2 comments before digging deepter:
1.) I really thinkg that Q(f)=b-a\cdot f is a strange choice. I would at least include another non-linearity as fees that are too high will probably result in the channel not being used. I think you kind of reflect this by reducing the predicted flow by a factor proportional to the fees from a given base load. However if the fee is too high this number would become negative and later when finding the optima we would have to restrict our domain to the interval on which the function stays positive. Also I am not sure how negative fees may mess this up as they would increase the base predicted demand.
2.) I don’t think this can be studied for a fixed channel. If Alice want’s to send to Bob she needs to study Q_{a,b}^{out}(f) as her own inbound fees on all of her channels. Vice versa Bob need not only to look at his inbound fees on the (A,B) channel but his outbound fees on all other channels. All those functions relate to each other and then of course one might have to consider the entire network of nodes and channels and study how changing one channel cascades through the network.
I thought I would leave those high level comments to get your input before trying to extend the observation / model. So what are your thoughts? Mine are that I am a bit afraid that I am overcomplicating the situation.