Stochastic Differential Equations (SDEs) constitute an important mathematical tool with appli-
cations in many areas of research such as fi physics and computer science. The analytical study
of these equations is problematic, especially in the multi-dimensional case, for this reason,
numerical techniques prove to be necessary to solve such equations. In this project, parallel
numerical techniques for SDEs are studied. Two kinds of parallelism will be explored: in space and
in time. Implementation of these techniques applied to several systems of SDEs will be realised
(using C++ and MPI) and performance measures like speedup and efficiency will be investigated on
medium-scale computer clusters.
In the second part of the thesis, a major application area in the fi of computer and com-
munication networks will be studied, that of second-order stochastic fl networks. Recently,
interest has been growing in networks with large numbers of components, with application in diverse
fi such as internet performance evaluation, the spread of computer viruses and biochemistry. Such
models have such a large state space that discrete-state models are numer- ically infeasible due to
the explosion in the size of the state space. Fluid approximations are therefore preferable and
tend to be more accurate in large state spaces. In fl models, an integer counter is replaced by a
real number representing a volume and the solution method becomes based on diff tial equations
rather than on diff equations. Some analytical solutions are possible in special cases but in
general, numerical methods are required. In this project, parallel numerical studies of second
order fl networks will be conducted and re- sults in the context of the performance of computer and
communication networks have been
analysed, facilitating design improvement of their architecture.