Algorithms for stochastic optimization of multicast content delivery with network coding

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.