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. (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.