Queueing and communication networks governed by generalised Lindley-Loynes equations.
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Date
1993
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Abstract
Several decades after A.K. Erlang originated the theory of queues and queueing
networks, D.V. Lindley added impetus to the development of this field
by determining a recursive relation for waiting times.
Part I of this thesis provides a theoretical treatment of single-server and
multiserver queues described by the basic Lindley relation and its extensions,
which are referred to collectively as Lindley-Loynes equations. The
concepts of stability, and minimal and maximal solutions are investigated.
The interdependence of theory and practice becomes evident in Part II, where
the results of recent and current research are highlighted. While the main
aim of the first part of the thesis is to provide a firm theoretical framework
for the sequel, the objective in Part II is to derive generalised forms of the
Lindley-Loynes equations from different network protocols. Such protocols
are regulated by different switching rules and synchronization constraints.
Parts I and II of the thesis are preceded by Chapter 0 in which several fundamental
ideas (including those on notation and probability) are described.
It is in this chapter too that a more detailed overview of the concept of the
thesis is provided.
Description
Thesis (M.Sc.)-University of Natal, Durban, 1993.
Keywords
Computer network protocols., Computer networks., Theses--Applied mathematics., Queueing theory.