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Blocking in wavelength-routed all-optical WDM network with wavelength conversion
Optik 122 (2011) 631–634
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Blocking in wavelength-routed all-optical WDM network with wavelength conversion Amit Wason ∗ , R.S. Kaler Electronics & Communication Engineering Department, Thapar University, Patiala, Punjab 147004, India
a r t i c l e
i n f o
Article history: Received 11 September 2009 Accepted 5 April 2010
Keywords: Blocking probability WDM networks RWA
a b s t r a c t The blocking probability in wavelength-routed all optical networks is very important measure of performance of the network, which can be affected by many factors such as network topology, traffic load, number of links, algorithms employed and whether wavelength conversion is available or not. In this paper, we have proposed a mathematical model to reduce the blocking probability of the WDM optical network for wavelength-convertible networks. The model can be used to evaluate the blocking performance of any network topology also it can be useful to improve its blocking performance of the given network topology. The blocking probability variation of the network for a particular load (per link) has been studied based on the load variation and total number of wavelengths used in the network. This model gives good results for high load (per link). © 2010 Elsevier GmbH. All rights reserved.
1. Introduction The rapid growth of internet traffic has been the driving force for faster and more reliable data communication networks. Wavelength division multiplexing (WDM) is probably the most powerful technique to unlock the enormous bandwidth in optical fiber and thus overcome the electronic bottleneck without laying new fiber [1]. In a WDM network several optical signals are sent on the same fibers using different wavelength channels. Sometimes the term dense wavelength division multiplexing (DWDM) is used to distinguish the technology from the broadband WDM systems where two widely separated signals (typically 1310 and 1550 nm) share a common fiber. Traditionally only a small fraction of the fiber capacity is in use, but by using WDM it is possible to exploit this huge capacity more efficiently. Optical wavelength division multiplexing network technologies promise to offer vast amount of bandwidth by delivering data over multiple channels using multiple wavelengths simultaneously. Currently, dense WDM technology can already achieve up to 320 wavelengths per fiber with each wavelength carrying 10 Gb/s, resulting in a total transmission capacity up to 3.2Tbps. There is a growing mismatch between the transmission capacity of optical fibers and the electronic switching capability. The transmission capacity of each wavelength is expected to increase further with the advancement of technology. Although electronic processing and switching are struggling to keep pace with the transmission capacity of fiber optics, it is just a matter of
∗ Corresponding author. Tel.: +919896240333. E-mail address: [email protected] (A. Wason). 0030-4026/$ – see front matter © 2010 Elsevier GmbH. All rights reserved. doi:10.1016/j.ijleo.2010.04.021
time for electronics to become the bottleneck. Moreover, the cost of high speed electronics is becoming economically unattractive. The design and operation of revenue generating optical WDM networks requires the reduction of cost. It is thus imperative to reduce costly electronics by enabling optical bypassing as much as possible. Wavelength-routed WDM networks consists of WXCs (routing nodes) interconnected by point-to-point fiber links in an arbitrary topology. Each end node (end user) is connected to a WXC is referred to as a (network) node [2]. Each node is equipped with a set of transmitters and receivers, for sending data into the network and receiving data from the network, respectively, both of which may be wavelength-tunable. In a wavelength-routed network, a message is sent from one node to another node using wavelength continuous route called a lightpath, without requiring any optical–electronic–optical conversion and buffering at the intermediate nodes. This process is known as wavelength routing. Note that the intermediate nodes route the lightpath in the optical domain using their WXCs. The end nodes of the lightpath access the lightpath using transmitters/receivers that are tuned to the wavelength on which the lightpath operates. Fig. 1 shows a wavelength-routed network containing two WDM cross-connects (S1 and S2) and five access stations (A through E). Three lightpaths have been set up (C to A on wavelength 1, C to B on 2, and D to E on 1). In wavelength-routed WDM networks, a connection is realized by a lightpath. In order to establish a connection between a source–destination pair, a wavelength continuous route needs to be found between the node pair. An algorithm used for selecting routes and wavelengths to establish lightpath is known as a routing and wavelength assignment (RWA) algorithm. Many problems in wavelength-routed WDM networks have RWA as a sub-problem.
