On load balancing in a dense wireless multihop network

We study the load balancing problem in a dense wireless multihop network, where a typical path consists of large number of hops, i.e., the spatial scales of a typical distance between source and destination, and mean distance between the neighboring nodes are strongly separated. In this limit, we present a general framework for analyzing the traffic load resulting from a given set of paths and traffic demands. We formulate the load balancing problem as a minmax problem and give two lower bounds for the achievable minimal maximum traffic load. The framework is illustrated by an example of uniformly distributed traffic demands in a unit disk with a few families of paths given in advance. With these paths we are able to decrease the maximum traffic load by factor of 33-40% depending on the assumptions. The obtained traffic load level also comes quite near the tightest lower bound