  This paper presents a radio resource block allocation optimization problem
for cellular communications systems with users running delay-tolerant and
real-time applications, generating elastic and inelastic traffic on the network
and being modelled as logarithmic and sigmoidal utilities respectively. The
optimization is cast under a utility proportional fairness framework aiming at
maximizing the cellular systems utility whilst allocating users the resource
blocks with an eye on application quality of service requirements and on the
procedural temporal and computational efficiency. Ultimately, the sensitivity
of the proposed modus operandi to the resource variations is investigated.
