Queueing Theory 2

5Non-extensive Maximum Entropy Formalisms and Inductive Inference of a Stable M/G/1 Queue with Heavy Tails

Demetres D. KOUVATSOS¹ and Ismail A. MAGEED¹

¹NetPEn – Networks and Performance Engineering Research Group, School of Electrical Engineering and Computer Science, University of Bradford, UK

An exposition is undertaken of Rényi’s and Tsallis’s non-extensive maximum entropy (NME) formalisms as methods of inductive inference for systems with long-range interactions of order, q (θ.5 < q < 1). The analytic forms of the respective NME state probabilities of a general physical system Q with a countably infinite set S of states are characterized, based on the maximization of the respective entropy functionals, subject to normalization and a finite number of suitable mean value constraints. The credibility of the NME formalisms is justified in terms of four consistency axioms associated with the classical Shannon’s extensive maximum entropy (EME) formalism of systems with short-range interactions of order q equal to 1. Consequently, focusing on an inductive application of Rényi’s and Tsallis’s formalisms on the analysis of a stable M/G/1 queue, novel state probabilities and are explicitly ...