The core of the Next Generation Network (NGN) is a converging point of various classes of session flows. As a result, despite the presence of admission control techniques, a competition for resources becomes inevitable. In such an environment, certain flows may be disadvantaged due to others consuming or withholding access to a resource that is limited in availability. Therefore, it is extremely important to explore a solution for equitable resource distribution, which does not disadvantage either class of session flow. In light of this, this paper develops an ecologically inspired graphical theory for equitable resource distribution in a multi-resource, multi-class environment. Optimal resource supply levels required for a stable coexistence could be accurately predicted by the proposed graphical theory. Analytical proof and simulation results are provided for supporting the above argument.