Extended Entropy Maximisation and Queueing Systems with Heavy-Tailed Distributions

Numerous studies on Queueing systems, such as Internet traffic flows, have shown to be bursty, self-similar and/or long-range dependent, because of the heavy (long) tails for the various distributions of interest, including intermittent intervals and queue lengths. Other studies have addressed vacation in no-customers’ queueing system or when the server fails. These patterns are important for capacity planning, performance prediction, and optimization of networks and have a negative impact on their effective functioning. Heavy-tailed distributions have been commonly used by telecommunication engineers to create workloads for simulation studies, which, regrettably, may show peculiar queueing characteristics. To cost-effectively examine the impacts of different network patterns on heavy- tailed queues, new and reliable analytical approaches need to be developed. It is decided to establish a brand-new analytical framework based on optimizing entropy functionals, such as those of Shannon, Rényi, Tsallis, and others that have been suggested within statistical physics and information theory, subject to suitable linear and non-linear system constraints. In both discrete and continuous time domains, new heavy tail analytic performance distributions will be developed, with a focus on those exhibiting the power law behaviour seen in many Internet scenarios. The exposition of two major revolutionary approaches, namely the unification of information geometry and classical queueing systems and unifying information length theory with transient queueing systems. After conclusions, open problems arising from this thesis and limitations are introduced as future work.

Grantor dc:publisher.institution

University of Bradford

Year dc:date.issued

2022

Author dc:creator

• Mohamed, Ismail A.M.

Advisor dc:contributor.advisor

• Zhang, Qichun

• Entropy
• Belief functions
• Belief updates
• Uncertain reasoning
• M/G/1 queue in stability phase
• Generalized entropies
• Extensive and non-extensive maximum entropy formalisms
• Information geometry
• Information length
• Transient queueing systems
• Heavy-tailed distributions

Statement dc:rights

• <a rel="license" href="http://creativecommons.org/licenses/by-nc-nd/3.0/"><img alt="Creative Commons License" style="border-width:0" src="http://i.creativecommons.org/l/by-nc-nd/3.0/88x31.png" /></a><br />The University of Bradford theses are licenced under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-nd/3.0/">Creative Commons Licence</a>.

Language dc:language.iso

en

Handle dc:identifier.uri

http://hdl.handle.net/10454/19756

OAI identifier oai:identifier

oai:bradscholars.brad.ac.uk:10454/19756