
  • Online publication: 05 June 2014
  • Chapter DOI: https://doi.org/10.1017/CBO9781139565363.015
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.

  • References
  • Frank Kelly, University of Cambridge, Elena Yudovina, University of Michigan, Ann Arbor
  • Book: Stochastic Networks
  • Online publication: 05 June 2014
  • Chapter DOI: https://doi.org/10.1017/CBO9781139565363.015
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.

  • References
  • Frank Kelly, University of Cambridge, Elena Yudovina, University of Michigan, Ann Arbor
  • Book: Stochastic Networks
  • Online publication: 05 June 2014
  • Chapter DOI: https://doi.org/10.1017/CBO9781139565363.015
Available formats
×