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A. Wason, R.S. Kaler / Optik 122 (2011) 631–634
Fig. 1. All optical wavelength-routed network.
Therefore, it is mandatory to use a good routing and wavelength assignment algorithm to establish lightpaths in an efficient manner. Wavelength assignment is a unique feature in wavelength-routed networks that distinguishes from conventional networks. A lightpath is an all-optical communication path between two nodes, established by allocating the same wavelength throughout the route of the transmitted data. Thus it is a high-bandwidth pipe, carrying data up to several gigabits per second, and is uniquely identified by a physical path and a wavelength. The requirement that the same wavelength must be used on all the links along the selected routed is known as wavelength continuity constraint. Two lightpaths cannot be assigned the same wavelength on any fiber. The requirement is known as distinct wavelength assignment constraint. However, two lightpaths can use the same wavelength if they use distinct set of links. This property is known as wavelength reuse. In wavelength-routed networks, lightpaths are used to carry messages. A message is transmitted between the end nodes (source–destination nodes) of a lightpath without undergoing any electrical–optical conversion at intermediate nodes. Wavelength converters play an important role in WDM networks. A wavelength converter is an optical device which is capable of shifting one wavelength to another wavelength. An ideal wavelength converter would change the wavelength of an optical signal independent of its bit-rate, data format, polarization, wavelength, or power as seen in Fig. 2. However, practical wavelength converters are far from ideal, and depending on the technique, are sensitive to some or all of the input signal parameters. Other important performance metrics for wavelength converters are a low noise figure and a high output extinction ratio. Wavelength conversion can eliminate the wavelength continuity constraint and can thus improve the blocking performance significantly [3]. A WXC having one or more wavelength converters is called as a wavelength interchange crossconnect (WIXC). A node with wavelength converting capability is
Fig. 2. Wavelength conversion.
called wavelength converting (WC) node. A WDM network with WC nodes is called wavelength-convertible network. A wavelengthconvertible network performs better than a wavelength-selective network. Wavelength converters relax the continuity constraint at a node. Therefore they help to reduce the bandwidth loss, resulting in better bandwidth utilization. Since the wavelength converters are very expensive now a days, much research work focuses on sparse wavelength conversion, in which only a part of network nodes have the capability of wavelength. If all the network nodes have the capability of wavelength conversion, this is referred to as full wavelength conversion. There are a number of models covered in literature for calculation of blocking probability of optical networks. The blocking probabilities of optical network models for the schemes: fixed routing and least-loaded routing are calculated by using generalized reduced load approximation techniques in [4]. The role of wavelength converter for increasing the capacity and flexibility has been discussed in [5] for future broadcast network. The routing and wavelength assignment problem on wavelength division multiplexing networks without wavelength conversion has been discussed in [6]. A new wavelength conversion algorithm has been proposed in a DWDM network using online routing in [7] also, the model for the algorithm has been theoretically developed and the corresponding call connection probability has been calculated. Many mathematical models have been proposed in the literature but a very few of them are for networks with wavelength conversion. Also, those models are complex in nature also high simulation statics are required. The model proposed in this paper is a low complexity model which is very useful for the calculation and reduction of blocking probability of the network which can be used for wavelength-routed all-optical WDM network with wavelength conversion. Also, this model does not require any simulation statistics and gives good results in reduction of blocking probability of the network. This paper is organized as follows: In Section 2, we have proposed a mathematical model for a wavelength-routed all-optical WDM network with wavelength conversion. Section 3 focuses on the results and discussion, which shows simulation results for variation of blocking probability with load and number of wavelength available for wavelength-convertible network. The conclusions are covered in Section 4.
2. Mathematical model We have proposed a mathematical model for the wavelengthrouted all-optical WDM network with wavelength conversion. We denote the path and the network-wide parameters by upper-case letters and link parameters by lower case letters. Subscripts and superscripts refer to specific instances of links, node pairs and routes. We have assumed the network without wavelength conversion.
