This Article 
 Bibliographic References 
 Add to: 
Performance of Acyclic Stochastic Networks with Network Coding
July 2011 (vol. 22 no. 7)
pp. 1238-1245
Yuan Yuan, National University of Defense Technology, Changsha
Kui Wu, University of Victoria, Victoria
Weijia Jia, City University of Hong Kong, Hong Kong
Yuming Jiang, NTNU, Trondheim
Network coding allows a network node to code the information flows before forwarding them. While it has been theoretically proved that network coding can achieve maximum network throughput, the theoretical results usually do not consider the burstiness of data traffic, delays, and the stochastic nature in information processing and transmission. There is currently no theory to systematically model and evaluate the performance of network coding, especially when node's capacity (i.e., coding and transmission) becomes stochastic. Without such a theory, the performance of network coding under various system settings is far from clear. To fill the vacancy, we develop an analytical approach by extending the stochastic network calculus theory to tackle the special difficulties in the evaluation of network coding. We prove the new properties of the stochastic network calculus and design an algorithm to obtain the performance bounds for acyclic stochastic networks with network coding. The tightness of theoretical bounds is validated with simulation.

[1] R. Ahlswede, N. Cai, S. Li, and R. Yeung, "Network Information Flow," IEEE Trans. Information Theory, vol. 46, no. 4, pp. 1204-1216, July 2000.
[2] J. Barros, R.A. Cost, D. Munaretto, and J. Widmer, "Effective Delay Control in Online Network Coding," Proc. IEEE INFOCOM '09, Apr. 2009.
[3] S. Chachulski, M. Jennings, S. Katti, and D. Katabi, "Trading Structure for Randomness in Wireless Opportunistic Routing," Proc. ACM SIGCOMM, Aug. 2007.
[4] C.-S. Chang, Performance Guarantees in Communication Networks. Springer-Verlag, 2000.
[5] F. Ciucu, A. Burchard, and J. Liebeherr, "Scaling Properties of Statistical End-to-End Bounds in the Network Calculus," IEEE Trans. Information Theory, vol. 52, no. 6, pp. 2300-2312, June 2006.
[6] R.L. Cruz, "A Calculus for Network Delay, Part I: Network Elements in Isolation," IEEE Trans. Information Theory, vol. 37, no. 1, pp. 114-131, Jan. 1991.
[7] C. Fragouli and E. Soljanin, "Network Coding Fundamentals," Foundations and Trends in Networking, vol. 2, no. 2, pp. 1-133, 2007.
[8] T. Ho and D. Lun, Network Coding: An Introduction. Cambridge Univ. Press, 2008.
[9] Y. Jiang, "A Basic Stochastic Network Calculus," Proc. ACM SIGCOMM, pp. 123-134, Sept. 2006.
[10] Y. Jiang and Y. Liu, Stochastic Network Calculus. Springer, 2008.
[11] S. Katti, D. Katabi, W. Hu, H.S. Rahul, and M. Médard, "The Importance of Being Opportunistic: Practical Network Coding for Wireless Environments," Proc. Allerton Conf. Comm., Control, and Computing, 2005.
[12] S. Katti, H. Rahul, W. Hu, D. Katabi, M. Médard, and J. Crowcroft, "XORs in the Air: Practical Wireless Network Coding," Proc. SIGCOMM, pp. 263-289, Sept. 2006.
[13] J. Le Boudec and P. Thiran, Network Calculus: A Theory of Deterministic Queuing Systems for the Internet. Springer-Verlag, 2001.
[14] C. Li, A. Burchard, and J. Liebeherr, "A Network Calculus with Effective Bandwidth," IEEE/ACM Trans. Networking, vol. 15, no. 6, pp. 1142-1453, Dec. 2007.
[15] A. Mahmino, J. Lecan, and C. Fraboul, "Guaranteed Packet Delays with Network Coding," Proc. First IEEE Int'l Workshop Wireless Network Coding, pp. 1-6, June 2008.
[16] M. Mitzenmacher and E. Upfal, Probability and Computing: Randomized Algorithms and Probabilistic Analysis. Cambridge Univ. Press, 2005.
[17] K. Wu, W. Jia, Y. Yuan, and Y. Jiang, "Performance Modeling of Stochastic Networks with Network Coding," Proc. Workshop Network Coding, Theory, and Applications (NetCod '09), June 2009.
[18] R. Yeung, Information Theory and Network Coding. Springer, 2008.

Index Terms:
Network calculus, stochastic networks, network coding.
Yuan Yuan, Kui Wu, Weijia Jia, Yuming Jiang, "Performance of Acyclic Stochastic Networks with Network Coding," IEEE Transactions on Parallel and Distributed Systems, vol. 22, no. 7, pp. 1238-1245, July 2011, doi:10.1109/TPDS.2010.192
Usage of this product signifies your acceptance of the Terms of Use.