  In this paper, we introduce a novel approach for optimal resource allocation
from multiple carriers for users with elastic and inelastic traffic in fourth
generation long term evolution (4G-LTE) system. In our model, we use
logarithmic and sigmoidal-like utility functions to represent the user
applications running on different user equipments (UE)s. We use utility
proportional fairness policy, where the fairness among users is in utility
percentage of the application running on the mobile station. Our objective is
to allocate the resources to the users optimally from multiple carriers. In
addition, every user subscribing for the mobile service is guaranteed to have a
minimum quality-of-service (QoS) with a priority criterion. Our rate allocation
algorithm selects the carrier or multiple carriers that provide the minimum
price for the needed resources. We prove that the novel resource allocation
optimization problem with joint carrier aggregation is convex and therefore the
optimal solution is tractable. We present a distributed algorithm to allocate
the resources optimally from multiple evolved NodeBs (eNodeB)s. Finally, we
present simulation results for the performance of our rate allocation
algorithm.