• N is the number of nodes in the WDM network; N ∈ V. • l is the length of the route or the number of links in the route or path selected. • r is the number of routes available where r ∈ R. • W is the total number of wavelengths used in the network. • C is the number of converters used in the network. • P r is the blocking probability of r routes. B • PB is the overall blocking probability of the network. • P r is the blocking probability caused by insufficient wavelength. BW • P r is the blocking probability caused by lack of converter. BC r • L is the load of the route r.
A. Wason, R.S. Kaler / Optik 122 (2011) 631–634
633
Given N node WDM network, all the nodes forms a set V, and all directed links are contained in as set E. Suppose fixed path routing policy is adopted the lightpath establishment, the predetermined directed routes are indicated with a set R. For each route r ∈ R, the blocking probability for the connections along route r can be r r . The total divided into two mutual exclusive parts; PBW and PBC blocking probability for a network with wavelength conversion is given by r r + PBC , PBr = PBW
PB =
r ∈R
(1)
Lr P r r ∈ R r B − PN r ∈R
L
Fig. 3. Blocking probability vs load.
r r Lr PBW Lr PBC r ∈ R r ∈ R PB = + − PN , r r r ∈R
r ∈R
PB =
L
r ∈R
(2)
L
W i C (L) /i! + (1/C!) i=0 (L)i /i!] i=0 r
(L)r+1 [(1/W !)/
r ∈R
(L)
−PN
(3)
where PN represents the probability of the system when the first blocking occurs and the wavelength is converted to the other fixed wavelength and its value can be calculated as in equation. PN =
total number of calls blocked . total number of calls generated
(4)
3. Results and discussion We have considered the network as wavelength-routed alloptical WDM network with wavelength conversion. The total r r , i.e. and PBC blocking probability of the network depends on the PBW the blocking probability caused by insufficient wavelength and the blocking probability caused by lack of converter. The expression (3) represents that the blocking probability depends on the total number of wavelengths available, number of links in the route or path selected, Load on the route r and the number of converters used in the network. The blocking probability of the network has been calculated according to this model for the wavelength-routed all-optical wavelength-convertible networks. We have used sparse wavelength conversion and calculated the variation of blocking probability of the network with the load and number of total wavelengths available in the network. Table 1 Blocking probability (%age). Load
W=1
W=2
W=3
W=4
W=5
1 2 3 4 5 6 7 8 9 10 20 30 40 50 100 200 500
50 66.66667 75 80 83.33333 85.71429 87.5 88.88889 90 90.90909 95.2381 96.77419 97.56098 98.03922 99.0099 99.50249 99.8004
20 25 27.27273 28.57143 29.41176 30 30.43478 30.76923 31.03448 31.25 32.25806 32.6087 32.78689 32.89474 33.11258 33.22259 33.28895
6.25 6.896552 7.142857 7.272727 7.352941 7.407407 7.446809 7.476636 7.5 7.518797 7.604563 7.633588 7.648184 7.656968 7.674597 7.683442 7.688759
1.538462 1.587302 1.604278 1.612903 1.618123 1.621622 1.62413 1.626016 1.627486 1.628664 1.633987 1.635769 1.636661 1.637197 1.63827 1.638807 1.639129
0.306748 0.309119 0.309917 0.310318 0.310559 0.31072 0.310835 0.310921 0.310988 0.311042 0.311284 0.311365 0.311405 0.311429 0.311478 0.311502 0.311517
Fig. 4. Blocking probability vs number of wavelengths.
Table 1 shows the value of blocking probability of the wavelength-convertible network for a particular load (per link) with the total number of wavelengths used in the network. For this model, it is clear from the table that the blocking probability of the network increases with load but it significantly decreases with increase in the total number of wavelengths used in the network. Figs. 3 and 5 show graphically the blocking probability distribution of the wavelength-convertible network with variation of load. The results shown in Fig. 4 shows that the blocking probability of the system is very high for high values of load. Its value decreases to a value comparable to zero when the total number of wavelengths available is increased to 5. This number of wavelengths can be easily achieved hence the blocking probability of the system is reduced to a very small value using this model (Fig. 5).
