# The Gain of Performance of Optical WDM Networks

Authors: Miroslav Bahleda; Karol Blunar
Journal: Journal of Computer Systems, Networks, and Communications
 (2008-02-21)

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## Abstract

We study the blocking probability and performance of single-fiber and multifiber optical networks with wavelength division multiplexing (WDM). We extend the well-known analytical blocking probability model by Barry and Humblet to the general model, which is proposed for both single-fiber and multifiber network paths with any kind of wavelength conversion (no, limited, or full wavelength conversion) and for uniform and nonuniform link loads. We investigate the effect of the link load, wavelength conversion degree, and the number of wavelengths, fibers, and hops on blocking probability. We also extend the definition of the gain of wavelength conversion by Barry and Humblet to the gain of performance, which is fully general. Thanks to this definition and implementation of our model, we compare different WDM node architectures and present interesting results.


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## Body

## 1. Introduction

Thanks to the latest technological advances in optical technology
in recent years, optical networks based on wavelength division multiplexing (WDM)
technology are a very attractive solution to satisfy the current bandwidth requirements of the internet infrastructure. Moreover, they promise to provide a
scalable solution to support the bandwidth needs of future applications. Hybrid
WDM/OTDM networks are mainly supposed to be implemented in future long-haul networks.
Under the difficult competitive open business environment in these days, a
certain quality of service provided to the customer is required for the implementation
of WDM networks into the real network infrastructure. The main focus of network
operators is to optimize their networks and to achieve an optimal compromise
between economic costs and quality of services. Hence interest in the
dimensioning and provisioning of WDM networks is still a
really up to date research
subject.The aim of this article is to study optical WDM networks in terms
of blocking probability and performance gain. The paper is structured as
follows. Section2 briefly introduces WDM optical networks. We propose our general
blocking probability model and present its simulation results in Section 3. We
define gain of performance and compare different WDM node architectures in Section
4. Finally, the conclusion and future work remarks are given in Section 5.


## 2. WDM Networks

The all-optical (photonic) networks enable switching and routing
functions at the optical layer. The optical signal still remains in the optical
domain between two access nodes and the latencies induced by optoelectronic conversions
at intermediate nodes disappear. In all-optical networks, different types of
multiple user technology can be used: OTDM (optical time division multiplex),
CDM (code division multiplex), or WDM (wavelength division multiplex). WDM is
the favorite choice because both CDM and OTDM are still limited by fiber
physical characteristics and the state of optical technology, especially due to
the difficult synchronization requirements.Optical networks, which employ wavelength division multiplex
(WDM) technology, are calledWDM networks.
They provide simultaneous transmission on a few different optical wavelengths
through the same optical fiber. However, thanks
to many connections simultaneously shared on the same fiber, the huge bandwidth
potential of optical fiber is much better utilized. This allows
different end-users to operate at electronic processing speeds, which are still
limited to about 40 Gb/s. Moreover, each connection established
between the end nodes on a WDM channel enables the specification of a different
bit rate and data format. This is referred to as WDM transparency. All connections using the same fiber link must
allocate different and distinct wavelengths. It is also known as distinct wavelength assignment constraint.The proposed model is designed for wavelength routed optical
networks based on optical channel switching. Such networks consist of two types
of nodes:(i)
optical cross-connects (OXCs) equipped with a few input and output ports, which are connected to other OXCs or optical access nodes by optical fibers;(ii)
end nodes (access nodes), which provide the interface between nonoptical end and optical systems.The OXC can be fitted with an optical converter to provide
optical conversion in the optical domain. If an OXC does not support any wavelength
conversion, the same wavelength must be used on next hop of the path. This is
known aswavelength continuity constraint [1]. If all network OXCs do not support any wavelength conversion, the same
wavelength must be used on all the fiber links along the physical path. Such a
network is called a no wavelength
conversion network [1]. A connection request is accepted only if there is
at least one wavelength which is simultaneously free on all the links along the
path. This means that a call can be blocked even if there are free wavelengths
on all the links, but they are not all the same.The maximum number of wavelengths is still limited by optical
device technology, the total available bandwidth, the component spectral range,
and the spacing between channels. Hence wavelength reuse is required by a
wavelength conversion in OXC. If an OXC enables a wavelength conversion, a different
wavelength can be assigned on the next path hop. If each OXC supports full
wavelength conversion, this is referred as afull wavelength conversion network. A connection request is
accepted if there is at least one free wavelength on each fiber link along the
path.Full wavelength conversion in the optical domain improves network
blocking performance significantly [1]. Unfortunately, the employment of full
wavelength conversion all-optical converters in each network node greatly
increases the network cost due to the complexity of the optical device
technology. The aim of researchers is to achieve high or similar network
performance by a limited range of wavelength conversion for each converter, a limited
number of converters in each OXC, and a limited number of OXCs supporting
wavelength conversion in the whole network. Another possibility to relax the
wavelength continuity constrain is to implement multifiber links.


### 2.1. Limited Wavelength Conversion Networks

If a network supports wavelength conversion with some
restrictions, it is called alimited
wavelength conversion network. These restrictions can be as follows [2]:(i)
a limited range of wavelengths to which an input wavelength may be converted. If any incoming wavelength can be converted to any wavelength from a limited set of k outgoing wavelengths on the output side of wavelength spectrum plane W, it is referred to as limited wavelength conversion with conversion degreek;(ii)
a limited number of wavelength converters are placed at each node. This is also known as partial wavelength conversion. A wavelength converter bank consisting of a collection of a few wavelength converters is shared. Share-per-node and share-per-link wavelength-convertible switch architectures have been proposed [1];(iii)
a limited number of nodes enabling wavelength conversion are placed in the network. If only a few network nodes enable a wavelength conversion, not all, this is called a sparse wavelength conversion [1].Two first limitations mentioned above are implemented in the network nodes
and last one is based on network restriction. The network costs can be
decreased by using converters with a limited range of wavelength conversion
rather than full range conversion, assuming a limited number of converters in each
node and a limited number of conversion nodes in the network rather than enabling
wavelength conversion in each network node. However, placement of converters in
a network, allocation of converters in a node, and specification of wavelength
conversion range issues are raised. Recent research has shown that limited conversion
is much easier and cheaper than full conversion. Moreover, limited wavelength
conversion networks are still able to provide enough conversion to use channels
efficiently, and at much better channel efficiency than no wavelength
conversion networks, depending on the design.Unfortunately, the detailed explanation of each limited wavelength
conversion scenario is outside the scope of this paper. However, it can be
found in [2]. We only discuss the first case of limited wavelength conversion
in more detail.In general, for limited wavelength conversion with conversion degreek, any incoming wavelength λi, i∈W can be converted to any wavelength λj, j∈k from a limited set of k(1<k<W) outgoing wavelengths on the output
side of the wavelength spectrum plane W [2]. In practice, the following types of limited wavelength conversion are
used:(i)
symmetrical: any incoming wavelength can be converted to any wavelength from d adjacent outgoing
wavelengths on the left and right side of the wavelength plane of the spectrum, as well as the same wavelength. This means that any incoming wavelength can be converted to one from k=2d+1 outgoing wavelengths;(ii)
nonsymmetrical: any incoming wavelength can be converted to the same wavelength or to one on the left (or the right) side of the wavelength plane. This means that it is possible to switch any incoming wavelength to a wavelength from k=d+1 outgoing wavelengths.Note that the conversion capability of the optical OXCs can be classified into three types depending on their range of wavelength conversionk:(i)
k=1, no wavelength conversion capability;(ii)
1<k<W, limited
wavelength conversion capability;(iii)
k=W, full wavelength conversion capability.


