In this paper, we consider a new edge coloring problem to model call scheduling op- timization issues in wireless mesh networks: the proportional coloring. It consists in finding a minimum cost edge coloring of a graph which preserves the propor- tion given by the weights associated to each of its edges. We show that deciding if a weighted graph admits a proportional coloring is pseudo-polynomial while de- termining its proportional chromatic index is NP-hard. We then give lower and upper bounds for this parameter that can be computed in pseudo-polynomial time. We finally identify a class of graphs and a class of weighted graphs for which the proportional chromatic index can be exactly determined.