In this paper, we introduce a novel approach for optimal resource allocation with frequency reuse for users with elastic and inelastic traffic in cellular networks. In our model, we represent users' applications running on different user equipments (UE)s by logarithmic and sigmoid utility functions. We applied utility proportional fairness allocation policy, i.e. the resources are allocated among users with fairness in utility percentage of the application running on each mobile station. Our

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... ective is to allocate the cellular system resources to mobile users optimally from a multi-cell network. In our model, a minimum quality-of-service (QoS) is guaranteed to every user subscribing for the mobile service with priority given to users with real-time applications. We show that the novel resource allocation optimization problem with frequency reuse is convex and therefore the optimal solution is tractable. We present a distributed algorithm to allocate the resources optimally from Mobility Management Entity (MME) to base stations (BS)s sectors. Finally, we present the simulation results for the performance of our rate allocation algorithm.