IJECT Vol. 6, Issue 3, July - Sept 2015
ISSN : 2230-7109 (Online) | ISSN : 2230-9543 (Print)
Random Assignment of Wavelength Using Normal
Distribution in WDM Networks
1
S. Suryanarayana, 2Dr. K.Ravindra, 3Dr. K. Chennakesava Reddy
Dept. of ECE, Kallam Haranadhareddy Institute of technology, Guntur, AP, India
Mallareddy Institute of Tech & Science, Dhulapally, Secunderabad, Telangana, India
3
JNTU College of Engg, Jagityal (JNTUH), Karimnagar, Telangana, India
1
2
Abstract
In this work, a new random assignment model is proposed based
on the normal distribution assignment. This model yields much
better results compared to the traditional random assignment
models that is based on uniform assignment. The performance
of the proposed model is similar to the first fit model. Also, the
flexibility of choosing any channel for maximum assignment of
load is part of the proposed model which is missing in the first
fit model. Over all, the proposed model over comes the issues
of both the first fit model and random assignment models. The
blocking probabilities are calculated based Erlang B formula and
the results are plotted for all the three models for several cases. In
all the cases, it is proved that random assignment model based on
the normal distribution yields best results among all
Keywords
WDM, RWA, Random Assignment, First Fit Assignment
I. Introduction
Optical fiber networks are popular for their bandwidth capacity
compared to other communication channels. However there are
certain limitations that exist in the optical fiber technology in
using the single channel transmission due to dispersive effects.
The Wavelength Division Multiplexing (WDM) has become an
important play in the promotion of the optical fiber technology due
to the versatility that WDM offers. One of the important features
of WDM is, it can provide multiple channels in each link. Each
channel is characterized by a unique wavelength. That means in
each of the optical fiber link, multiple communication channels can
be established simultaneously and each communication channel is
supported by a distinct wavelength [1-2]. WDM has become the
most preferred technology in the area of communication since it
can offer up to 128 channels in just one strand of the optical fiber.
WDM can also offer solution to the problems of different data
formats and integration of the data with voice communications.
The success of the WDM lies in the assignment of the wavelength
as and when call request comes and the routing of the request in the
communication network. This challenge of optimal Routing and
Wavelength Assignment (RWA) is the core of the WDM technology
[3]. RWA may be defined in brief terms as the establishment
of the lightpath in the shortest path among all available paths
between the source node and end node; and further assigning
the wavelengths along the selected shortest path. Establishment
of the light path in the shortest path is known as the routing
and assignment of the channel with a wavelength is known as
wavelength assignment. These two features put together are known
as Routing and Wavelength Assignment (RWA).
The routing can be a fixed routing, fixed alternate routing or
adaptive routing. The fixed routing can be established using any of
the algorithms that can determine the shortest path in the network.
There are several algorithms availed that can be used in the fixed
routing. One of the most popular algorithms in this field is Dijkstra
algorithm [4]. In this method, the shortest path is found between
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the source node and destination node offline and, once the path is
chosen then the wavelength is assigned for the lightpath. In Fixed
alternate routing, instead limiting to one shortest path between the
source and destination nodes, all possible paths are determined
[4-5]. In adapting routing, all paths are calculated just before the
assignment of the wavelength and it is carried out online in contrast
to the other two methods mentioned above, which determines the
shortest paths offline [6].
The wavelength assignment can be carried out on two popular
methods reported in the literature [6-8]. These are Random
wavelength assignment and First-fit assignment. In Random
Assignment method, the channel is allocated by selecting randomly
from the available free channels. That means the wavelengths are
chosen randomly from the available wavelengths and assigned to
the request. The random selection of the channels follows uniform
distribution [7]. In the other method i.e. in First-fit assignment,
the first channel is assigned to the request. In order achieve this,
all the channels are numbered starting from the lowest frequency
band.
The performance of the network is analyzed using the blocking
probability and it has been determined that the first fit assignment
yields best results compared to the random wavelength assignment
[9-10].
In this work, it has been proven that random assignment also
yields best results like first fit assignment and in fact, the algorithm
developed in this work shows that the random assignment based
on uniform distribution and first fit algorithms are special cases
under certain conditions of a common assignment solution.
