Among the important issues, the question of justice and equality in the design of the network is being used. There have been various concepts of equality, including equality between generations, equality between landowners and equality between the users of the system. As well as ways for considering the measure in question is investigated, such as problem solving multi-objective or add conditions of equality as a restriction. In this study, the purpose of social justice that is considered urban development plan including toll of civilians and their spending in a way that conflicts of interests between any pair of area traffic network users does not exceed acceptable value. A parallel programming model to solve two problem of pricing and in terms of social justice networks is investigated. The results of two-state solution with and without observing the conditions of justice about the optimal toll rate has similar results. In the event that the optimal toll rate for non-compliance with the requirement of justice was equal to 1.85 currency, in the case of compliance with the conditions of social justice and equality, this rate was equal to 1.6 currency. Observation shoed that optimality of the objective function and answer are reduced, the general interest of the users of the network declined.