Blocking probability has been one of the key performance to solve Routing and Wavelength Assignment problem (RWA) indexes in the design of wavelength-routed all-optical WDM networks. To evaluate blocking probability different analytical model are introduced.

1. ICRTEDC-2014 44
Vol. 1, Spl. Issue 2 (May, 2014) e-ISSN: 1694-2310 | p-ISSN: 1694-2426
GV/ICRTEDC/11
ANALYSIS AND STUDY OF
MATHEMATICAL MODELS FOR RWA
PROBLEM IN OPTICAL NETWORKS
1
Preeti Verma, 2
Reena Rani, 3
Dr. Amit Wason
1,2
Swami Devi Dyal Institute of Engineering &Technology, Barwala
3
Ambala College of Engineering & Applied Research, Ambala, Haryana
Abstract- Blocking probability has been one of the
key performance to solve Routing and Wavelength
Assignment problem (RWA) indexes in the design of
wavelength-routed all-optical WDM networks. To
evaluate blocking probability different analytical
model are introduced. Simulation results on different
network topologies and routing policies considered
demonstrate that the simulation results match closely
with the blocking probabilities computed by our
methods for different multiclass call traffic loading
scenarios.
Keywords- Blocking probability, RWA, optical WDM
networks, throughput, performance evaluation
I. NTRODUCTION
Optical networking has been making rapid advances in
recent history. It pays a key role in today’s Internet. They
provide huge capacity through fiber links. During the last
decades, Wavelength Division Multiplexing (WDM)
Optical Networks have emerged as an attractive
architecture for backbone networks. WDM networks
provide high bandwidth, on the order of tens of Gigabits
per second per channel. Hence All-Optical networks based
on WDM using wavelength routing techniques is
considered as a very promising approach for the
realization of future large bandwidth networks. However
recently two observations are driving the research
community to explore the traffic grooming problem in
WDM networks. First, the bandwidth requirements of
most of the current applications are just a fraction of the
bandwidth offered by a single wavelength in WDM
networks. Second, the dominant cost factor in WDM
networks is not the number of wavelengths but rather than
the network components.
The blocking problem is referred as Routing and
Wavelength Assignment problem (RWA). There are many
wavelength assignment algorithms and analytical model
which helps in reducing the blocking probability.
This paper is organised in four sections. Introduction on
optical network and RWA problem is presented in section
I. Section II describes the overview of related work done
regarding RWA problem in optical networks and its
related research papers. Section III describes the analysis
of analytical models to analysis the blocking probability in
different networks. Finally conclusion is given in section
IV.
II. LITERATURE SURVEY
Kalyan Kuppuswamy et al. [1] developed an analytical
methodology for computing approximate blocking
probabilities for multiclass services in optical WDM
networks with wavelength continuity constraints. The
knapsack approximation used in computing the probability
distribution of the no. of the idle wavelength on links and
applied this methodology to the three dynamic RWA
policies- FR, LLR and FAR all with random wavelength
selection. In addition the methodology adds some analytic
insights. In analysis it is observed that the per-class
pairwise approximate blocking probability for the FR
policy can be decomposed as a sum of two terms: one that
represent blocking probability with no wavelength
continuity constraints and other with the wavelength
continuity constraints.
Ding Zhemin et al. [2] designed a framework based on
blocking island (BI) to solve the problems of placement of
wavelength converters (WC) as well as RWA in all optical
networks. A simple heuristic for the placement of WCs in
an arbitrary mesh network and a general RWA algorithm
have been proposed. The proposed algorithms and
analytical models also helps to solve various additional
problems including traffic grooming, Optical traffic
engineering, and network failure allocation.
Jong-Seon Kim et al. [3] proposed three dynamic RWA
algorithms-named F (w, l), MCR, and LSNLR which
make a routing decision on the basis of per-route status
then subsequently choose a wavelength and also selects
the set of predetermined routes which results in
significantly lower blocking probabilities than the
shortest-route-based method also requires much less
online computation for call processing than well-known
algorithms such as SPREAD. In particular algorithm F (w,
l) significantly outperforms other existing algorithms in
terms of blocking and also requires much less online
computation for call processing.
Yvan Pointurier et al. [4] presented two classes of adaptive
Quality of Transmission (QoT)-aware RWA algorithms
for networks with physical impairments. The proposed
RWA algorithms can sharply decrease the blocking
probability, increase QoT & fairness, low bit error rate
(BER) and also mitigate crosstalk effects in comparison
with traditional algorithms even when the networks are
large and heavily loaded.
Jijun Zhao et al. [5] proposed a bidirectional Quality of
Service (QoS) differentiation framework that allows to
simultaneously consider both the PLIs and the set up
delay, giving rise to the design of our ISD-RWA
algorithm. The results showed that this algorithm performs

