Fairness of schedules in the control of packet-switched networks

Fairness is one of the most important issues found in many resource allocation problems. In this paper we describe the problem of optimizing two fairness measures: the Relative Fairness Bound (RFB) and the Absolute Fairness Bound (AFB), which are used in the packet-switched networks to evaluate the fairness of the packet scheduling disciplines. In our work we use the apportionment theory to prove some properties of the RFB measure. We examine the properties of the AFB measure on the basis of transformation to the Product Rate Variation problem considered in the context of Just-in-Time production systems.