Fig. 5. Blocking probability vs load.
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A. Wason, R.S. Kaler / Optik 122 (2011) 631–634
4. Conclusions
References
The mathematical model proposed here is a closed-form expression and does not require simulation statistics, it has low implementation complexity and the computation is quite efficient for wavelength-convertible networks. The results explain that this model is good for network having high load. Also, we can see from the results that we can have better results for higher number of wavelengths, even for the large load per link. The value of blocking probability can be reduced to very low value comparable to zero using this model. The computation efficiency of the model is very high as it completes the simulation within 1 second with computer with Intel Pentium IV and 512MB RAM.
[1] G.I. Papadimitriou, P.A. Tsimoulas, M.S. Obaidat, A.S. Pomportsis, Multiwavelength Optical LANs, John Wiley & Sons Ltd., England, 2003. [2] C. Siva Ram Murthy, M. Gurusamy, WDM Optical Networks—Concepts, Design and Algorithms, Prentice-Hall of India Private Limited, New Delhi, India, 2002. [3] B. Ramamurthy, B. Mukherjee, Wavelength conversion in WDM networking, IEEE J. Selected Areas Commun. 16 (7) (1998) 1061–1073. [4] A. Birman, Computation approximation blocking probabilities for a class of alloptical network, IEEE J. Selected Areas Commun. 14 (5) (1996) 852– 857. [5] S. Singh, R.S. Kaler, All optical wavelength converters based on cross phase modulation in SOA-MZI configuration, Optik-Int. J. Light Electron Opt. 118 (2007) 390–394. [6] P. Singh, A.K. Sharma, S. Rani, Routing and wavelength assignment in WDM networks with dynamic link weight assignment, Optik-Int. J. Light Electron Opt. 118 (2007) 527–532. [7] A. Mukherjee, S.P. Singh, V.K. Chaubey, Wavelength conversion algorithm in an intelligent WDM network, Opt. Commun. 230 (2004) 59–65.
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Blocking in wavelength-routed all-optical WDM network with wavelength conversion Amit Wason ∗ , R.S. Kaler Electronics & Communication Engineering Department, Thapar University, Patiala, Punjab 147004, India
a r t i c l e
i n f o
Article history: Received 11 September 2009 Accepted 5 April 2010
Keywords: Blocking probability WDM networks RWA
a b s t r a c t The blocking probability in wavelength-routed all optical networks is very important measure of performance of the network, which can be affected by many factors such as network topology, traffic load, number of links, algorithms employed and whether wavelength conversion is available or not. In this paper, we have proposed a mathematical model to reduce the blocking probability of the WDM optical network for wavelength-convertible networks. The model can be used to evaluate the blocking performance of any network topology also it can be useful to improve its blocking performance of the given network topology. The blocking probability variation of the network for a particular load (per link) has been studied based on the load variation and total number of wavelengths used in the network. This model gives good results for high load (per link). © 2010 Elsevier GmbH. All rights reserved.