2. 45 ICRTEDC -2014
well in different network topologies and reduces the
blocking probability of the transparent optical networks
significantly.
Ling Li et al. [6] proposed two new dynamic routing
algorithms based on path and neighborhood link
congestion in all-optical wavelength-routed networks. The
fixed-paths least congestion (FPLC) routing used with the
first fit wavelength-assignment methods to achieve good
performance. The routing using neighborhood information
algorithm employed as a trade-off between network
performance in terms of blocking probability versus set up
delay and control overhead.
Shizhong Xu et al. [7] discussed the RWA problem in
multifiber networks. In this, RWA problem reduces to the
problem of finding a shortest path by making use of the
special structure of layered graph. In this two strategies
PACK and SPREAD are proposed for this problem and
also used the shortest path algorithm M_Dijkstra based on
layered graph. The algorithm used can also effectively
deal with the failure of fiber/link and node and thus
improves the blocking probability.
Xiaowen Chu et al. [8] proposed a new dynamic RWA
algorithm, called WLCR-FF algorithm to solve the RWA
problem in the presence of wavelength conversion. This
algorithm makes a good trade-off between the average
route length and the link utilization and also improves the
blocking performance when compared with conventional
dynamic RWA algorithms.
Xi Yang et al. [9] proposed the problem of dynamic
routing in translucent WDM optical networks. In this
sparse placement of regenerators used to overcome
physical impairments and wavelength contention
introduced by fully transparent networks. To solve the
RWA problem they introduced an intradomain routing
algorithm IDDBR which establishes the end-to-end
lightpaths crossing multiple domain thus boost efficiency
and improves the blocking probability in the network.
III.ANALYSIS OF ANALYTICAL MODEL
The approximate analytical models developed for the clear
channel blocking probability of the network with arbitrary
topology, both with or without wavelength translations.
The goal of our analysis is to calculate the blocking
probability.
In order to do analysis the following assumptions are
made:
1.The network is connected in an arbitrary topology. Each
link has a fixed number of wavelengths.
2.Each station has array of transmitters and receivers,
where W is the wavelength carried by the fiber.
3.Point to point traffic is considered.
4.There is no Queuing of connection request. The
connection blocked will suddenly be discarded.
5.Link loads are mutually independent.
6.Static Routing and Dynamic Routing both are assumed.
Kalyan Kuppuswamy et al. [1] analysed the fixed-point
approximate blocking probability computations with
different loading scenarios. Blocking probability of the
network is compared depending upon the number of
channels, number of links and traffic load per link (in
Erlang).
Ding Zhemin et al. [2] examined the performance of
placement of wavelength converters and the performance
of the BI-RWA algorithms using the NSFNet. They
employed a dynamic traffic model in which calls arrive at
each node according to an independent Poisson process
with arrival rate . An arriving section is equally likely to
be delivered to any node in the network.
Jong-Seon Kim et al. [3] evaluated the blocking
probabilities of the proposed dynamic RWA algorithms on
two network topologies (NSFNET network for irregular as
well as regular topology) and analysed the comparison of
blocking probability with the traffic load (Erlang) for both
uniform and non-uniform traffic distribution. As the load
increases the blocking probability also increases.
Yuan Pointurier et al. [4] evaluated the QoT-aware
adaptive RWA algorithm with optional coding by using
NSFNET topology. When optional coding is used and all
physical impairments are accounted then blocking
probabilities lowered but the crosstalk effects were not
completely removed.
Jijun Zhao et al. [5] evaluated the performance of the ISD-
RWA algorithm by using network topologies of the US
nation-wide network and the COST 239 network. They
analysed the comparison of blocking probability with the
network load (Erlang) for dynamic traffic and also
considered different connection requests with different
QoS levels.
Ling Li et al. [6] assessed the accuracy of analytical model
and the analytical model is applied to two network
topologies, a regular Mesh-Torus network and an irregular
NSFNet T1 backbone network. They compared the
network blocking probability versus the traffic load per
source-destination (s-d) pair for eight wavelengths per link
for different correlation models. In both networks the
analytical results are good for heavy to moderate load but
not for the light traffic load.
Shizhong Xu et al. [7] used two dynamic RWA algorithms
PACK & SPREAD and then studied the performance of
these algorithms on two regular network topologies and
two irregular network topologies. The blocking
performance of two kinds of networks is studied with
respect to load (Erlang). One is the network with even
links and other is the network with uneven links.
Xiaowen Chu et al. [8] investigated the performance of
WLCR-FF algorithm over the other algorithms in 8-node
ring topology, 25-node mesh-torus topology and 14-node
NSFNET topology. In all simulations, the lightpath
connection requests are generated as a Poisson Process
and the connection holding time is exponentially
distributed.
IV.CONCLUSION
The performance optimization of all-optical WDM
network is necessary because of its increasing demand.
Blocking probability effects more on the RWA problem so
they analysed the response of blocking probability for
varying traffic load (Erlang). The analysis showed that as
the load per link increases the blocking probability also
increases and the response of wavelength conversions are
much better than without wavelength conversions. For
lower load values, limited wavelength conversion and full
wavelength conversion gives similar results but as load per
link increases, sparse wavelength conversion has less
blocking as compared to even full wavelength conversion
and finally the throughput is also found to be better.

3. ICRTEDC-2014 46
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