Wireless mesh network performance issues have been modeled by the Joint Routing and Scheduling Problem (JRSP) in which a maximum per-flow throughput is computed. A classical relaxation of JRSP, denoted as the Round Weighting Problem (RWP), consists in assigning enough weight to sets of compatible simultaneous transmissions (rounds), while minimizing the sum of them, thus maximizing the relative weight of each round, which model the throughput. In this work, we present a new linear formulation of RWP focused on the transport capacity over the network cuts, thus eliminating the routing. We prove its equivalence with existing formulations with flows and formalize a primal-dual algorithm that quickly solves this problem using a cross line and column generations process. An asset of this formulation is to point out a bounded region, a "bottleneck" of the network, that is enough to optimize in order to get the optimal RWP of the whole network. The size and location of this area is experimentally made through simulations, highlighting a few hop distant neighborhood of the mesh gateways. One would then apply approximated methods outside this zone to route the traffic without degrading the achieved capacity.