On optimization formulations for radio resource allocation subject to common transmission rate

We study a radio resource allocation problem in mobile communication systems. As the distinct characteristic of this problem, a common data transmission rate is used on all channels allocated to a user. Because the channels differ in their quality, for each user the achievable rate varies by channel. Thus allocating more channels does not necessarily increase the total rate, as the common rate is constrained to be the lowest one supported by the allocated channels. Radio resource allocation subject to the common-rate constraint is of practical relevance, though little attention has been paid to modeling and solving the problem. We take a mathematical optimization perspective with focus on modeling. We first provide a complexity analysis. Next, several integer linear programming (ILP) formulations for the problem, including compact as well as non-compact models, are derived. The bulk of our analysis consists in a rigorous comparative study of their linear programming (LP) relaxations, to reveal the relationship between the formulations in terms of bounding. Computational experiments are presented to illustrate the numerical performance in bounding and LP-assisted problem solving. Our theoretical analysis and numerical results together serve the aim of setting a ground for the next step of developing model-based and tailored optimization methods.