1. Introduction The rapid growth of internet traffic has been the driving force for faster and more reliable data communication networks. Wavelength division multiplexing (WDM) is probably the most powerful technique to unlock the enormous bandwidth in optical fiber and thus overcome the electronic bottleneck without laying new fiber [1]. In a WDM network several optical signals are sent on the same fibers using different wavelength channels. Sometimes the term dense wavelength division multiplexing (DWDM) is used to distinguish the technology from the broadband WDM systems where two widely separated signals (typically 1310 and 1550 nm) share a common fiber. Traditionally only a small fraction of the fiber capacity is in use, but by using WDM it is possible to exploit this huge capacity more efficiently. Optical wavelength division multiplexing network technologies promise to offer vast amount of bandwidth by delivering data over multiple channels using multiple wavelengths simultaneously. Currently, dense WDM technology can already achieve up to 320 wavelengths per fiber with each wavelength carrying 10 Gb/s, resulting in a total transmission capacity up to 3.2Tbps. There is a growing mismatch between the transmission capacity of optical fibers and the electronic switching capability. The transmission capacity of each wavelength is expected to increase further with the advancement of technology. Although electronic processing and switching are struggling to keep pace with the transmission capacity of fiber optics, it is just a matter of
∗ Corresponding author. Tel.: +919896240333. E-mail address: [email protected] (A. Wason). 0030-4026/$ – see front matter © 2010 Elsevier GmbH. All rights reserved. doi:10.1016/j.ijleo.2010.04.021
time for electronics to become the bottleneck. Moreover, the cost of high speed electronics is becoming economically unattractive. The design and operation of revenue generating optical WDM networks requires the reduction of cost. It is thus imperative to reduce costly electronics by enabling optical bypassing as much as possible. Wavelength-routed WDM networks consists of WXCs (routing nodes) interconnected by point-to-point fiber links in an arbitrary topology. Each end node (end user) is connected to a WXC is referred to as a (network) node [2]. Each node is equipped with a set of transmitters and receivers, for sending data into the network and receiving data from the network, respectively, both of which may be wavelength-tunable. In a wavelength-routed network, a message is sent from one node to another node using wavelength continuous route called a lightpath, without requiring any optical–electronic–optical conversion and buffering at the intermediate nodes. This process is known as wavelength routing. Note that the intermediate nodes route the lightpath in the optical domain using their WXCs. The end nodes of the lightpath access the lightpath using transmitters/receivers that are tuned to the wavelength on which the lightpath operates. Fig. 1 shows a wavelength-routed network containing two WDM cross-connects (S1 and S2) and five access stations (A through E). Three lightpaths have been set up (C to A on wavelength 1, C to B on 2, and D to E on 1). In wavelength-routed WDM networks, a connection is realized by a lightpath. In order to establish a connection between a source–destination pair, a wavelength continuous route needs to be found between the node pair. An algorithm used for selecting routes and wavelengths to establish lightpath is known as a routing and wavelength assignment (RWA) algorithm. Many problems in wavelength-routed WDM networks have RWA as a sub-problem.
632
A. Wason, R.S. Kaler / Optik 122 (2011) 631–634
Fig. 1. All optical wavelength-routed network.
Therefore, it is mandatory to use a good routing and wavelength assignment algorithm to establish lightpaths in an efficient manner. Wavelength assignment is a unique feature in wavelength-routed networks that distinguishes from conventional networks. A lightpath is an all-optical communication path between two nodes, established by allocating the same wavelength throughout the route of the transmitted data. Thus it is a high-bandwidth pipe, carrying data up to several gigabits per second, and is uniquely identified by a physical path and a wavelength. The requirement that the same wavelength must be used on all the links along the selected routed is known as wavelength continuity constraint. Two lightpaths cannot be assigned the same wavelength on any fiber. The requirement is known as distinct wavelength assignment constraint. However, two lightpaths can use the same wavelength if they use distinct set of links. This property is known as wavelength reuse. In wavelength-routed networks, lightpaths are used to carry messages. A message is transmitted between the end nodes (source–destination nodes) of a lightpath without undergoing any electrical–optical conversion at intermediate nodes. Wavelength converters play an important role in WDM networks. A wavelength converter is an optical device which is capable of shifting one wavelength to another wavelength. An ideal wavelength converter would change the wavelength of an optical signal independent of its bit-rate, data format, polarization, wavelength, or power as seen in Fig. 2. However, practical wavelength converters are far from ideal, and depending on the technique, are sensitive to some or all of the input signal parameters. Other important performance metrics for wavelength converters are a low noise figure and a high output extinction ratio. Wavelength conversion can eliminate the wavelength continuity constraint and can thus improve the blocking performance significantly [3]. A WXC having one or more wavelength converters is called as a wavelength interchange crossconnect (WIXC). A node with wavelength converting capability is
Fig. 2. Wavelength conversion.