Probability model
The wavelength assignment problem that is mentioned above in
RWA can be addressed with random assignment of wavelength or
with first fit models. In order to establish the light path successfully,
there are two constraints that need to be satisfied. They are:
• Wavelength continuity constraint
• Distinct wavelength constraint
The first constraint requires the wave length assigned must be
same in all the links for a selected lightpath. The second constraint
requires that each lightpath in a link must be assigned a distinct
wavelength. The call is said to be blocked when there is no free
wavelength available for assignment in a link. The blocking
probability is calculated using
Pblocking =
N block
N gen
(1)
where Pblocking is the blocking probability, N block is the number
of calls blocked and N gen is the number of calls generated. The
blocking probability can be calculated using the in-famous Erlang
B formula
LC
C!
Pblocking ( L, C ) =
C
Lj
∑ j!
j =0
(2)
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IJECT Vol. 6, Issue 3, July - Sept 2015
where Pblocking ( L, C ) is the blocking probability, L is the load and
C is the number of channels or wavelengths.
When calculating the blocking probability, the main assumptions
made are, there are definite number of links connected in a arbitrary
network topology and each link has certain number of wavelengths
available for assignment. When a call is arrived, it is assigned a
wavelength in first link and if all the channels are busy, then the
call is not kept in the queue, but will be discarded. The routing
is determined offline and it is already predetermined when the
wavelengths are assigned. The load on each link is independent
of the load on the other links.
In this work, three algorithms are simulated for the wavelength
assignment, namely,
• First Fit assignment
• Random assignment based on uniform distribution
• Random assignment based on Normal Distribution
The first fit assignment and random assignment based on uniform
distribution are a well known assignment algorithms in the literature
[9-10]. The third assignment model, i.e. random assignment based
on normal distribution is proposed in this work and it is shown
that the random assignment based on normal distribution yields
lower blocking probabilities compared to random assignment
based on uniform distribution and also yields the performance
similar to first fit model. Hence it is proposed to use assignment
based on normal distribution in place of the first fit assignment
and random assignment based on uniform distribution.
In First fit assignment, the wavelengths in the traffic matrix are
sorted out in a non-decreasing order. When a call arrives, the first
available wavelength is assigned. When a next call arrives, the
next available wavelength is assigned. In case the first wavelength
that was assigned is free when the second call arrives, then the
second wavelength is never assigned. In this assignment model,
the wavelengths in the lower bands are always loaded most and
the ones in the higher bands are least loaded. All the channels are
not equally utilized.
In an uniform distribution based assignment model, all the channels
are uniformly assigned. When a call arrives, then a random number
is generated based on the uniform distribution, and the channel
number is selected based on the random number generated. In
this model, all the channels are equally utilized. However, if
the channels in a link have non uniform frequency bands, then
this model many not be suitable. For example, if the channels at
the center bands are reserved for integrated higher data or voice
communication, then the first model or uniform model fails. This
is due to the reason that first fit model does not differentiate when
a call arrives if it is to be assigned to a center band channels. First
fit model always assigns first available free channels. Similarly,
uniform distribution based assignment model also does not resolve
this issue since it assigns the channels randomly. If uniform
distribution based assignment model is chosen for assignment,
the performance of the uniform distribution based assignment
model compared to the first fit model is very poor [9].
A third model is proposed in this work which overcomes the
problems of inability in assigning a selected channel to a particular
call sequences, and lower performance of the random assignment
model. The proposed model uses normal distribution which allows
the flexibility to assign any selected channel to be assigned most,
not just limited to the first free channel, and to get the performance
of the random assignment model close enough to that of the first
fit model. The normal distribution is characterized by mean and
standard deviation. The number of times each channel to be loaded
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can be predetermined based on the requirement and appropriate
values for the mean and standard deviations can be set to achieve
the performance similar to the first fit model. The distribution
of the channel loading can be designed a priory and yet get the
performance similar to first fit model which was not possible to
achieve both in first fit assignment model and uniform distribution
based assignment model. Other techniques on WDM be found in
[11-12] for definitions and applications.
III. Simulation Results
In this section, simulation results are presented for several
algorithms that are based on first fit, uniform distribution based
random assignment and normal distribution based random
assignment. The normal distribution based random assignment
model is developed in this work and presented the results with the
well known first fit, uniform distribution based random assignment
models for comparison purpose. The models are simulated for a
tandem networks that has the 10 nodes with 7 channels per link
and 20 nodes with 11 channels per link. In the normal distribution
based random assignment model, 5 sub models are developed.
The normal distribution has two important characteristics which
defines the distribution. They are mean and standard deviation. In
5 sub models, the mean 0.1, 0.2, 0.3, 0.4 and 0.5 are used while
having the constant standard deviation of 0.1. Table 1 shows the
details of different models used in this paper.
Table 1: Models used in the Simulations
Model
Name
Distribution used in
Mean
Wavelength Assignment
Standard
Deviation
FIRST FIT
N.A.
