Anonymity and Fairness in Packet Scheduling: A Quantitative Tradeoff

Abstract

Fairness among multiple users sharing a common resource is an important criterion in the design and evaluation of scheduling algorithms in networks. Anonymous networking, where sources of transmitted packets are undecipherable to an eavesdropper, requires packets arriving at routers from multiple sources to be randomly reordered prior to transmission, which works against the notion of temporal fairness in packet scheduling. Consequently, it is important to understand the relationship between temporal fairness and achievable anonymity. In this paper, this relationship is investigated for three fair scheduling paradigms: First-Come-First-Serve (FCFS), Fair Queuing, and the Proportional Method. Using an information-theoretic metric for anonymity and a common temporal fairness index that measures the degree of out-of-order transmissions, the anonymity achievable under these scheduling paradigms is characterized and their anonymity-fairness tradeoffs are compared. The FCFS and Fair Queuing algorithms have little inherent anonymity, and a significant improvement in anonymity is achieved by relaxing their respective fairness paradigms. The analysis of the relaxed FCFS criterion, in particular, is accomplished by modeling the problem as a stochastic control system that is solved using dynamic programming. The proportional method of scheduling, while unpopular in networks today, is shown to outperform the other fair scheduling algorithms when trading temporal fairness for anonymity, and is also proven to be asymptotically optimal as the buffer size of the scheduler is increased.