### 2.2. Multifiber Networks

Networks that employ bundles of fibers between the network nodes
are calledmultifiber networks. In multifiber
WDM networks, each link consists of multiple fibers and each fiber carries information on multiple wavelengths [3]. Generally, each network link can consist
of a different number of fibers F, and each fiber can use a different
number of wavelengths W.Thanks to decreasing fiber costs in recent years, current
research tends toward the multifiber
networks. In fact, most of the optical networks deployed to date, employ
multiple fibers between end nodes due to the economic advantage of installing
bundles of fibers for the purposes of fault tolerance and future network
growth. Performance improvement, in terms of blocking probability and
throughput, can be achieved by using these fibers or adding more fibers to the existed
system.Theoretically, multifiber WDM networks can be implemented with
no, limited, or full wavelength conversion. However, the benefit of using no
wavelength conversion multifiber networks is important. If a wavelength cannot
continue on the next hop on the same fiber, and the same wavelength is
available on any other fibers on the next hop, then the incoming wavelength can
be switched to another fiber. Thus the functionality of a multifiber network
withF fibers per link and W wavelengths per fiber is equivalent to
a limited wavelength conversion of degree F single-fiber network, with F⋅W wavelengths [1, 3].The design aim of a multifiber network is to decide how many
fibers per link are required to guarantee high network performance or to
achieve high network performance with the minimum number of fibers per link.


## 2.1. Limited Wavelength Conversion Networks

If a network supports wavelength conversion with some
restrictions, it is called alimited
wavelength conversion network. These restrictions can be as follows [2]:(i)
a limited range of wavelengths to which an input wavelength may be converted. If any incoming wavelength can be converted to any wavelength from a limited set of k outgoing wavelengths on the output side of wavelength spectrum plane W, it is referred to as limited wavelength conversion with conversion degreek;(ii)
a limited number of wavelength converters are placed at each node. This is also known as partial wavelength conversion. A wavelength converter bank consisting of a collection of a few wavelength converters is shared. Share-per-node and share-per-link wavelength-convertible switch architectures have been proposed [1];(iii)
a limited number of nodes enabling wavelength conversion are placed in the network. If only a few network nodes enable a wavelength conversion, not all, this is called a sparse wavelength conversion [1].Two first limitations mentioned above are implemented in the network nodes
and last one is based on network restriction. The network costs can be
decreased by using converters with a limited range of wavelength conversion
rather than full range conversion, assuming a limited number of converters in each
node and a limited number of conversion nodes in the network rather than enabling
wavelength conversion in each network node. However, placement of converters in
a network, allocation of converters in a node, and specification of wavelength
conversion range issues are raised. Recent research has shown that limited conversion
is much easier and cheaper than full conversion. Moreover, limited wavelength
conversion networks are still able to provide enough conversion to use channels
efficiently, and at much better channel efficiency than no wavelength
conversion networks, depending on the design.Unfortunately, the detailed explanation of each limited wavelength
conversion scenario is outside the scope of this paper. However, it can be
found in [2]. We only discuss the first case of limited wavelength conversion
in more detail.In general, for limited wavelength conversion with conversion degreek, any incoming wavelength λi, i∈W can be converted to any wavelength λj, j∈k from a limited set of k(1<k<W) outgoing wavelengths on the output
side of the wavelength spectrum plane W [2]. In practice, the following types of limited wavelength conversion are
used:(i)
symmetrical: any incoming wavelength can be converted to any wavelength from d adjacent outgoing
wavelengths on the left and right side of the wavelength plane of the spectrum, as well as the same wavelength. This means that any incoming wavelength can be converted to one from k=2d+1 outgoing wavelengths;(ii)
nonsymmetrical: any incoming wavelength can be converted to the same wavelength or to one on the left (or the right) side of the wavelength plane. This means that it is possible to switch any incoming wavelength to a wavelength from k=d+1 outgoing wavelengths.Note that the conversion capability of the optical OXCs can be classified into three types depending on their range of wavelength conversionk:(i)
k=1, no wavelength conversion capability;(ii)
1<k<W, limited
wavelength conversion capability;(iii)
k=W, full wavelength conversion capability.


## 2.2. Multifiber Networks

Networks that employ bundles of fibers between the network nodes
are calledmultifiber networks. In multifiber
WDM networks, each link consists of multiple fibers and each fiber carries information on multiple wavelengths [3]. Generally, each network link can consist
of a different number of fibers F, and each fiber can use a different
number of wavelengths W.Thanks to decreasing fiber costs in recent years, current
research tends toward the multifiber
networks. In fact, most of the optical networks deployed to date, employ
multiple fibers between end nodes due to the economic advantage of installing
bundles of fibers for the purposes of fault tolerance and future network
growth. Performance improvement, in terms of blocking probability and
throughput, can be achieved by using these fibers or adding more fibers to the existed
system.Theoretically, multifiber WDM networks can be implemented with
no, limited, or full wavelength conversion. However, the benefit of using no
wavelength conversion multifiber networks is important. If a wavelength cannot
continue on the next hop on the same fiber, and the same wavelength is
available on any other fibers on the next hop, then the incoming wavelength can
be switched to another fiber. Thus the functionality of a multifiber network
withF fibers per link and W wavelengths per fiber is equivalent to
a limited wavelength conversion of degree F single-fiber network, with F⋅W wavelengths [1, 3].The design aim of a multifiber network is to decide how many
fibers per link are required to guarantee high network performance or to
achieve high network performance with the minimum number of fibers per link.


