Abstract:
The performance modeller may attempt to quantitatively analyse
the behaviour of computer systems by building performance models.
Such models may become unwieldy, and so high-level structured
modelling modelling techniques have been developed. A stochastic
process algebra (SPA) provides such a technique, a
compositional modelling calculus. Hillston's PEPA is an SPA, a
classical process algebra enhanced to represent the performance of
systems. This thesis uses PEPA as a foundation, and examines
different ways to assist the SPA performance modeller.
A weak stage in the SPA methodology is the calculation of concrete
performance measures, since much research does not focus beyond a
steady-state probability vector. A framework is developed for
specifying steady-state performance measures for PEPA models. The
technique is used at the high-level of the process algebra, and not
applied directly to states, or the stochastic process. It employs
an enhanced modal logic to allow the modeller to identify
interesting model behaviour. Furthermore, the modeller may choose
to study only the behaviour of subcomponents in the model context.
The method automatically specifies a Markov reward model (MRM). The
modal logic is suitably expressive`; it is shown to characterise
PEPA's strong equivalence relation. Conditions are given
under which model subcomponents may be aggregated such that the MRM
is guaranteed to be strongly lumpable. The technique is
compared to various other solutions to the reward specification
problem.
If a randomly distributed model feature possesses the
insensitivity property, then the equilibrium solution of the
model only depends on the mean of the distribution. A new SPA
combinator is defined which builds a model from a set of simple
components restricted to queue to perform particular
activities. It is demonstrated that a subset of the activities of
these SPA models are insensitive, and therefore may have generally
distributed durations. Furthermore, it is proven that a model of
this structure exhibits a product form solution over its
submodels, allowing its solution to be expressed as a product over
the smaller solutions of its parts. This work leads to a more
general examination of insensitivity in SPA models. An extension to
PEPA is defined which allows activities with generally
distributed durations. Balance conditions are given which
guarantee the insensitivity of these activities. However these
conditions are strong, and at the level of the stochastic
process.
Models of transaction processing systems (TPS) are presented
as a case study. These systems consist of a centralised database,
and a set of transactions which access database objects.
Sample performance measures are specified for TPS models, and a
model of a TPS is constructed using the new combinator,
guaranteeing the insensitivity of a subset of its activities.
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