'Institute of Electrical and Electronics Engineers (IEEE)'
Doi
Abstract
Cataloged from PDF version of article.In this paper, we study the blocking probabilities
in a wavelength division multiplexing-based asynchronous
bufferless optical packet/burst switch equipped with a bank of
tuneable wavelength converters dedicated to each output fiber
line. Wavelength converter sharing, also referred to as partial
wavelength conversion, corresponds to the case of a number
of converters shared amongst a larger number of wavelength
channels. In this study, we present a probabilistic framework for
exactly calculating the packet blocking probabilities for optical
packet/burst switching systems utilizing wavelength converter
sharing. In our model, packet arrivals at the optical switch are
first assumed to be Poisson and later generalized to the more
general Markovian arrival process to cope with very general
traffic patterns whereas packet lengths are assumed to be exponentially
distributed. As opposed to the existing literature based
on approximations and/or simulations, we formulate the problem
as one of finding the steady-state solution of a continuous-time
Markov chain with a block tridiagonal infinitesimal generator. To
find such solutions, we propose a numerically efficient and stable
algorithm based on block tridiagonal LU factorizations. We show
that exact blocking probabilities can be efficiently calculated
even for very large systems and rare blocking probabilities, e.g.,
systems with 256 wavelengths per fiber and blocking probabilities
in the order of 10−40. Relying on the stability and speed of the
proposed algorithm, we also provide a means of provisioning
wavelength channels and converters in optical packet/burst
switching systems