## 3. The Analysis of Path Blocking Probability

The proposed model is derived from the model by Barry and Humblet
taking into consideration the type of wavelength conversion and the multifiber network scenario and, hence, is general.


### 3.1. Assumptions and Notations

Three independence assumptions are considered, which generally lead
to the overestimation of blocking probability:(i)
link independence assumption: the link states on different links are independent [4];(ii)
wavelength independence assumption: the individual wavelengths are utilized independently of the utilizations of other wavelengths on the same link [4];(iii)
fiber independence assumption: the fiber is utilized independently.The blocking probability analysis is simpler due to the factors
above, but the model is not very accurate. However, the computational
complexity of the model is moderate. In this paper, the following parameters
and notations are used:(i)
W: number of wavelengths on each link per fiber;(ii)
H: number of hops along a path;(iii)
F: number of fibers per hop;(iv)
N: number of network nodes;(v)
Ch: number of channels in a hop; Ch=W⋅F;(vi)
li,j: direct link between directly consecutive node i and j;(vii)
an,m: end-to-end traffic load on a path from node n to node m;(viii)
ai,jn,m: amount of traffic an,m going through link lij;(ix)
ρi,j: load per wavelength over link li,j;(x)
R: network path, that is, consecutive links li,j between access nodes n, m;(xi)
No: no wavelength conversion capability;(xii)
Lim: limited wavelength conversion capability;(xiii)
Full: full wavelength conversion capability.We consider the single-fiber and multifiber wavelengths routed
optical networks based on optical channel switching (Figure1). The network path R is defined as a set of consecutive
links li,j, between any two end nodes n, m.
This consists of H hops and N nodes.WDM network. (a) The model of a single-fiber
WDM network(F=1). (b) The physical network path between nodes
A, B consists of 3 hops and 4 nodes (N=4,H=3). The network is modeled as a
directed graph. (c) The optical domain consists of 3 wavelengths (λ1,λ2,andλ3) on each link (W=3).
(a)(b)(c)(d)In the model, it is assumed that the call request arrives on each
link as a Poisson process with arrival rateλ and that the connection holding time is exponentially distributed with service
rate μ. Hence the load is expressed
as a=λ/μ. The wavelength utilization
(load per wavelength) ρ is the
probability that a wavelength is used on a link on the fiber. Following the
traffic model in [4], the load per wavelength between any two access nodes n, m on a link li,j can be expressed by
(1)ρi,j=∑∀n,mai,jn,mW.
The sum ∑∀n,mai,jn,m expresses the traffic load contributions from
all the end-to-end originating demands passing through the relevant li,j. If there is the same
link load over all links (i.e., ρi,j=ρ),
this is referred to as uniform link load.
Otherwise, this is known as nonuniform
link load.In general, each network link can consist of a different number
of fibersF and each fiber may have a
different number of wavelengths W. However,
in our model we assume the same number of fibers on all network links and the
same number of wavelengths on each network fiber.


### 3.2. The Proposed Analytical Blocking  Probability Model

The proposed model is designed to compute the end-to-end blocking
probability between any pair of network nodesn, m along the path R, of both single-fiber and multifiber
WDM networks with any range of wavelength conversion (no, limited, or full
wavelength conversion) with regard to independence, traffic, and network
assumptions mentioned above. The model presents the blocking probability as a
function of the load ρ, the wavelength
conversion degree k, the number of
wavelengths W, the number of hops H, and the number fibers F.The blocking probabilityPb,WDM of WDM optical network path R is the
probability that, for each wavelength, there is at least one hop of the path on
which all wavelengths from a set of wavelengths k are used on all fibers. For uniform link load, this is expressed as
(2)Pb,WDM=[1−(1−ρF⋅k)H]W/k,
and for nonuniform link load, this is derived as follows:
(3)Pb,WDM′=[1−∏i,j∈R;H(1−ρi,jF⋅k)]W/k.The uniform link load model is derived as follows: note thatρ is the probability that a wavelength
is used on a hop. Then ρk expresses the expected probability that all k wavelengths, on which any incoming wavelength can be converted, are occupied on
the hop. For the F fibers hop, the
expected probability that all k wavelengths on each fiber are occupied is ρkF.
The probability that a suitable wavelength is free on a hop is 1−ρkF. Hence the probability
that a suitable wavelength is free on all hops along its path is (1−ρkF)H. The factor W/k represents the effect of limited
wavelength conversion with conversion degree k. It is supposed that the waveband W is split to a few subwavebands W/k depending on the
conversion degree. Any connection using a wavelength from any subwaveband is
supposed not to change this subwaveband along the optical path between end nodes.
The factor W/k expresses the number of possibilities in which the limited set of
wavelengths k from waveband W, can be divided. Note that this is an
analytical model. In real configurations, W/k can only be an integer.Note also that depending on the conversion degreek, the proposed models (2) and (3) are
general for no (k=1), limited (1<k<W),
and full (k=W) wavelengths conversion networks. Depending on the number of
fibers F, the model is also valid for
single-fiber (F=1) and multifiber (F>1) network paths. Hence the
proposed model is general and is valid for any type of wavelength conversion
and for any number of fibers. The model overview of uniform link load is
presented in Table 1, and the model overview of nonuniform load is published in
[6]. The model for any type of wavelength conversion of single-fiber network
paths (2c) was
presented for the first time in [5]. Note that for single-fibre network paths, if no wavelength conversion is
considered then k=1 and the
expression (2) can be modified to the model by Barry and Humblet without
wavelength conversion (2a)
also presented in [4]. Similarly, for full wavelength conversion (k=W),
the proposed model (2) can be changed to the model by Barry and Humblet with
full wavelength conversion (2b) published in [4].Table 1
The blocking probability model for uniform link load.
Single-fiber WDM network pathF=1Mutlifiber WDM network pathF>1No(k=1)Pb,no=[1−(1−ρ)H]W(2a)Pb,no′=[1−(1−ρF)H]W(2d)Full(k=W)Pb,full=1−(1−ρW)H(2b)Pb,full′=1−(1−ρF⋅W)H(2e)Lim(1<k<W)Pb,lim=[1−(1−ρk)H]W/k(2c)Pb,lim′=[1−(1−ρF⋅k)H]W/k(2)The nonuniform link load model can be easily extended from the
uniform link load model by taking into consideration the link load independence
assumptions (see Section3.1).Taking into consideration both link and wavelength load
independence assumptions, the blocking probability of any arbitrary WDM network
can be determined as follows: a network can be divided into the corresponding number
of particular network pathsR, between each two access nodes in line
with the routing algorithm. The corresponding amount of the traffic ai,j going through link li.j on each network path R, is given by (1). The blocking
probability Pb,WDMn,m of each network path can be computed by using (2)
or (3). Then following [1] the overall blocking probability B of the network can be formulated as
(4)B=∑n,man,mPb,WDMn,m∑n,man,m.The accuracy of
the proposed model is assumed to be similar to the model by Barry and Humblet
because the same assumptions are used. The problem of model accuracy is
exhaustively presented in [4] and, unfortunately, it is outside the scope of this paper.