N.A.
N.A.
UNIFORM
Uniform
N.A.
N.A.
NORM 0.1
Normal
0.1
0.1
NORM 0.2
Normal
0.2
0.1
NORM 0.3
Normal
0.3
0.1
NORM 0.4
Normal
0.4
0.1
NORM 0.5
Normal
0.5
0.1
Fig. 1: Blocking Probability of First Fit, Uniform Distribution
based and 5 Normal Distribution based Random Assignment
models for a load 2 Erlangs per link and with 10 Nodes, 7 channels
and 2000 iterations
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IJECT Vol. 6, Issue 3, July - Sept 2015
the similar results as that of first fit model in terms of blocking
probability. In this case, fit model may be considered as a special
case of normal distribution based random assignment model when
mean is taken as 0.1.
Fig. 2: Blocking Probability of First Fit and Uniform Distribution
based Random Assignment models for a load 2 Erlangs per link
and with 10 Nodes, 7 channels and 2000 iterations
Figs, 1 to 4 show the Blocking Probabilities based on First Fit,
uniform distribution based and normal distribution based random
assignment of channels for a load 2 Erlangs per link. These models
are run on the 10 node network that has 7 channels per link.
The models are simulated with 2000 iterations. Fig. 1 shows the
blocking probability for all the 7 models. For better, clarity, the
blocking probabilities of the base line models, i.e. first fit and
uniform distribution random assignment models are presented
in Fig. 2. It can be observed that the first fit assignment yields
best results with a maximum of 10% compared to the uniform
distribution random assignment that has a maximum of 80%.
Fig. 4: Blocking Probability of First Fit, Uniform Distribution
based and 2 Normal Distribution based Random Assignment
models for a load 2 Erlangs per link and with 10 Nodes, 7 channels
and 2000 iterations
Fig. 3: Blocking Probability of First Fit and 5 Normal Distribution
based Random Assignment models for a load 2 Erlangs per link
and with 10 Nodes, 7 channels and 2000 iterations
Fig. 5: Number of times the channel was used by First Fit, Uniform
Distribution based and 5 Normal Distribution based Random
Assignment models for a load 2 Erlangs per link and with 10
Nodes, 7 channels and 2000 iterations
In Fig. 1, it can be observed that the Normal Distribution based
Random Assignment models have the blocking probability close
to that of first fit, though they are based on random assignment.
Uniform distribution based Random Assignment model has very
poorer performance than the Normal Distribution based Random
Assignment models when compared with that of First fit model.
In Fig.3, the blocking probabilities are magnified around the
results of first fit model. It can be observed that all the normal
distribution based random assignment models are close to best
fit model. However, at the mean of 0.1, the model NORM 0.1 is
the closest model to first fit results. Hence, NORM 0.1 is yielding
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In Fig. 4, the models of NORM 0.3, NORM 0.4 and NOR 0.5 is
removed from the plots and results are compared with the uniform
distribution based Random Assignment models. When compared
to uniform distribution, the normal distribution models with 0.1
and 0.2 are performing similar to first fit model. But NORM 0.1
is more closer to first fit model than the NORM 0.2.
Since there are 7 channels available in each link, it is required to
know the number of times each channel was used by the models
when simulated for 2000 iterations. In uniform distribution model,
all the channels were utilized uniformly. NORM 0.1 has used the
channel 1 maximum number of times. This is the reason behind the
closeness in the performance with first fit model, which also used
channel 1 maximum number of times. That means with uniform
distribution model, one has the flexibility to choose the channels
that is to be used maximum during the assignment. Though other
channels were used maximum in other normal distribution models,
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IJECT Vol. 6, Issue 3, July - Sept 2015
ISSN : 2230-7109 (Online) | ISSN : 2230-9543 (Print)
the performance is still very close to that of first fit model, but
NORM 0.1 is the closest to the first fit model. NORM 0.2 and
NORM 0.3 has used channels 2 and 3 maximum respectively;
and NORM 0.4 and NORM 0.5 has used channel 4 maximum
number of times.
