Entropy Maximisation and Queues With or Without Balking. An investigation into the impact of generalised maximum entropy solutions on the study of queues with or without arrival balking and their applications to congestion management in communication networks.

Abstract

An investigation into the impact of generalised maximum entropy solutions on the study of queues with or without arrival balking and their applications to congestion management in communication networks Keywords: Queues, Balking, Maximum Entropy (ME) Principle, Global Balance (GB), Queue Length Distribution (QLD), Generalised Geometric (GGeo), Generalised Exponential (GE), Generalised Discrete Half Normal (GdHN), Congestion Management, Packet Dropping Policy (PDP) Generalisations to links between discrete least biased (i.e. maximum entropy (ME)) distribution inferences and Markov chains are conjectured towards the performance modelling, analysis and prediction of general, single server queues with or without arrival balking. New ME solutions, namely the generalised discrete Half Normal (GdHN) and truncated GdHN (GdHNT) distributions are characterised, subject to appropriate mean value constraints, for inferences of stationary discrete state probability distributions. Moreover, a closed form global balance (GB) solution is derived for the queue length distribution (QLD) of the M/GE/1/K queue subject to extended Morse balking, characterised by a Poisson prospective arrival process, i.i.d. generalised exponential (GE) service times and finite capacity, K. In this context, based on comprehensive numerical experimentation, the latter GB solution is conjectured to be a special case of the GdHNT ME distribution. ii Owing to the appropriate operational properties of the M/GE/1/K queue subject to extended Morse balking, this queueing system is applied as an ME performance model of Internet Protocol (IP)-based communication network nodes featuring static or dynamic packet dropping congestion management schemes. A performance evaluation study in terms of the model’s delay is carried out. Subsequently, the QLD’s of the GE/GE/1/K censored queue subject to extended Morse balking under three different composite batch balking and batch blocking policies are solved via the technique of GB. Following comprehensive numerical experimentation, the latter QLD’s are also conjectured to be special cases of the GdHNT. Limitations of this work and open problems which have arisen are included after the conclusions