Abstract
The usage of network resources by content providers is commonly governed by Service-Level Agreements (SLA) between the content provider and the network service provider. Resource usage exceeding the limits specified in the SLA incurs the content provider additional charges, usually at a higher cost. Hence, the content provider's goal is to provision adequate resources in the SLA based on forecasts of future demand. We study capacity purchasing strategies when the content provider employs network coded multicast as the media delivery mechanism, with uncertainty in its future customer set explicitly taken into consideration. The latter requires the content provider to make capacity provisioning decisions based on market predictions and historical customer usage patterns. The probabilistic element suggests a stochastic optimization approach. We model this problem as a two-stage stochastic optimization problem with recourse. Such optimizations are #P-hard to solve directly, and we design two approximation algorithms for them. The first is a heuristic algorithm that exploits properties unique to network coding, so that only polynomial-time operations are needed. It performs well in general scenarios, but the gap from the optimal solution is not bounded by any constant in the worst case. This motivates our second approach, a sampling algorithm partly inspired from the work of Gupta et al. [2004a]. We employ techniques from duality theory in linear optimization to prove that the sampling algorithm provides a 3-approximation to the stochastic multicast problem. We conduct extensive simulations to illustrate the efficacy of both algorithms, and show that the performance of both is usually within 10% of the optimal solution in practice.
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- Ahlswede, R., Cai, N., Li, S. R., and Yeung, R. W. 2000. Network information flow. IEEE Trans. Inf. Theory 46, 4, 1204--1216. Google ScholarDigital Library
- Beale, E. M. L. 1955. On minimizing a convex function subject to linear inequalities. J. Roy. Statist. Soc. 17, 2, 173--184.Google Scholar
- Birge, J. R. and Louveaux, F. 1997. Introduction to Stochastic Programming. Springer, New York.Google Scholar
- Bouillet, E., Mitra, D., and Ramakrishnan, K. G. 2002. The structure and management of service level agreements in networks. IEEE J. Select. Areas Comm. 20, 4, 691--699. Google ScholarDigital Library
- BRITE. 2012. Boston University Representative Internet Topology gEnerator. http://www.cs.bu.edu/brite/.Google Scholar
- Dantzig, G. 1955. Linear programming under uncertainty. Manag. Sci. 1, 197--206.Google ScholarDigital Library
- Duan, Z., Zhang, Z. L., and Hou, Y. T. 2003. Service overlay networks: SLAs, QoS, and bandwidth provisioning. IEEE/ACM Trans. Netw. 11, 6. Google ScholarDigital Library
- Dyer, M. and Stougie, L. 2006. Computational complexity of stochastic programming problems. Math. Program. 106, 3, 423--432. Google ScholarDigital Library
- Gupta, A. and Kumar, A. 2009. A constant-factor Approximation for stochastic Steiner forest. In Proceedings of the ACM Symposium on Theory of Computing (STOC). Google ScholarDigital Library
- Gupta, A., Pál, M., Ravi, R., and Sinha, A. 2004a. Boosted sampling: approximation algorithms for stochastic optimization. In Proceedings of the ACM Symposium on Theory of Computing (STOC). Google ScholarDigital Library
- Gupta, A., Ravi, R., and Sinha, A. 2004b. An edge in time saves nine: LP rounding approximation algorithms for stochastic network design. In Proceedings of the IEEE Symposium on Foundations of Computer Science (FOCS). Google ScholarDigital Library
- Heckmann, O., Schmitt, J., and Steinmetz, R. 2002. Robust bandwidth allocation strategies. In Proceedings of the IEEE International Workshop on Quality of Service.Google Scholar
- Immorlica, N., Karger, D., Minkoff, M., and Mirrokni, V. S. 2004. On the costs and benefits of procrastination: approximation algorithms for stochastic combinatorial optimization problems. In Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA). Google ScholarDigital Library
- Jain, K., Mahdian, M., and Salavatipour, M. R. 2003. Packing Steiner trees. In Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA). Google ScholarDigital Library
- Kall, P. and Wallace, S. W. 1994. Stochastic Programming. Wiley, Chichester, UK.Google Scholar
- Khalil, I. and Braun, T. 2002. Edge provisioning and fairness in VPN-DiffServ networks. J. Netw. Syst. Manag. 10, 1, 11--37. Google ScholarDigital Library
- Koetter, R. and Médard, M. 2003. An algebraic approach to network coding. IEEE/ACM Trans. Netw. 11, 5, 782--795. Google ScholarDigital Library
- Li, Z. 2007. Min-Cost multicast of selfish information flows. In Proceedings of the IEEE INFOCOM Conference.Google ScholarDigital Library
- Li, Z. and Li, B. 2004. Network coding in undirected networks. In Proceedings of the 38th Annual Conference on Information Sciences and Systems (CISS).Google Scholar
- Li, Z. and Li, B. 2005. Efficient and distributed computation of maximum multicast rates. In Proceedings of the IEEE INFOCOM Conference.Google Scholar
- Li, Z., Li, B., Jiang, D., and Lau, L. C. 2005. On achieving optimal throughput with network coding. In Proceedings of the IEEE INFOCOM Conference.Google Scholar
- Lun, D. S., Ratnakar, N., Koetter, R., Médard, M., Ahmed, E., and Lee, H. 2005. Achieving minimum-cost multicast: A decentralized approach based on network coding. In Proceedings of the IEEE INFOCOM Conference.Google Scholar
- Ma, H. and Shin, K. G. 2002. Multicast video-on-demand services. SIGCOMM Comput. Commun. Rev. 32, 1, 31--43. Google ScholarDigital Library
- Mitra, D. and Wang, Q. 2005. Stochastic traffic engineering for demand uncertainty and risk-aware network revenue management. IEEE/ACM Trans. Netw. 13, 2, 221--233. Google ScholarDigital Library
- Nisan, N., Roughgarden, T., Tardos, E., and Vazirani, V. 2007. Algorithmic Game Theory. Cambridge University Press. Google ScholarDigital Library
- Sen, S., Doverspike, R. D., and Cosares, S. 1994. Network planning with random demand. Telecomm. Syst. 3, 1, 11--30.Google ScholarDigital Library
- Shmoys, D. B. and Swamy, C. 2004. Stochastic optimization is (almost) as easy as deterministic optimization. In Proceedings of the IEEE Symposium on Foundations of Computer Science (FOCS). Google ScholarDigital Library
- Slyke, R. V. and Wets, R. J. B. 1969. L-shaped linear programs with application to optimal control and stochastic optimization. SIAM J. Appl. Math. 17, 638--663.Google ScholarCross Ref
- Thimm, M. 2001. On the approximability of the Steiner tree problem. In Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science. Google ScholarDigital Library
- Verma, D. C. 2004. Service level agreements on IP networks. Proc. IEEE 92, 9, 1382--1388.Google ScholarCross Ref
- Wardrop, J. 1952. Some theoretical aspects of road traffic research. In Proceedings of the Institute of Civil Engineers, Part II.Google ScholarCross Ref
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- Algorithms for stochastic optimization of multicast content delivery with network coding
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