Fig. 6: Blocking Probability of First Fit, Uniform Distribution
based and 5 Normal Distribution based Random Assignment
models for a load 2 Erlangs per link and with 10 Nodes, 7 channels
and 10000 iterations
Fig. 9: Blocking Probability of First Fit, Uniform Distribution
based and 2 Normal Distribution based Random Assignment
models for a load 2 Erlangs per link and with 10 Nodes, 7 channels
and 10000 iterations
Figs, 6 to 9 show the Blocking Probabilities based on First Fit,
uniform distribution based and normal distribution based random
assignment of channels for a load 2 Erlangs per link. These models
are run on the 10 node network that has 7 channels, but models
are simulated with 10000 iterations. The difference in this case
is only the number of iterations that were used in the simulations
compared to the results presented in Figs. 1 to 5. All the profiles
are smoother in this case with fewer oscillations. This is because
of the reason that higher number of iterations is used. There is
much change in the conclusion observed.
Fig. 7: Blocking Probability of First Fit and Uniform Distribution
based Random Assignment models for a load 2 Erlangs per link
and with 10 Nodes, 7 channels and 10000 iterations
Fig. 10: Number of times the channel was used by First Fit,
Uniform Distribution based and 5
Normal Distribution based Random Assignment models for a
load 2 Erlangs per link and with 10 Nodes, 7 channels and 10000
iterations
Fig. 8: Blocking Probability of First Fit and 5 Normal Distribution
based Random Assignment models for a load 2 Erlangs per link
and with 10 Nodes, 7 channels and 10000 iterations
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International Journal of Electronics & Communication Technology
Fig. 10 shows the number of times the channel was used vs
channel number. The profiles are almost same compared to the
2000 iterations simulation.
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Fig. 11: Blocking Probability of First Fit, Uniform Distribution
based and 5 Normal Distribution based Random Assignment
models for a load 5 Erlangs per link and with 20 Nodes, 11 channels
and 2000 iterations
IJECT Vol. 6, Issue 3, July - Sept 2015
Fig. 14: Blocking Probability of First Fit, Uniform Distribution
based and 2 Normal Distribution based Random Assignment
models for a load 5 Erlangs per link5 Erlangs per link and with
20 Nodes, 11 channels and 2000 iterations
Figs, 11 to 14 show the Blocking Probabilities based on First
Fit, uniform distribution based and normal distribution based
random assignment of channels for a load 5 Erlangs per link.
These models are run on the 20 node network that has 11 channels.
The models are simulated with 2000 iterations. In this case, the
network model larger in size. It can be observed that uniform
distribution model has reached 100% blocking probability from
node 12 onwards, that means according the uniform distribution
random model, and the call cannot propagate beyond node 12
under any circumstances. The fist fit model exhibits too many
oscillations in the blocking probability; whereas NORM 0.1 in
fact has better performance than the first fit model at some nodes
and with fewer oscillations.
Fig. 12: Blocking Probability of First Fit and Uniform Distribution
based Random Assignment models for a load 5 Erlangs per link
and with 20 Nodes, 11 channels and 2000 iterations
Fig. 15: Number of times the channel was used by First Fit,
Uniform Distribution based and 5 Normal Distribution based
Random Assignment models for a load 5 Erlangs per link and
with 20 Nodes, 11 channels and 2000 iterations
Fig. 13: Blocking Probability of First Fit and 5 Normal Distribution
based Random Assignment models for a load 5 Erlangs per link
and with 20 Nodes, 11 channels and 2000 iterations
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Fig. 15 shows the number of times the channel was used vs
channel number. Again, in this case, there many oscillations in
the distribution which can be overcome when the number iteration
is increased to 10000.
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IJECT Vol. 6, Issue 3, July - Sept 2015
Fig. 16: Blocking Probability of First Fit, Uniform Distribution
based and 5 Normal Distribution based Random Assignment
models for a load 3 Erlangs per link and with 20 Nodes, 11 channels
and 2000 iterations
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Fig. 19: Blocking Probability of First Fit, Uniform Distribution
based and 2 Normal Distribution based Random Assignment
models for a load 4Erlangs per link 3 Erlangs per link and with
20 Nodes, 11 channels and 2000 iterations
Figs, 16 to 19 show the Blocking Probabilities based on First
Fit, uniform distribution based and normal distribution based
random assignment of channels for a load 3 Erlangs per link.
These models are run on the 20 node network that has 11 channels.
It can be observed that when the load was reduced form 5 Erlangs
to 3 Erlangs, the random assignment model based on uniform
distribution is yielding very high probability of a maximum of
98%, where as the random assignment model based on normal
distribution is yielding a maximum of 3%, and the first model
yields maximum of 2%. For NORM 0.1 model, the maximum
blocking probability is only 1.5%.
