Stochastic Multicast with Network Coding

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 in this setting when the content provider employs network coded multicast as the data delivery mechanism. We model this problem as a two-stage stochastic optimization problem with recourse, and we design two approximation algorithms to solve such problems. The first is a heuristic that exploits properties unique to network coding. It performs well in general scenarios, but may be unbounded with respect to the optimal solution in the worst case. This motivates our second approach, a sampling algorithm partly inspired from the work of Gupta et al. [Gupta et al., ACM STOC 2004]. We employ techniques from duality theory in linear optimization to prove that sampling provides a 3-approximate solution to the stochastic multicast problem. We conduct 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.

[1]  Zongpeng Li,et al.  Efficient and distributed computation of maximum multicast rates , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

[2]  Nicole Immorlica,et al.  On the costs and benefits of procrastination: approximation algorithms for stochastic combinatorial optimization problems , 2004, SODA '04.

[3]  R. Ravi,et al.  Boosted sampling: approximation algorithms for stochastic optimization , 2004, STOC '04.

[4]  Zongpeng Li,et al.  On achieving optimal throughput with network coding , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

[5]  Tim Roughgarden,et al.  Algorithmic Game Theory , 2007 .

[6]  Chaitanya Swamy,et al.  Stochastic optimization is (almost) as easy as deterministic optimization , 2004, 45th Annual IEEE Symposium on Foundations of Computer Science.

[7]  Muriel Médard,et al.  Achieving minimum-cost multicast: a decentralized approach based on network coding , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

[8]  J. G. Wardrop,et al.  Some Theoretical Aspects of Road Traffic Research , 1952 .

[9]  Martin E. Dyer,et al.  Computational complexity of stochastic programming problems , 2006, Math. Program..

[10]  J G Wardrop,et al.  CORRESPONDENCE. SOME THEORETICAL ASPECTS OF ROAD TRAFFIC RESEARCH. , 1952 .

[11]  Mohammad R. Salavatipour,et al.  Packing Steiner trees , 2003, SODA '03.

[12]  R. Wets,et al.  L-SHAPED LINEAR PROGRAMS WITH APPLICATIONS TO OPTIMAL CONTROL AND STOCHASTIC PROGRAMMING. , 1969 .

[13]  Ibrahim Khalil,et al.  Edge Provisioning and Fairness in VPN-DiffServ Networks , 2004, Journal of Network and Systems Management.

[14]  Zongpeng Li,et al.  Network Coding in Undirected Networks , 2004 .

[15]  Antonio Alonso Ayuso,et al.  Introduction to Stochastic Programming , 2009 .

[16]  Robert D. Doverspike,et al.  Network planning with random demand , 1994, Telecommun. Syst..

[17]  Eric Bouillet,et al.  The structure and management of service level agreements in networks , 2002, IEEE J. Sel. Areas Commun..

[18]  Rudolf Ahlswede,et al.  Network information flow , 2000, IEEE Trans. Inf. Theory.

[19]  Zongpeng Li,et al.  A Constant Bound on Throughput Improvement of Multicast Network Coding in Undirected Networks , 2009, IEEE Transactions on Information Theory.

[20]  Peter Kall,et al.  Stochastic Programming , 1995 .

[21]  George B. Dantzig,et al.  Linear Programming Under Uncertainty , 2004, Manag. Sci..

[22]  Oliver Heckmann,et al.  Robust bandwidth allocation strategies , 2002, IEEE 2002 Tenth IEEE International Workshop on Quality of Service (Cat. No.02EX564).

[23]  Muriel Médard,et al.  An algebraic approach to network coding , 2003, TNET.

[24]  Andrew Hiles.  Service Level Agreements , 1994 .

[25]  Kang G. Shin,et al.  Multicast Video-on-Demand services , 2002, CCRV.

[26]  R. Ravi,et al.  An edge in time saves nine: LP rounding approximation algorithms for stochastic network design , 2004, 45th Annual IEEE Symposium on Foundations of Computer Science.

[27]  Yiwei Thomas Hou,et al.  Service overlay networks: SLAs, QoS, and bandwidth provisioning , 2003, TNET.

[28]  E. Beale.  ON MINIMIZING A CONVEX FUNCTION SUBJECT TO LINEAR INEQUALITIES , 1955 .

[29]  Martin Thimm,et al.  On the approximability of the Steiner tree problem , 2003, Theor. Comput. Sci..

[30]  Zongpeng Li,et al.  Min-Cost Multicast of Selfish Information Flows , 2007, IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications.

[31]  Arne A. Nilsson,et al.  On service level agreements for IP networks , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[32]  Debasis Mitra,et al.  Stochastic traffic engineering for demand uncertainty and risk-aware network revenue management , 2004, IEEE/ACM Transactions on Networking.