About the relation between the Relative Fairness Bound (RFB) measure and the apportionment problem

Fairness is one of the most important issues found in many resource allocation problems. In this article we describe the Relative Fairness Bound measure which is often used to evaluate fairness of different packet scheduling algorithms found in communication networks. We examine this measure using the apportionment theory which is used to analyze the apportionment of seats in a parliament. The main result of our analysis is that there exists no practical algorithm optimizing the RFB measure. We show that any algorithm optimizing the relative fairness bound must use potentially huge buffer to collect incoming packets that have to be scheduled. We show that a method optimizing the RFB measure is neither house monotone nor population monotone.