### 3.3. Numerical Results of the Proposed Blocking Probability Model

All simulation results presented in this section are realized in a
Matlab environment. The results are presented only for network paths as
depicted in Figure1(b). Different types of wavelength conversion (no, limited,
and full) and single-fiber and multifiber scenarios are considered.In Figures2 and 3, the blocking probability of no, full, and
limited wavelength conversion network paths is plotted as a function of
wavelength utilization ρ for single-fiber
and multifiber network paths, respectively. For both single-fiber and multifiber
scenarios, the number of wavelengths is W=15
and the degree of limited wavelength conversion is k=3. The single-fiber path is plotted for H=10, 20 hops and multifiber path is drawn for H=20, 40 hops and F=15 fibers.
As can be seen from both figures, the blocking probability increases with the
wavelength utilization ρ and the number
of hops H. Note that the wavelength
conversion reduces the blocking probability and, thus, increases wavelength
utilization ρ.Figure 2
The blocking probabilityPb=f(ρ), W=15, k=3, and F=1.Figure 3
The blocking probabilityPb=f(ρ), W=15, k=3, and F=15.In Figure4, the blocking probability of no, limited, and full
wavelength conversion single-fiber network paths is plotted as a function of
the number of hops H for W=10, 20 wavelengths, ρ=0.2, and k=3. As expected, the blocking probability increases as the number
of hops increases. The blocking probability of no wavelength conversion network
paths depends on the number of hops, significantly unlike limited or full
wavelength conversion scenario. The effect of the path length is really dramatic
for no wavelength conversion.Figure 4
The blocking probabilityPb=f(H), ρ=0.2, k=3, and F=1.Figure5 shows the blocking probability of a single-fiber network
path as a function of the conversion degree k for W=20, ρ=0.5, and H=5, 10, 20
hops. Note that when no wavelength conversion is considered, k equals 1 and for full wavelength
conversion, the conversion degree k is equal to W. From the figure, the
proper conversion degree can be estimated. As k increases at the beginning, the blocking probability rapidly
decreases. After a point, the blocking probability slowly decreases as the
conversion degree increases. The performance improvement of limited wavelength
conversion with small conversion degree is considerable, compared with the no wavelength
conversion performance, as shown in Figure 5.Figure 5
The blocking probabilityPb=f(k), ρ=0.5, W=20, and F=1.Similar results can be obtained for multifiber networks.
Unfortunately, detailed explanation and graphic presentation of the results of
multifiber scenarios are beyond the scope of this paper. However, they are
described quite exhaustively in [6].The blocking probability as a function of the number of fibers
for no, limited, and full wavelength conversion and forW=10, ρ=0.8, and k=3 is plotted in Figure 6. It can be
clearly seen that the blocking probability decreases significantly as the
number of fibers increases.Figure 6
The blocking probabilityPb=f(F), ρ=0.8, W=10, and k=3.The results of the proposed model are briefly summarized as
follows:(i)
the blocking probability always increases
with the wavelength utilizationρ and
number of hops H;(ii)
the blocking probability decreases
with the wavelength conversion degreek,
the number of wavelengths W, and the
number of fibers F;(iii)
the blocking probability of a no
wavelength conversion network path dramatically increases with the number of
hopsH, in contrast to the network path
with wavelength conversion;(iv)
no wavelength conversion multifiber
paths perform in very similar fashion to the limited wavelength conversion single-fiber
paths, in terms of blocking probability;(v)
for given parametersρ, H,
and W no wavelength conversion single-fiber
paths achieve the highest blocking probability and full wavelength conversion multifiber
paths achieve the lowest blocking probability;(vi)
limited wavelength conversion paths
present continual transition from no(k=1)
to full (k=W) wavelength conversion paths in terms of throughput, dependent on
the conversion degree (1<k<W);(vii)
the performance of limited
wavelength paths with small values of the conversion degree is very close to
the blocking performance of full wavelength conversion paths, for both single-fiber
and multifiber network path scenarios, respectively.


## 3.1. Assumptions and Notations

Three independence assumptions are considered, which generally lead
to the overestimation of blocking probability:(i)
link independence assumption: the link states on different links are independent [4];(ii)
wavelength independence assumption: the individual wavelengths are utilized independently of the utilizations of other wavelengths on the same link [4];(iii)
fiber independence assumption: the fiber is utilized independently.The blocking probability analysis is simpler due to the factors
above, but the model is not very accurate. However, the computational
complexity of the model is moderate. In this paper, the following parameters
and notations are used:(i)
W: number of wavelengths on each link per fiber;(ii)
H: number of hops along a path;(iii)
F: number of fibers per hop;(iv)
N: number of network nodes;(v)
Ch: number of channels in a hop; Ch=W⋅F;(vi)
li,j: direct link between directly consecutive node i and j;(vii)
an,m: end-to-end traffic load on a path from node n to node m;(viii)
ai,jn,m: amount of traffic an,m going through link lij;(ix)
ρi,j: load per wavelength over link li,j;(x)
R: network path, that is, consecutive links li,j between access nodes n, m;(xi)
No: no wavelength conversion capability;(xii)
Lim: limited wavelength conversion capability;(xiii)
Full: full wavelength conversion capability.We consider the single-fiber and multifiber wavelengths routed
optical networks based on optical channel switching (Figure1). The network path R is defined as a set of consecutive
links li,j, between any two end nodes n, m.
This consists of H hops and N nodes.WDM network. (a) The model of a single-fiber
WDM network(F=1). (b) The physical network path between nodes
A, B consists of 3 hops and 4 nodes (N=4,H=3). The network is modeled as a
directed graph. (c) The optical domain consists of 3 wavelengths (λ1,λ2,andλ3) on each link (W=3).
(a)(b)(c)(d)In the model, it is assumed that the call request arrives on each
link as a Poisson process with arrival rateλ and that the connection holding time is exponentially distributed with service
rate μ. Hence the load is expressed
as a=λ/μ. The wavelength utilization
(load per wavelength) ρ is the
probability that a wavelength is used on a link on the fiber. Following the
traffic model in [4], the load per wavelength between any two access nodes n, m on a link li,j can be expressed by
(1)ρi,j=∑∀n,mai,jn,mW.
The sum ∑∀n,mai,jn,m expresses the traffic load contributions from
all the end-to-end originating demands passing through the relevant li,j. If there is the same
link load over all links (i.e., ρi,j=ρ),
this is referred to as uniform link load.
Otherwise, this is known as nonuniform
link load.In general, each network link can consist of a different number
of fibersF and each fiber may have a
different number of wavelengths W. However,
in our model we assume the same number of fibers on all network links and the
same number of wavelengths on each network fiber.


