Analytical Performance Models for Multistage Interconnection Networks with finite, infinite and zero length buffers

Multistage Interconnection Networks (MINs) with crossbar switches have been used
to interconnect processors and memory modules in parallel multiprocessor systems.
They also play an increasingly important role in the development of ATM networks.
In this paper we analyze the general case of MINs, made of kxk switches with
finite, infinite or zero length buffers (unbuffered). The exact solution of the steady
state distribution of the first stage is derived for all cases. We use this to get an
approximation for the steady state distributions in the second stage and beyond. In
the case of unbuffered switches we reach the known exact solution for all the stages
of the MIN. Our results are validated by extensive simulations.