called wavelength converting (WC) node. A WDM network with WC nodes is called wavelength-convertible network. A wavelengthconvertible network performs better than a wavelength-selective network. Wavelength converters relax the continuity constraint at a node. Therefore they help to reduce the bandwidth loss, resulting in better bandwidth utilization. Since the wavelength converters are very expensive now a days, much research work focuses on sparse wavelength conversion, in which only a part of network nodes have the capability of wavelength. If all the network nodes have the capability of wavelength conversion, this is referred to as full wavelength conversion. There are a number of models covered in literature for calculation of blocking probability of optical networks. The blocking probabilities of optical network models for the schemes: fixed routing and least-loaded routing are calculated by using generalized reduced load approximation techniques in [4]. The role of wavelength converter for increasing the capacity and flexibility has been discussed in [5] for future broadcast network. The routing and wavelength assignment problem on wavelength division multiplexing networks without wavelength conversion has been discussed in [6]. A new wavelength conversion algorithm has been proposed in a DWDM network using online routing in [7] also, the model for the algorithm has been theoretically developed and the corresponding call connection probability has been calculated. Many mathematical models have been proposed in the literature but a very few of them are for networks with wavelength conversion. Also, those models are complex in nature also high simulation statics are required. The model proposed in this paper is a low complexity model which is very useful for the calculation and reduction of blocking probability of the network which can be used for wavelength-routed all-optical WDM network with wavelength conversion. Also, this model does not require any simulation statistics and gives good results in reduction of blocking probability of the network. This paper is organized as follows: In Section 2, we have proposed a mathematical model for a wavelength-routed all-optical WDM network with wavelength conversion. Section 3 focuses on the results and discussion, which shows simulation results for variation of blocking probability with load and number of wavelength available for wavelength-convertible network. The conclusions are covered in Section 4.
2. Mathematical model We have proposed a mathematical model for the wavelengthrouted all-optical WDM network with wavelength conversion. We denote the path and the network-wide parameters by upper-case letters and link parameters by lower case letters. Subscripts and superscripts refer to specific instances of links, node pairs and routes. We have assumed the network without wavelength conversion.
• N is the number of nodes in the WDM network; N ∈ V. • l is the length of the route or the number of links in the route or path selected. • r is the number of routes available where r ∈ R. • W is the total number of wavelengths used in the network. • C is the number of converters used in the network. • P r is the blocking probability of r routes. B • PB is the overall blocking probability of the network. • P r is the blocking probability caused by insufficient wavelength. BW • P r is the blocking probability caused by lack of converter. BC r • L is the load of the route r.
A. Wason, R.S. Kaler / Optik 122 (2011) 631–634
633
Given N node WDM network, all the nodes forms a set V, and all directed links are contained in as set E. Suppose fixed path routing policy is adopted the lightpath establishment, the predetermined directed routes are indicated with a set R. For each route r ∈ R, the blocking probability for the connections along route r can be r r . The total divided into two mutual exclusive parts; PBW and PBC blocking probability for a network with wavelength conversion is given by r r + PBC , PBr = PBW
PB =
r ∈R
(1)
Lr P r r ∈ R r B − PN r ∈R
L
Fig. 3. Blocking probability vs load.
