Generalised Entropy Maximisation and Queues with Bursty and/or Heavy Tails

• Published in: Network Performance Engineering pp. 357 - 392
• Main Authors: Kouvatsos, Demetres D., Assi, Salam A.
• Format: Book Chapter
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg 2011
• Series: Lecture Notes in Computer Science
• Subjects: burstiness; Extensive maximum entropy (EME) formalism; fractional Brownian motion (fBm); generalised (modified) geometric (GGeo) distribution; generalised exponential (GE) distribution; generalised Zipf-Mandelbrot (G-Z-M) distribution; heterogeneous networks; long-range dependence (LRD); non-extensive maximum entropy formalism (NME); performance evaluation; queueing systems; self-similarity; short-range dependence (SRD); traffic characterisation
• ISBN: 3642027415; 9783642027413
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-642-02742-0_17

An exposition of the ‘extensive’ (EME) and ‘non-extensive’ (NME) maximum entropy formalisms is undertaken in conjunction with their applicability into the analysis of queues with bursty and/or heavy tails that are often observed in performance evaluation studies of heterogeneous networks and Internet exhibiting traffic burstiness, self-similarity and long-range dependence (LRD). The credibility of these formalisms, as methods of inductive inference, for the study of physical systems with both short-range and long-range interactions is explored in terms of four potential consistency axioms. Focusing on stable single server queues, it is shown that the EME and NME state probabilities are characterized by generalised types of modified geometric and Zipf-Mandelbrot distributions depicting, respectively, bursty generalized exponential and/or heavy tails with asymptotic power law behaviour. Numerical experiments are included to highlight the credibility of the maximum entropy solutions and assess the combined impact of traffic burstiness and self-similarity on the performance of the queue.