## 3.2. The Proposed Analytical Blocking  Probability Model

The proposed model is designed to compute the end-to-end blocking
probability between any pair of network nodesn, m along the path R, of both single-fiber and multifiber
WDM networks with any range of wavelength conversion (no, limited, or full
wavelength conversion) with regard to independence, traffic, and network
assumptions mentioned above. The model presents the blocking probability as a
function of the load ρ, the wavelength
conversion degree k, the number of
wavelengths W, the number of hops H, and the number fibers F.The blocking probabilityPb,WDM of WDM optical network path R is the
probability that, for each wavelength, there is at least one hop of the path on
which all wavelengths from a set of wavelengths k are used on all fibers. For uniform link load, this is expressed as
(2)Pb,WDM=[1−(1−ρF⋅k)H]W/k,
and for nonuniform link load, this is derived as follows:
(3)Pb,WDM′=[1−∏i,j∈R;H(1−ρi,jF⋅k)]W/k.The uniform link load model is derived as follows: note thatρ is the probability that a wavelength
is used on a hop. Then ρk expresses the expected probability that all k wavelengths, on which any incoming wavelength can be converted, are occupied on
the hop. For the F fibers hop, the
expected probability that all k wavelengths on each fiber are occupied is ρkF.
The probability that a suitable wavelength is free on a hop is 1−ρkF. Hence the probability
that a suitable wavelength is free on all hops along its path is (1−ρkF)H. The factor W/k represents the effect of limited
wavelength conversion with conversion degree k. It is supposed that the waveband W is split to a few subwavebands W/k depending on the
conversion degree. Any connection using a wavelength from any subwaveband is
supposed not to change this subwaveband along the optical path between end nodes.
The factor W/k expresses the number of possibilities in which the limited set of
wavelengths k from waveband W, can be divided. Note that this is an
analytical model. In real configurations, W/k can only be an integer.Note also that depending on the conversion degreek, the proposed models (2) and (3) are
general for no (k=1), limited (1<k<W),
and full (k=W) wavelengths conversion networks. Depending on the number of
fibers F, the model is also valid for
single-fiber (F=1) and multifiber (F>1) network paths. Hence the
proposed model is general and is valid for any type of wavelength conversion
and for any number of fibers. The model overview of uniform link load is
presented in Table 1, and the model overview of nonuniform load is published in
[6]. The model for any type of wavelength conversion of single-fiber network
paths (2c) was
presented for the first time in [5]. Note that for single-fibre network paths, if no wavelength conversion is
considered then k=1 and the
expression (2) can be modified to the model by Barry and Humblet without
wavelength conversion (2a)
also presented in [4]. Similarly, for full wavelength conversion (k=W),
the proposed model (2) can be changed to the model by Barry and Humblet with
full wavelength conversion (2b) published in [4].Table 1
The blocking probability model for uniform link load.
Single-fiber WDM network pathF=1Mutlifiber WDM network pathF>1No(k=1)Pb,no=[1−(1−ρ)H]W(2a)Pb,no′=[1−(1−ρF)H]W(2d)Full(k=W)Pb,full=1−(1−ρW)H(2b)Pb,full′=1−(1−ρF⋅W)H(2e)Lim(1<k<W)Pb,lim=[1−(1−ρk)H]W/k(2c)Pb,lim′=[1−(1−ρF⋅k)H]W/k(2)The nonuniform link load model can be easily extended from the
uniform link load model by taking into consideration the link load independence
assumptions (see Section3.1).Taking into consideration both link and wavelength load
independence assumptions, the blocking probability of any arbitrary WDM network
can be determined as follows: a network can be divided into the corresponding number
of particular network pathsR, between each two access nodes in line
with the routing algorithm. The corresponding amount of the traffic ai,j going through link li.j on each network path R, is given by (1). The blocking
probability Pb,WDMn,m of each network path can be computed by using (2)
or (3). Then following [1] the overall blocking probability B of the network can be formulated as
(4)B=∑n,man,mPb,WDMn,m∑n,man,m.The accuracy of
the proposed model is assumed to be similar to the model by Barry and Humblet
because the same assumptions are used. The problem of model accuracy is
exhaustively presented in [4] and, unfortunately, it is outside the scope of this paper.


