Source anonymity in fair scheduling: A case for the proportional method

Fairness amongst multiple users sharing a common resource has been an important criterion in the evaluation of scheduling algorithms in networks. Anonymous networking, where sources of transmitted packets are undecipherable to an eavesdropper, requires that packets from multiple sources are randomly reordered prior to transmission which works against the notion of fair scheduling. Consequently, it is important to understand the relationship between fairness and achievable anonymity in networking. In this paper, this relationship is characterized for the class of fair scheduling axioms defined by considering the equal treatment ex ante and demand mono-tonicity, under which the proportional method is known to be the unique scheduling algorithm that achieves the desired fairness. Using an information theoretic quantitative framework, the anonymity of this scheduling algorithm is characterized and proven to be asymptotically optimal with increase in buffer size. The anonymity achieved by the proportional method is also shown to be significantly better than conventional fair scheduling algorithms such as first come first serve and round robin, thus making a case for its application in data networks.