A Structural Property of Solutions to Path Optimization Problems in Random Access Networks

The inherent nature of the physical setup and transmission mechanism in wireless ad hoc networks with random channel access, results in correlation between the link metrics of adjacent links, when considering path optimization problems. We identify a special structure inherent to the solution of Dynamic Programming (DP) problem arising in such an optimization over paths. According to this structure, the optimal policy tries to equalize the link metrics of adjacent links in a multi-hop route. We validate this structural property with simulations.