Paper
Comparative effectiveness of certain queueing systems with adaptive demand and service mechanisms

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Abstract

This paper sets out to evaluate simple queueing models embodying the concept of adaptation of service to demand and vice versa, systems which hold out the promise of improved operational characteristics by comparison with conventional non-adaptive systems. Over the many years during which research in queueing theory has been in progress there has been little concern with models of this kind, yet it is in the direction of environmental adaptation that one must look for operational improvements. The models studied are mainly of birth and death type. Some consideration is given to renewal models which, in a certain sense, are the equivalents of birth and death types. The emphasis in the paper is placed on the requirements of an operational assessment and on its realization. The use of digital computers in research of this kind is underlined. For illustration extracts from [9] are used to describe the performance of three fundamental adaptive systems.

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Cited by (2)

  • A state-dependent queueing system with asymptotic logarithmic distribution

    2018, Journal of Mathematical Analysis and Applications
    Citation Excerpt :

    A systematic study of the birth–death queue with varying arrival and service rates has been carried out by Abate, Conolly, Chan, Gupta and Srinivasa Rao, Hadidi, Kyriakidis, Natvig, Parthasarathy and Servaraju, Sharma, Sudhesh, Van Doorn. These authors give transient and stationary solutions for the queue length process, waiting time, busy period and output for special birth–death queues with adaptive demand and service mechanism (see [1,5,11–13,22,24,25,32–34,36,39,40,44]). The transient analysis of the state-dependent queueing systems often presents considerable difficulties and also numerical solutions are generally difficult to get.

Jimmy Chan is an Operational Research Scientist in the Management Service Division of the North-East Thames Regional Health Authority. He was an undergraduate and postgraduate student at Chelsea College, University of London. The subject matter of this paper is a condensed version of part of his Ph.D. Thesis.

Brian Conolly is the Professor of Mathematics (Operational Research) in the University of London, at Chelsea College. He is interested in all aspects of applicable mathematics and has published extensively, in particular in the area of Applied Probability. He is a member of the editorial advisory board of this journal.

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