Effects of Routing on the Capacity of Multi-Hop Wireless Networks

We consider multi-hop wireless mesh networks and examine whether capacity may be improved by distributing the data flows for each origin-destination (OD) pair across multiple routes. The network geometry and the application of technologies, such as beamforming or full-duplex, are described by a matrix that describes which pairs of transmissions (or 'links') are compatible in that they can occur simultaneously without collisions or other conflicts. Under a binary interference framework, the conflict matrix is used to derive the maximal sets of compatible links, and secondly, these are used to derive a system of linear inequalities that bounds links' data flows. These steps are computationally expensive, but we show how the system usually collapses when re-expressed in terms of flows on routes. The theory is illustrated in terms of a simple 'Braess' network example with a single OD pair. We then consider networks with two OD pairs whose data flows have some nodes in common and thus contend with each other. We show how to design networks that exploit multiple relay nodes and routes so as to increase capacity. We then examine the same problem on ensembles of random networks. We find that in many cases, capacity can be improved if the OD pairs distribute their traffic over several routes. We pose and solve a set of linear programs that model (i) cooperative behavior; (ii) the optimization of one OD pair when presented with a fixed route assignment by the other; and (iii) variants of these games when both OD pairs are in contention with background (single-hop) traffic.