r r Lr PBW Lr PBC r ∈ R r ∈ R PB = + − PN , r r r ∈R
r ∈R
PB =
L
r ∈R
(2)
L
W i C (L) /i! + (1/C!) i=0 (L)i /i!] i=0 r
(L)r+1 [(1/W !)/
r ∈R
(L)
−PN
(3)
where PN represents the probability of the system when the first blocking occurs and the wavelength is converted to the other fixed wavelength and its value can be calculated as in equation. PN =
total number of calls blocked . total number of calls generated
(4)
3. Results and discussion We have considered the network as wavelength-routed alloptical WDM network with wavelength conversion. The total r r , i.e. and PBC blocking probability of the network depends on the PBW the blocking probability caused by insufficient wavelength and the blocking probability caused by lack of converter. The expression (3) represents that the blocking probability depends on the total number of wavelengths available, number of links in the route or path selected, Load on the route r and the number of converters used in the network. The blocking probability of the network has been calculated according to this model for the wavelength-routed all-optical wavelength-convertible networks. We have used sparse wavelength conversion and calculated the variation of blocking probability of the network with the load and number of total wavelengths available in the network. Table 1 Blocking probability (%age). Load
W=1
W=2
W=3
W=4
W=5
1 2 3 4 5 6 7 8 9 10 20 30 40 50 100 200 500
50 66.66667 75 80 83.33333 85.71429 87.5 88.88889 90 90.90909 95.2381 96.77419 97.56098 98.03922 99.0099 99.50249 99.8004
20 25 27.27273 28.57143 29.41176 30 30.43478 30.76923 31.03448 31.25 32.25806 32.6087 32.78689 32.89474 33.11258 33.22259 33.28895
6.25 6.896552 7.142857 7.272727 7.352941 7.407407 7.446809 7.476636 7.5 7.518797 7.604563 7.633588 7.648184 7.656968 7.674597 7.683442 7.688759
1.538462 1.587302 1.604278 1.612903 1.618123 1.621622 1.62413 1.626016 1.627486 1.628664 1.633987 1.635769 1.636661 1.637197 1.63827 1.638807 1.639129
0.306748 0.309119 0.309917 0.310318 0.310559 0.31072 0.310835 0.310921 0.310988 0.311042 0.311284 0.311365 0.311405 0.311429 0.311478 0.311502 0.311517
Fig. 4. Blocking probability vs number of wavelengths.
Table 1 shows the value of blocking probability of the wavelength-convertible network for a particular load (per link) with the total number of wavelengths used in the network. For this model, it is clear from the table that the blocking probability of the network increases with load but it significantly decreases with increase in the total number of wavelengths used in the network. Figs. 3 and 5 show graphically the blocking probability distribution of the wavelength-convertible network with variation of load. The results shown in Fig. 4 shows that the blocking probability of the system is very high for high values of load. Its value decreases to a value comparable to zero when the total number of wavelengths available is increased to 5. This number of wavelengths can be easily achieved hence the blocking probability of the system is reduced to a very small value using this model (Fig. 5).
Fig. 5. Blocking probability vs load.
634
A. Wason, R.S. Kaler / Optik 122 (2011) 631–634
4. Conclusions
References
The mathematical model proposed here is a closed-form expression and does not require simulation statistics, it has low implementation complexity and the computation is quite efficient for wavelength-convertible networks. The results explain that this model is good for network having high load. Also, we can see from the results that we can have better results for higher number of wavelengths, even for the large load per link. The value of blocking probability can be reduced to very low value comparable to zero using this model. The computation efficiency of the model is very high as it completes the simulation within 1 second with computer with Intel Pentium IV and 512MB RAM.
[1] G.I. Papadimitriou, P.A. Tsimoulas, M.S. Obaidat, A.S. Pomportsis, Multiwavelength Optical LANs, John Wiley & Sons Ltd., England, 2003. [2] C. Siva Ram Murthy, M. Gurusamy, WDM Optical Networks—Concepts, Design and Algorithms, Prentice-Hall of India Private Limited, New Delhi, India, 2002. [3] B. Ramamurthy, B. Mukherjee, Wavelength conversion in WDM networking, IEEE J. Selected Areas Commun. 16 (7) (1998) 1061–1073. [4] A. Birman, Computation approximation blocking probabilities for a class of alloptical network, IEEE J. Selected Areas Commun. 14 (5) (1996) 852– 857. [5] S. Singh, R.S. Kaler, All optical wavelength converters based on cross phase modulation in SOA-MZI configuration, Optik-Int. J. Light Electron Opt. 118 (2007) 390–394. [6] P. Singh, A.K. Sharma, S. Rani, Routing and wavelength assignment in WDM networks with dynamic link weight assignment, Optik-Int. J. Light Electron Opt. 118 (2007) 527–532. [7] A. Mukherjee, S.P. Singh, V.K. Chaubey, Wavelength conversion algorithm in an intelligent WDM network, Opt. Commun. 230 (2004) 59–65.