## 3.3. Numerical Results of the Proposed Blocking Probability Model

All simulation results presented in this section are realized in a
Matlab environment. The results are presented only for network paths as
depicted in Figure1(b). Different types of wavelength conversion (no, limited,
and full) and single-fiber and multifiber scenarios are considered.In Figures2 and 3, the blocking probability of no, full, and
limited wavelength conversion network paths is plotted as a function of
wavelength utilization ρ for single-fiber
and multifiber network paths, respectively. For both single-fiber and multifiber
scenarios, the number of wavelengths is W=15
and the degree of limited wavelength conversion is k=3. The single-fiber path is plotted for H=10, 20 hops and multifiber path is drawn for H=20, 40 hops and F=15 fibers.
As can be seen from both figures, the blocking probability increases with the
wavelength utilization ρ and the number
of hops H. Note that the wavelength
conversion reduces the blocking probability and, thus, increases wavelength
utilization ρ.Figure 2
The blocking probabilityPb=f(ρ), W=15, k=3, and F=1.Figure 3
The blocking probabilityPb=f(ρ), W=15, k=3, and F=15.In Figure4, the blocking probability of no, limited, and full
wavelength conversion single-fiber network paths is plotted as a function of
the number of hops H for W=10, 20 wavelengths, ρ=0.2, and k=3. As expected, the blocking probability increases as the number
of hops increases. The blocking probability of no wavelength conversion network
paths depends on the number of hops, significantly unlike limited or full
wavelength conversion scenario. The effect of the path length is really dramatic
for no wavelength conversion.Figure 4
The blocking probabilityPb=f(H), ρ=0.2, k=3, and F=1.Figure5 shows the blocking probability of a single-fiber network
path as a function of the conversion degree k for W=20, ρ=0.5, and H=5, 10, 20
hops. Note that when no wavelength conversion is considered, k equals 1 and for full wavelength
conversion, the conversion degree k is equal to W. From the figure, the
proper conversion degree can be estimated. As k increases at the beginning, the blocking probability rapidly
decreases. After a point, the blocking probability slowly decreases as the
conversion degree increases. The performance improvement of limited wavelength
conversion with small conversion degree is considerable, compared with the no wavelength
conversion performance, as shown in Figure 5.Figure 5
The blocking probabilityPb=f(k), ρ=0.5, W=20, and F=1.Similar results can be obtained for multifiber networks.
Unfortunately, detailed explanation and graphic presentation of the results of
multifiber scenarios are beyond the scope of this paper. However, they are
described quite exhaustively in [6].The blocking probability as a function of the number of fibers
for no, limited, and full wavelength conversion and forW=10, ρ=0.8, and k=3 is plotted in Figure 6. It can be
clearly seen that the blocking probability decreases significantly as the
number of fibers increases.Figure 6
The blocking probabilityPb=f(F), ρ=0.8, W=10, and k=3.The results of the proposed model are briefly summarized as
follows:(i)
the blocking probability always increases
with the wavelength utilizationρ and
number of hops H;(ii)
the blocking probability decreases
with the wavelength conversion degreek,
the number of wavelengths W, and the
number of fibers F;(iii)
the blocking probability of a no
wavelength conversion network path dramatically increases with the number of
hopsH, in contrast to the network path
with wavelength conversion;(iv)
no wavelength conversion multifiber
paths perform in very similar fashion to the limited wavelength conversion single-fiber
paths, in terms of blocking probability;(v)
for given parametersρ, H,
and W no wavelength conversion single-fiber
paths achieve the highest blocking probability and full wavelength conversion multifiber
paths achieve the lowest blocking probability;(vi)
limited wavelength conversion paths
present continual transition from no(k=1)
to full (k=W) wavelength conversion paths in terms of throughput, dependent on
the conversion degree (1<k<W);(vii)
the performance of limited
wavelength paths with small values of the conversion degree is very close to
the blocking performance of full wavelength conversion paths, for both single-fiber
and multifiber network path scenarios, respectively.


## 4. The Gain of Performance

In this section, we extend the gain of wavelength conversion by
Barry and Humblet [4] to the gain of performance of optical WDM networks. Thanks
to this definition, any two different optical network path scenarios N1, N2
can be compared. The gain of performance is defined as the increase in
wavelength utilization for the same blocking probability. It is expressed as
the ratio between wavelength utilization (ρN1,ρN2) of two different optical
network path scenarios, for the same blocking probability Pb and the number of hops H:
(5)G=ρN1ρN2|Pb,H,
where the wavelength utilization of each network path can be expressed in terms of the blocking probability (2) as follows:
(6)ρ=[1−(1−Pbk/W)1/H]1/(F⋅k).It is assumed that the wavelength utilizationρN1 belongs to the
network path with the higher wavelength utilization, and that the utilization ρN2 belongs to the
network path with the lower wavelength utilization. Then ρN1 is equal to or higher than ρN2. Hence the
performance gain G is equal to or
higher than 1.In general, the gain of performance can be determined for any two
arbitrary WDM optical network paths. In fact, the gain of performance expresses
the gain by using network pathN1 instead
of network path N2. If the number of
fibers F and wavelengths W are the same for both compared optical
network paths, we can speak about the gain
of wavelength conversionGk instead of the gain of performance [2] because only the wavelength
conversion degree is different. Thus the full wavelength conversion network
path (k=W) can be compared with limited (1<k<W) or no (k=1) wavelength conversion network path.
If the number of wavelengths W and
the conversion degree k are the same
for both optical network paths, this can be expressed as the gain of using multiple fibersGF or gain of multifiber network paths. Thanks to this, the multifiber (FN1>1) and single-fiber (FN2=1) network paths or two
different mutlifiber network paths (FN1>1,FN2>1) can
be compared to each other. Finally, if the number of fibers F and the conversion degree k are the same, the gain of the using multiple wavelengthsGW (or the gain of multiwavelength network paths) is
defined. Thus, for example, two network paths with different numbers of
wavelengths (WN1,WN2) can be
compared. All these definitions are summarized in Table 2.Table 2
Overview of the gain of performance.
Gain ofExpressionEqual parametersDifferent parametersPerformanceG=ρN1/ρN2|Pb,H—FN1≠FN2, WN1≠WN2,kN1≠kN2Wavelength conversionGk=ρN1/ρN2|Pb,H,F,WFN1=FN2=F,k1≠k2WN1=WN2=WUsing multiple fibersGF=ρN1/ρN2|Pb,H,W,kWN1=WN2=W,FN1≠FN2kN1=kN2=kUsing multiple wavelengthsGW=ρN1/ρN2|Pb,H,F,kFN1=FN2=F,WN1≠WNkN1=kN2=k


