Two-hop ad-hoc networks, in which some nodes forward traffic for multiple sources, with which they also compete for channel access suffer from large queues building up in bottleneck nodes. This problem can often be alleviated by using IEEE 802.11e to give preferential treatment to bottleneck nodes. Previous results have shown that differentiation parameters can be used to allocate capacity in a more efficient way in the two-hop scenario. However, the overall throughput of the bottleneck may differ considerably, depending on the differentiation method used. By applying a very fast and accurate analysis method, based on steady-state analysis of an QBD-type infinite Markov chain, we find the maximum throughput that is possible per differentiation parameter. All possible parameter settings are explored with respect to the maximum throughput conditioned on a maximum buffer occupancy. This design space exploration cannot be done with network simulators like NS2 or Opnet, as each simulation run simply takes to long. The results, which have been validated by detailed simulations, show that by differentiating TXOP it is possible to achieve a throughput that is about 50% larger than when differentiating AIFS and CW_min.