Fig. 17: Blocking Probability of First Fit and Uniform Distribution
based Random Assignment models for a load 3 Erlangs per link
and with 20 Nodes, 11 channels and 2000 iterations
Fig. 18: Blocking Probability of First Fit and 5 Normal Distribution
based Random Assignment models for a load 3Erlangs per link
and with 20 Nodes, 11 channels and 2000 iterations
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International Journal of Electronics & Communication Technology
IV. Conclusion
In this work a new random assignment model is developed based
on the normal distribution in the selection of the channel for the
assignment. The normal distribution based random assignment
yields the blocking probabilities that is very close to the first
fit model. The uniform distribution based random assignment
yields the blocking probabilities very high. In case of 20 Nodes,
11 channels and 3 Erlangs load, the normal distribution based
random assignment yield the blocking probabilities a maximum
of 1.5% when the mean is 0.1 which is better than that of best fit
model. Hence, the normal distribution based random assignment
model has the advantages of the random models but yields
the performance similar to that of first fit which the uniform
distribution based random assignment model has failed to deliver.
The normal distribution based random assignment model can be
assigned the mean standard deviation to such a value so that the
normal distribution based random assignment model also yields
the performance similar to uniform distribution based random
assignment model. Hence, the uniform distribution based random
assignment model and first fit can be considered as special cases
of normal distribution based random assignment model.
References
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[2] T. E. Stern, K. Bala.,“Multiwavelength optical Networks”,
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[3] B. Mukherjee,“Optical Communication Networks”,
McGraw-Hill, New York, 1997.
[4] A. Girard, “Routing and wavelength assignment in all-optical
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[5] H. Harai, M. Murata, H. Miyahara,“Performance of Alternate
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[6] Ahmed Mokhtar, Murat Azizoglu,“Adaptive Wavelength
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[7] R. A. Barry, P .A. Humblet,“Models of blocking Probability
in All-Optical Networks with and without Wavelength
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[8] I. Chlamtac, A. Ganz, G. Karmi,“Lightpath Communications:
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[9] A. Wason R. S. Kaler,“Wavelength Assignment Problem in
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[10]A. Sangeetha, K.Anusudha,S. Mathur, M.K. Chaluvadi,
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S.Suryanarayana received his B.Tech
degree in Electronics& Communication
Engg from College of Engg,
Kakinada(JNTU), Andhra pradesh
, India , in 1991, the M.E. degree in
Microwave engineering from Birla
Institute of Technology(BIT), Ranchi,
in 1994. He worked in NBKRIST,
GRIET, CVR College of engg,
CMRIT and presently as professor
in Kallam Haranadhareddy Institute
of technology, Guntur, India. Prof.
S.Suryanarayana has 12 technical papers to his credit published
in various International, National Journals and Conferences. His
research interests include digital Communication, optical and
microwave techniques. He is a life member of ISTE, IETE and
IEEE.
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IJECT Vol. 6, Issue 3, July - Sept 2015
Dr.K.Ravindra received his
B.Tech. degree in Electronics and
Communication Engineering from
Andhra University, M.E. with Honors
from IIT Roorkee and Ph.D. in the
field of Mobile Communications
from Osmania University. He is a
recipient of GOLD MEDAL from
Roorkee University for standing first
in Masters Degree. He has Engineering
teaching experience of over 30 years
in various capacities. Dr. Ravindra served as Senior Scientist in
the “Research and Training Unit for Navigational Electronics”
Osmania University from December 2000 to December 2002. He
is presently working as PRINCIPAL in Malla Reddy Institute of
Technology & Science,Secunderabad-500100. Prof. Ravindra has
41 technical papers to his credit published in various International,
National Journals and Conferences. He co-authored 2 technical
reports in the field of GPS. He is the resource person for video
lectures produced by SONET, Andhra Pradesh. He is presently
guiding 6 research scholars in the fields of Optical & Mobile
Communications, Cellular and Next generation networks, Image
Processing etc. He is a recipient of Educational Leadership
Award 2013 from KRDWG, New Delhi. He is a reviewer for an
International Journal. He is visiting Professor of ISTE. He is a
life member of ISTE, IETE and SEMCE(I).
Dr. K. Chennakeshava Reddy,
Presently working as Professor of ECE
at Bharath College of Engineering &
Technology. He has completed his
B.E. in 1973 and M. Tech. in1976 from
REC Warangal, A.P. India, and Ph.D.
in 2001 from JNTU Hyderabad. He has
worked in various positions starting
from lecturer to Director of Evaluation
in JNT University, Hyderabad, A. P.
India. He has about 100 publications
in international and National journals and Conferences and he
has successfully guided 14 Ph.Ds and many are under progress.
He is a member of various technical Associations.
International Journal of Electronics & Communication Technology 121