[Paper Review] A Utility Proportional Fairness Radio Resource Block Allocation in Cellular Networks

Mo Ghorbanzadeh, Ahmed Abdelhadi+1 more|arXiv (Cornell University)|Jun 9, 2014

Advanced Wireless Network Optimization12 references3 citations

TL;DR

This paper proposes a utility proportional fairness radio resource block (RB) allocation scheme for cellular networks that optimizes resource allocation for users with real-time (sigmoidal utility) and delay-tolerant (logarithmic utility) applications. By using Lagrangian relaxation to convert the integer nonlinear RB allocation problem into a convex continuous rate optimization, and applying boundary mapping to select discrete RB candidates, the method ensures proportional fairness, guarantees minimum QoS, and achieves low computational complexity with fast runtime—demonstrated at 0.24–0.30 seconds in MATLAB and under 16 seconds for dynamic bandwidth changes.

ABSTRACT

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.

Motivation & Objective

• To address the challenge of efficient and fair radio resource block (RB) allocation in cellular networks with mixed traffic types—real-time (inelastic) and delay-tolerant (elastic).
• To ensure quality of service (QoS) for real-time applications while maintaining fairness and system utility in dynamic, resource-constrained environments.
• To develop a computationally efficient and temporally fast algorithm suitable for practical deployment in LTE and similar cellular infrastructures.
• To investigate the sensitivity of the allocation scheme to variations in available bandwidth and user demand.

Proposed method

• Formulates the RB allocation as an integer nonlinear optimization problem, modeling user satisfaction via sigmoidal (real-time) and logarithmic (delay-tolerant) utility functions.
• Applies Lagrangian relaxation to transform the discrete, non-convex problem into a continuous, convex dual optimization problem solvable via Lagrange multipliers.
• Uses boundary mapping to generate discrete RB candidates—lower and upper bounds—around each continuous optimal rate, reducing the search space.
• Selects only RB configurations that satisfy the total bandwidth constraint, eliminating infeasible candidates to reduce computational complexity.
• Evaluates feasible RB sets using the utility proportional fairness framework to maximize overall system utility.
• Employs a semi-logarithmic computational complexity analysis to demonstrate scalability, showing reduction from O(n^M) to O(2^M) by excluding infeasible RB assignments.

Experimental results

Research questions

• RQ1 How can resource block allocation be optimized to fairly serve users with real-time and delay-tolerant applications under a utility proportional fairness framework?
• RQ2 What is the computational complexity of the proposed RB allocation scheme, and how can it be reduced without sacrificing optimality?
• RQ3 How does the algorithm perform in terms of runtime and scalability under dynamic bandwidth and user demand changes?
• RQ4 To what extent does the algorithm prioritize real-time applications while guaranteeing minimum QoS for all users?
• RQ5 How sensitive is the resource allocation outcome to variations in available bandwidth and user utility parameters?

Key findings

• The proposed algorithm achieves a runtime of 0.24–0.30 seconds in MATLAB for fixed eNB bandwidth, and under 16 seconds when bandwidth changes from 50 to 100 units, indicating high temporal efficiency.
• Computational complexity is reduced from O(n^M) to O(2^M) by excluding infeasible RB candidates, significantly improving scalability—e.g., from 10^200 to 2^100 computations for 100 UEs with 10 candidates each.
• The scheme guarantees minimum QoS for all users, with no user drops, due to its proportional fairness foundation and constraint-based filtering.
• Real-time applications are prioritized over delay-tolerant ones, as evidenced by higher resource allocation and utility gains under the same bandwidth conditions.
• When eNB bandwidth exceeds the sum of utility inflection points, delay-tolerant users receive significantly more RBs, indicating adaptive fairness.
• The algorithm demonstrates strong sensitivity to resource availability: higher bandwidth leads to lower user bids and increased RB allocations, especially for delay-tolerant users.