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  • Cited by 52
Publisher:
Cambridge University Press
Online publication date:
June 2014
Print publication year:
2014
Online ISBN:
9781139565363

Book description

Communication networks underpin our modern world, and provide fascinating and challenging examples of large-scale stochastic systems. Randomness arises in communication systems at many levels: for example, the initiation and termination times of calls in a telephone network, or the statistical structure of the arrival streams of packets at routers in the Internet. How can routing, flow control and connection acceptance algorithms be designed to work well in uncertain and random environments? This compact introduction illustrates how stochastic models can be used to shed light on important issues in the design and control of communication networks. It will appeal to readers with a mathematical background wishing to understand this important area of application, and to those with an engineering background who want to grasp the underlying mathematical theory. Each chapter ends with exercises and suggestions for further reading.

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Contents

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.
Asmussen, S. 2003. Applied Probability and Queues. 2nd edn. New York, NY: Springer.
Baccelli, F. and Bremaud, P. 2003. Elements of Queueing Theory. Berlin: Springer.
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.
Berry, R. A. and Johari, R. 2013. Economic Modeling: A Primer with Engineering Applications. Foundations and Trends in Networking. Delft: now publishers.
Bonald, T. and Massoulie, L. 2001. Impact of fairness on Internet performance. Performance Evaluation Review, 29, 82–91.
Boyd, S. and Vandenberghe, L. 2004. Convex Optimization. Cambridge: Cambridge University Press.
Bramson, M. 2006. Stability and Heavy Traffic Limits for Queueing Networks: St. Flour Lecture Notes. Berlin: Springer.
Chang, C.-S. 2000. Performance Guarantees in Communication Networks. London: Springer.
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.
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.
Courcoubetis, C. and Weber, R. 2003. Pricing Communication Networks: Economics, Technology and Modelling. Chichester: Wiley.
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.
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.
Doyle, P. G. and Snell, J. L. 2000. Random Walks and Electric Networks. Carus Mathematical Monographs. Washington D.C.: The Mathematical Association of America.
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.
Foster, F. G. 1953. On the stochastic matrices associated with certain queueing processes. Annals of Mathematical Statistics, 24, 355–360.
Gale, D. 1960. The Theory ofLinear Economic Models. Chicago, IL: The University of Chicago Press.
Gallager, R. G. 1977. A minimum delay routing algorithm using distributed computation. IEEE Transactions on Communications, 25, 73–85.
Ganesh, A., O'Connell, N. and Wischik, D. 2004. Big Queues. Berlin: Springer.
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.
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.
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.
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.
Jiang, L. and Walrand, J. 2012. Stability and delay of distributed scheduling algorithms for networks of conflicting queues. Queueing Systems, 72, 161–187.
Johari, R. and Tsitsiklis, J. N. 2004. Efficiency loss in a network resource allocation game. Mathematics of Operations Research, 29, 407–435.
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.
Kelly, F. P. 1991. Loss networks. Annals of Applied Probability, 1, 319–378.
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.
Kelly, F. P. 2003a. Fairness and stability of end-to-end congestion control. European Journal ofControl, 9, 159–176.
Kelly, F. P. 2011. Reversibility and Stochastic Networks. Cambridge: Cambridge University Press.
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.
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.
Kelly, T. 2003b. Scalable TCP: improving performance in highspeed wide area networks. Computer Communication Review, 33, 83–91.
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.
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.
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.
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.
Kingman, J. F. C. 1993. Poisson Processes. Oxford: Oxford University Press.
Kleinrock, L. 1964. Communication Nets: Stochastic Message Flow and Delay. New York, NY: McGraw Hill.
Kleinrock, L. 1976. Queueing Systems, vol II: Computer Applications. NewYork,NY: Wiley.
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.
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.
Mazumdar, R. 2010. Performance Modeling, Loss Networks, and Statistical Multiplexing. San Rafael, CA: Morgan and Claypool.
Meyn, S. P. and Tweedie, R. L. 1993. Markov Chains and Stochastic Stability. London: Springer.
Moallemi, C. and Shah, D. 2010. On the flow-level dynamics of a packet-switched network. Performance Evaluation Review, 38, 83–94.
Modiano, E., Shah, D. and Zussman, G. 2006. Maximizing throughput in wireless networks via gossiping. Performance Evaluation Review, 34, 27–38.
Nash, J. F. 1950. The bargaining problem. Econometrica, 18, 155–162.
Norris, J. R. 1998. Markov Chains. Cambridge: Cambridge University Press.
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.
Pallant, D. L. and Taylor, P. G. 1995. Modeling handovers in cellular mobile networks with dynamic channel allocation. Operations Research, 43, 33–42.
Pitman, J. 2006. Combinatorial Stochastic Processes. Berlin: Springer.
Rawls, J. 1971. A Theory of Justice. Cambridge, MA: Harvard University Press.
Ross, K. W. 1995. Multiservice Loss Models for Broadband Communication Networks. London: Springer.
Shah, D. and Shin, J. 2012. Randomized scheduling algorithm for queueing networks. Annals of Applied Probability, 22, 128–171.
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.
Shah, D., Walton, N. S. and Zhong, Y. 2012. Optimal queue-size scaling in switched networks. Performance Evaluation Review, 40, 17–28.
Shakkottai, S. and Srikant, R. 2007. Network Optimization and Control. Foundations and Trends in Networking. Hanover, MA: now publishers.
Songhurst, D. J. 1999. Charging Communication Networks: From Theory to Practice. Amsterdam: Elsevier.
Srikant, R. 2004. The Mathematics of Internet Congestion Control. Boston, MA: Birkhausen
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.
Tian, Y.-P. 2012. Frequency-Domain Analysis and Design of Distributed Control Systems. Singapore: Wiley.
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.
Walrand, J. 1988. An Introduction to Queueing Networks. Englewood Clifs, NJ: Prentice Hall.
Walton, N. S. 2009. Proportional fairness and its relationship with multi-class queueing networks. Annals of Applied Probability, 19, 2301–2333.
Whittle, P. 1971. Optimization Under Constraints. New York, NY: Wiley.
Whittle, P. 1986. Systems in Stochastic Equilibrium. New York, NY: Wiley.
Whittle, P. 2007. Networks: Optimisation and Evolution. Cambridge: Cambridge University Press.
Wischik, D. 1999. The output of a switch, or, effective bandwidths for networks. Queue-ing Systems, 32, 383–396.
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.
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.

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