| Summary: | In this study the maximum entropy formalism [JAYN 57] is suggested
as an alternative theory for general queueing systems of computer
performance analysis. The motivation is to overcome some of the
problems arising in this field and to extend the scope of the results
derived in the context of Markovian queueing theory.
For the M/G/l model a unique maximum entropy solution., satisfying
locALl balance is derived independent of any assumptions about the service
time distribution. However, it is shown that this solution is identical
to the steady state solution of the underlying Marko-v process when the
service time distribution is of the generalised exponential (CE) type.
(The GE-type distribution is a mixture of an exponential term and a unit
impulse function at the origin). For the G/M/1 the maximum entropy
solution is identical in form to that of the underlying Markov process,
but a GE-type distribution still produces the maximum overall similar
distributions.
For the GIG11 model there are three main achievements:
first, the spectral methods are extended to give exaft formulae for
the average number of customers in the system for any G/G/l with rational
Laplace transform. Previously, these results are obtainable only through
simulation and approximation methods.
(ii) secondly, a maximum entropy model is developed and used to obtain
unique solutions for some types of the G/G/l. It is also discussed how
these solutions can be related to the corresponding stochastic processes.
(iii) the importance of the G/GE/l and the GE/GE/l for the analysis of
general networks is discussed and some flow processes for these systems
are characterised.
For general queueing networks it is shown that the maximum entropy
solution is a product of the maximum entropy solutions of the individual
nodes. Accordingly, existing computational algorithms are extended to
cover general networks with FCFS disciplines. Some implementations are
suggested and a flow algorithm is derived. Finally, these results are
iised to improve existing aggregation methods.
In addition, the study includes a number of examples, comparisons,
surveys, useful comments and conclusions.
|
|---|
