Cost Minimization for Cooperative Traffic Relaying Between Primary and Secondary Networks

Cooperation between primary and secondary networks offers significant benefits in data forwarding. But, cost implication in such cooperation is not well understood. In this paper, we explore cost incurred in both primary and secondary networks when they are allowed to relay each other's traffic in a cooperative manner. We model costs in both networks and formulate a multiobjective optimization problem. For this problem, we present a novel algorithm to construct an <inline-formula><tex-math notation="LaTeX">$\epsilon$</tex-math><alternatives> <inline-graphic xlink:href="yuan-ieq1-2795607.gif"/></alternatives></inline-formula>-approximation curve and prove its error bounds in both cost dimensions. Based on the <inline-formula><tex-math notation="LaTeX">$\epsilon$</tex-math> <alternatives><inline-graphic xlink:href="yuan-ieq2-2795607.gif"/></alternatives></inline-formula>-approximation curve, we develop three important applications. The first application is to show the minimum cost value for a single objective (by fixing the other objective as constant) or the relationship between the two objectives over the entire range of possible values. The second application is to address different cost parameters in the primary and secondary networks. We show how to obtain a new approximation curve by scaling the original <inline-formula> <tex-math notation="LaTeX">$\epsilon$</tex-math><alternatives><inline-graphic xlink:href="yuan-ieq3-2795607.gif"/> </alternatives></inline-formula>-approximation curve with appropriate factors and quantify its error bounds. The third application is to use the <inline-formula><tex-math notation="LaTeX">$\epsilon$</tex-math><alternatives> <inline-graphic xlink:href="yuan-ieq4-2795607.gif"/></alternatives></inline-formula>-approximation curve to study a single objective optimization problem with a guaranteed error bound. The results in this paper offer some deep theoretical insights on potential costs incurred in both networks when they are allowed to relay each other's traffic cooperatively.