Photon Netw Commun (2006) 12:211–218
DOI 10.1007/s11107-006-0032-3
ORIGINAL ARTICLE
Blocking performance analysis on adaptive routing over WDM
networks with finite wavelength conversion capability
Gee-Swee Poo · Aijun Ding
Received: 27 July 2005 / Revised: 2 March 2006 / Accepted: 2 March 2006 / Published online: 9 September 2006
© Springer Science+Business Media, LLC 2006
Abstract Analytical blocking probability analysis is
important for network design. In this paper, we present
an analytical model for the blocking probability analy-
sis on adaptive routing over the WDM networks with
finite wavelength conversion capability. Modeling the
finite nature of wavelength conversion has been a diffi-
cult task. We make use of the idea of segmented route
to handle the finite wavelength conversion property. In
this approach, a route is divided into a number of seg-
ments separated by wavelength converting nodes. We
then combine the single-link model and the overflow
model to derive the network-wide blocking probability.
There are two distinct features in our technique. First, a
concept of segmented route is used. Second, link state is
considered when calculating the traffic flow. The latter
ensures that the analytical results match closely to prac-
tical network status. Extensive simulations show that the
analytical technique is effective in modeling the block-
ing probability performance for sparse networks.
Keywords Blocking probability · Adaptive routing ·
WDM · Wavelength conversion
Introduction
It is costly and time-consuming to construct a WDM
testbed and measure its performance. An analytical
model is a very useful alternative. However, blocking
performance is difficult to analyze theoretically as the
G.-S. Poo (
B
) · A. Ding
NTRC, School of Electrical and Electronic Engineering,
Nanyang Technological University, 639798 Singapore
e-mail: egspoo@ntu.edu.sg
corresponding queuing network model is complex and
a solution is not readily available.
Extensive research on the theoretical analysis of
blocking probability has been made recently. Girard [1]
has compiled a good book on blocking probability anal-
ysis in circuit-switched networks. Much reference has
been made to the book. For instance, techniques such
as the Brockmeyer model and the Bernoulli–Poisson–
Pascal approximation method are used to analyze non-
Poisson traffic [2–4].
However, most existing results are for static rout-
ing, which includes fixed and alternate routing. In other
words, a certain number of routes are pre-calculated and
fixed in advance. The routes are searched in a fixed order
to find a suitable one to cater for the coming request.
The overflow model is extensively used to analyze static
routing algorithms [5].
Overflow traffic (where the peakedness is always
greater than 1) may be assumed Poisson (where the
peakedness is 1; also known as regular traffic) in most
cases. The assumption makes the Erlang loss formula
applicable. Though overflow traffic is non-Poisson, the
analytical results are normally accurate enough. More-
over, even though the Brockmeyer model or the Ber-
noulli–Poisson–Pascal approximation can be used to
analyze overflow traffic more accurately, the overall
results are not necessarily better.
Birman [6] proposes a single-link model, which mod-
els the random number of idle wavelengths on a link as
a birth-and-death process, to analyze fixed routing and
least loaded routing (LLR). The present work extends
the single-link model and will be described in detail
below.
The wavelength assignment algorithm heavily affects
the analytical model. The available wavelength assign-
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