# Approximate Dynamic Programming with Bezier Curves/Surfaces for Top-percentile traffic routing

Multi-homing is used by Internet Service Provider (ISP) to connect to the Internet via different network providers. This study investigates the optimal routing strategy under multi-homing in the case where network providers charge ISPs according to top-percentile pricing (i.e. based on the $\theta$-th highest volume of traffic shipped). We call this problem the Top-percentile Traffic Routing Problem (TpTRP). Solution approaches based on Stochastic Dynamic Programming require discretization in state space, which introduces a large number of state variables. This is known as the curse of dimensionality. To overcome this we suggested to use Approximate Dynamic Programming (ADP) to construct approximations of the value function in previous work, which works nicely for medium size instances of TpTRP. In this work we keep working on the ADP model, use Bezier Curves/Surfaces to do the aggregation over time. This modification accelerates the efficiency of parameter training in the solution of the ADP model, which makes the real-sized TpTRP tractable.

## Citation

Technical Report ERGO 10-008, School of Mathematics, University of Edinburgh, Dec/2010.