This paper analysis a different methods to find optimal path for services and power allocation to heterogeneous wireless network. Under heterogeneous wireless networks, a user can send data through a single or multi RATs (Radio Access Technology) simultaneously. The objective of this paper is to choose the optimal path for the services and power allocation to that bandwidth (BW) distributed joint allocation algorithm using Newton and modified Newton are adopted and the total system capacity compared. The analysis is done in Matlab and simulation results are compared. The numerical result shows that compare to Newton method, modified Newton method maximize the total system capacity.