This is the abstract from my Thesis, which I submitted at the end of August 2000, and which I successfully defended at my viva six weeks later...
This Thesis describes work carried out by Martin David Biddiscombe on the subject of the allocation and management of telecommunications or computer network resources. The core of the Thesis relates to the distribution of resources between users competing for access to a congested network.
In a communication network where there is competition between users, or consortia of users, there must be an agreed strategy for dividing resources when the combined demand from the users exceeds the network's available capacity. This Thesis focuses on one such allocation strategy: proportional fairness, by which access to resources is allocated in proportion to users' bids. In this manner, the network becomes analogous to a market place – user bids may be monetary, although they are certainly not restricted to so being. For example, user bids may also be pre-determined by policy or service level agreement. The advantages of such an analogy and proportional fairness in particular are outlined.
Several analytical results relating to proportional fairness are proved, and it is shown that the original definition is flawed in a minor way. This flaw is corrected and the revised definition is shown to be consistent with results obtained both analytically and numerically. A simple method for determining proportionally fair resource allocations on arbitrarily complex networks is developed and demonstrated. The performance of this method is investigated.
Any control strategy must be stable and its implementation should be technically feasible. The stability and feasibility of methods for implementing proportional fairness are discussed, along with the impact of slackening the assumptions relied upon to demonstrate the advantages of proportionally fair allocations. In particular, the requirements of real-time traffic within integrated networks, and handling of such real-time traffic within the framework of proportional fairness are considered.
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