  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 objective 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.