### 4.1. Numerical Results of the Performance Gain

The gain of performance enables to comparison of the wavelength
utilization between two different optical network path scenarios. Typical
graphical characteristics of the performance gainG versus the number of wavelengths W are plotted in Figures 7–10 for blocking probability Pb=10−3. The
results are presented only for network path as is depicted in Figure 1(b).Figure 7
The gain of wavelength conversionGW=f(W), Pb=10−3, F=10, and full/no.Figure 8
The gain of wavelength conversionGW=f(W), Pb=10−3, F=1, k=3, and lim/no.Figure 9
The gain of wavelength conversionGW=f(W), Pb=10−3, F=10, k=3,
and lim/no.Figure 10
The
gain of performanceGW=f(W), Pb=10−3, and F=10 no/F=1 no.The typical characteristics of the gain of wavelength conversionGW, which are presented in
[4], only compare full with no wavelength conversion of single-fiber network
path. According to this, the wavelength utilization is better for the full
wavelength conversion network, in contrast to the no wavelength conversion
network. The performance gain of this case is rather high, for example, it is
still higher than 4 for 2<W<50
and H=10. This figure also shows that
the gain G increases as the number of
hops H increases quite considerably.In Figure7, the gain of wavelength conversion GW of the full and no wavelength
conversion scenario is plotted for multifiber network paths. From the beginning,
as the number of wavelengths W increases, the gain GW increases quite dramatically and almost linearly. The maximum peak of gain GW is somewhere near W=H/2
based on observation. After that, the gain GW slowly decreases and the convergence of the gain GW=1 is extremely slow for W→∞.It can be seen from Figure7 that the gain of this scenario is really
small, for example, it is still lower than GW<1.2
for any number of the wavelengths (although the figure is plotted only for W<50) and H=10 hops. This is due to the fact that, although the no wavelength
conversion multifiber network path provide no wavelength conversion, a different
fiber may be used on each subsequent hop. Hence the performance of the no
wavelength conversion multifiber network paths is quite similar to the performance
of the limited wavelength conversion single-fiber network paths. Also it can be
seen from this figure that the effect of the number of hops is not very
significant.In Figures8 and 9, the gain of wavelength conversion GW of the limited (k=3) and no wavelength conversion scenarios
is plotted for both single-fiber and multifiber network paths, respectively. If
the number of wavelengths is smaller than or equal to the conversion degree W≤k,
the limited wavelength conversion network path performs the same as the full
wavelength conversion network path. Therefore, at the beginning, the curves are
exactly the same as in the previous case. The gain GW increases quite dramatically as the number of
wavelengths W increases. The peak
value of gain GW is for W=k.
After that, gain GW decreases and the convergence of gain GW=1
is quite slow for W→∞.It can be seen from Figure8 that the gain is still rather high,
but not as high as the gain of full instead of no wavelength conversion optical
single-fiber path scenario presented in [4], for example, GW>2.5 for 1<W<50, H=10, and k=3. It can be observed for the multifiber network path scenario in
Figure 9, that the curves are very similar, again. However, the gain is really
poor, for example, GW<1.16
for H=10 and W<50.The graphical characteristic of the gain of using multifibersGF is plotted in Figure 10
for the no wavelength conversion scenario like a comparison of using multifiber
network path F=10 instead of the single-fiber
network path F=1. The gain is
extremely high for W=1, for example, G≈4000 for H=10, because the probability that there
is no wavelength continuous lightpath is too high for no wavelength conversion
single-fiber network paths in contrast to no wavelength conversion multifiber paths F=10. The gain GF decreases dramatically as the number of wavelengths
increases until about W<10. Then
it decreases very slowly and almost linearly. The convergence of the gain GF=1 is extremely slow for W→∞. From the figure, it can be seen
that the gain is still high, for example, GF≈8 for W=20 and H=10.Figure11 is plotted for the comparison of full wavelength
conversion multifiber network paths F=10
and no wavelength conversion single-fiber network paths F=1. It can be observed that the curves are very similar to the previous
case although the multifiber network path enables full wavelength conversion. The
gain G is for F≤W quite high, for
example, G≈9 for W=20 and H=10. However, the difference in gain is not very significant in
comparison to previous case.Figure 11
The gain of performanceG=f(W), Pb=10−3,
and F=10 full/F=1 no.Note that the performance gain compares the wavelength
utilization between any two different optical networks. Generally, there are 15
possibilities. Unfortunately, the detailed explanation and graphical
presentation of all possibilities are beyond the scope of this paper. However, this
research is the subject of a PhD Thesis [6] which is recommended to be read.
The numerical results of all possibilities are summarized in Table 3 for W=5, H=10,
and Pb=10−3;
and in Table 4 for W=20, H=10, and Pb=10−3 [6].Table 3
The gain of performance,W=5, H=10, and Pb=10−3.
F=1No1Lim4.09891Full5.55911.35621F=10No24.57365.99514.42041Lim28.29676.90345.09021.15151Full29.17227.11705.24761.18711.03091H=10,NoLimFullNoLimFullW=5,F=1F=10Pb=10−3Table 4
The gain of performance,W=20, H=10, Pb=10−3.
F=1No1Lim3.02221Full5.44841.80281F=10No6.96042.30311.27751Lim7.77442.57241.42691.11691Full8.24632.72861.51351.18481.06071H=10,NoLimFullNoLimFullW=20,F=1F=10Pb=10−3The performance gain of using single-fiber network paths with small
conversion degreek=3 (limited
wavelength conversion) instead of single-fiber network paths with no wavelength
conversion is rather high. Hence the implementation of the limited wavelength
conversion into single-fiber network paths is profitable. For full wavelength
conversion scenarios the gain is even higher.The gain of using multifiber network paths is also really high.
Hence the application of multifiber network paths is really significant.
Moreover, the cable cost of multifiber cables is still decreasing. The
difference between using limited or full wavelength conversion multifiber
network paths instead of no wavelength multifiber network paths is negligible. Hence
there is no reason to replace single-fiber network paths by limited or full
wavelength conversion multifiber network paths, but only with no wavelength
conversion multifiber network paths. In this case, no wavelength conversion
multifiber network paths seem to be the optimal solution in terms of network
performance and cost.The results of comparison of different optical path scenarios in
term of the gain are briefly summarized as follows:(i)
the gain of wavelength conversionGW is rather high for single-fiber network paths;(ii)
the gain of wavelength conversionGW is quite small for
multifiber network paths;(iii)
the gain of using multiple fibersGF is still quite high depend
on the range of wavelength conversion of single-fiber network paths.


