Fairness in Communication and Computer Network Design

Abstract: In communication networks, fair sharing of resources is an important issue for one main reason. The growth of network capacity is in general not matching the rapid growth of traffic. Consequently, the resources consumed by each user have to be limited. This implies that users cannot always be assigned the end-to-end bandwidth they ask for. Instead, the limited network resources should be distributed to users in a way that assures fair end-to-end bandwidth assignment among them. Obtaining fairness between network users and at the same time assuring efficient network utilization, is a source of non-trivial network optimization problems. Complicating factors are that each user has limited access to the (limited) network resources and that different users require and consume different amounts and types of resources. In this thesis different types of optimization problems associated with fair resource sharing in communication networks are studied. Initially, the notions of max-min fairness, proportional fairness, alpha-fairness etc., are put in a formal framework of fair rational preference relations. A clear, unified definition of fairness is presented. The theory is first applied to different types of allocation problems. Focus is put on convex and non-convex max-min fair traffic allocation problems, and a difference in difficulty between the two groups of problems is demonstrated. The studies are continued by an investigation of proportionally fair dimensioning. Two different cases are studied -- a simpler, when no resilience to failures is required, and a more complicated, assuming the possibility of link failures. In the context of fair sharing of the resources of a communication network, this thesis presents several original theoretical findings as well as solution algorithms for the studied problems. The results are accompanied by numerical results, illustrating algorithm efficiency for virtually all of the studied problems.