In this paper, we propose a new caluculation method of user equilibrium assignment and derive the equilibrium arrangement of housings and jobs theoretically in the urban model with constrained capacity. When doing formulization, we show that minimizing the summation of the costs, commuting travel cost, working travel cost and location cost caused by the density of housings or jobs node, is non-convex quadratic programming problem and the problem results in quadratic programming problem using reformulation-linearization technique, and as a result we are able to derive the equilibrium arrangement of distribution of housings and jobs.