## 4.1. Numerical Results of the Performance Gain

The gain of performance enables to comparison of the wavelength
utilization between two different optical network path scenarios. Typical
graphical characteristics of the performance gainG versus the number of wavelengths W are plotted in Figures 7–10 for blocking probability Pb=10−3. The
results are presented only for network path as is depicted in Figure 1(b).Figure 7
The gain of wavelength conversionGW=f(W), Pb=10−3, F=10, and full/no.Figure 8
The gain of wavelength conversionGW=f(W), Pb=10−3, F=1, k=3, and lim/no.Figure 9
The gain of wavelength conversionGW=f(W), Pb=10−3, F=10, k=3,
and lim/no.Figure 10
The
gain of performanceGW=f(W), Pb=10−3, and F=10 no/F=1 no.The typical characteristics of the gain of wavelength conversionGW, which are presented in
[4], only compare full with no wavelength conversion of single-fiber network
path. According to this, the wavelength utilization is better for the full
wavelength conversion network, in contrast to the no wavelength conversion
network. The performance gain of this case is rather high, for example, it is
still higher than 4 for 2<W<50
and H=10. This figure also shows that
the gain G increases as the number of
hops H increases quite considerably.In Figure7, the gain of wavelength conversion GW of the full and no wavelength
conversion scenario is plotted for multifiber network paths. From the beginning,
as the number of wavelengths W increases, the gain GW increases quite dramatically and almost linearly. The maximum peak of gain GW is somewhere near W=H/2
based on observation. After that, the gain GW slowly decreases and the convergence of the gain GW=1 is extremely slow for W→∞.It can be seen from Figure7 that the gain of this scenario is really
small, for example, it is still lower than GW<1.2
for any number of the wavelengths (although the figure is plotted only for W<50) and H=10 hops. This is due to the fact that, although the no wavelength
conversion multifiber network path provide no wavelength conversion, a different
fiber may be used on each subsequent hop. Hence the performance of the no
wavelength conversion multifiber network paths is quite similar to the performance
of the limited wavelength conversion single-fiber network paths. Also it can be
seen from this figure that the effect of the number of hops is not very
significant.In Figures8 and 9, the gain of wavelength conversion GW of the limited (k=3) and no wavelength conversion scenarios
is plotted for both single-fiber and multifiber network paths, respectively. If
the number of wavelengths is smaller than or equal to the conversion degree W≤k,
the limited wavelength conversion network path performs the same as the full
wavelength conversion network path. Therefore, at the beginning, the curves are
exactly the same as in the previous case. The gain GW increases quite dramatically as the number of
wavelengths W increases. The peak
value of gain GW is for W=k.
After that, gain GW decreases and the convergence of gain GW=1
is quite slow for W→∞.It can be seen from Figure8 that the gain is still rather high,
but not as high as the gain of full instead of no wavelength conversion optical
single-fiber path scenario presented in [4], for example, GW>2.5 for 1<W<50, H=10, and k=3. It can be observed for the multifiber network path scenario in
Figure 9, that the curves are very similar, again. However, the gain is really
poor, for example, GW<1.16
for H=10 and W<50.The graphical characteristic of the gain of using multifibersGF is plotted in Figure 10
for the no wavelength conversion scenario like a comparison of using multifiber
network path F=10 instead of the single-fiber
network path F=1. The gain is
extremely high for W=1, for example, G≈4000 for H=10, because the probability that there
is no wavelength continuous lightpath is too high for no wavelength conversion
single-fiber network paths in contrast to no wavelength conversion multifiber paths F=10. The gain GF decreases dramatically as the number of wavelengths
increases until about W<10. Then
it decreases very slowly and almost linearly. The convergence of the gain GF=1 is extremely slow for W→∞. From the figure, it can be seen
that the gain is still high, for example, GF≈8 for W=20 and H=10.Figure11 is plotted for the comparison of full wavelength
conversion multifiber network paths F=10
and no wavelength conversion single-fiber network paths F=1. It can be observed that the curves are very similar to the previous
case although the multifiber network path enables full wavelength conversion. The
gain G is for F≤W quite high, for
example, G≈9 for W=20 and H=10. However, the difference in gain is not very significant in
comparison to previous case.Figure 11
The gain of performanceG=f(W), Pb=10−3,
and F=10 full/F=1 no.Note that the performance gain compares the wavelength
utilization between any two different optical networks. Generally, there are 15
possibilities. Unfortunately, the detailed explanation and graphical
presentation of all possibilities are beyond the scope of this paper. However, this
research is the subject of a PhD Thesis [6] which is recommended to be read.
The numerical results of all possibilities are summarized in Table 3 for W=5, H=10,
and Pb=10−3;
and in Table 4 for W=20, H=10, and Pb=10−3 [6].Table 3
The gain of performance,W=5, H=10, and Pb=10−3.
F=1No1Lim4.09891Full5.55911.35621F=10No24.57365.99514.42041Lim28.29676.90345.09021.15151Full29.17227.11705.24761.18711.03091H=10,NoLimFullNoLimFullW=5,F=1F=10Pb=10−3Table 4
The gain of performance,W=20, H=10, Pb=10−3.
F=1No1Lim3.02221Full5.44841.80281F=10No6.96042.30311.27751Lim7.77442.57241.42691.11691Full8.24632.72861.51351.18481.06071H=10,NoLimFullNoLimFullW=20,F=1F=10Pb=10−3The performance gain of using single-fiber network paths with small
conversion degreek=3 (limited
wavelength conversion) instead of single-fiber network paths with no wavelength
conversion is rather high. Hence the implementation of the limited wavelength
conversion into single-fiber network paths is profitable. For full wavelength
conversion scenarios the gain is even higher.The gain of using multifiber network paths is also really high.
Hence the application of multifiber network paths is really significant.
Moreover, the cable cost of multifiber cables is still decreasing. The
difference between using limited or full wavelength conversion multifiber
network paths instead of no wavelength multifiber network paths is negligible. Hence
there is no reason to replace single-fiber network paths by limited or full
wavelength conversion multifiber network paths, but only with no wavelength
conversion multifiber network paths. In this case, no wavelength conversion
multifiber network paths seem to be the optimal solution in terms of network
performance and cost.The results of comparison of different optical path scenarios in
term of the gain are briefly summarized as follows:(i)
the gain of wavelength conversionGW is rather high for single-fiber network paths;(ii)
the gain of wavelength conversionGW is quite small for
multifiber network paths;(iii)
the gain of using multiple fibersGF is still quite high depend
on the range of wavelength conversion of single-fiber network paths.


## 5. Conclusion

In this paper, a new theoretical model for analyzing blocking
performance in both single-fiber and multifiber optical network paths with no,
limited, or full wavelength conversion is proposed. The method of computing overall
blocking probability of any arbitrary WDM networks using the proposed model is
also presented. The numerical results of the model are also presented. Taking
into consideration both the wavelength utilization and the blocking probability
determined by this model, the optimal network could be designed. The simplicity
of the model enables detailed analysis of any optical network and it can be
also used to solve the optimal wavelength placement converter problem.The model is general and, moreover, it shows that a no wavelength
conversion multifiber network path withF fibers per link and with W wavelengths on each fiber yields same performance as a limited wavelength
conversion of degree F single-fiber network
path with F⋅W wavelengths per fiber
on each link.Thanks to the proposed model and gain of performance, any two
different optical network path scenarios can be compared in terms of their
performance or blocking probability. The results, which appear interesting, are
presented in the paper. The most important conclusions from this paper are that
a no wavelength conversion multifiber network path has similar blocking performance
to a limited or full wavelength conversion single-fiber network path, the gain
of wavelength conversionGW is rather high for single-fiber in contrast to multifiber network path and the
gain of using multiple fibers GF is still quite high. Most of the current optical networks are built on multiple
fibers. Multifiber WDM networks without wavelength conversion is not only a
feasible, but also a desirable choice using current technologies. Moreover, the
multifiber networks may also offer a cost advantage depending on the relative
cost of optical components.



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*Source: 289690-2008-03-17.xml*