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Performance analysis of traffic groomed optical network
Optik 123 (2012) 788–791
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Performance analysis of traffic groomed optical network Vithal J. Gond ∗ , Aditya Goel Department of Electronics and Communication, Maulana Azad National Institute of Technology, Bhopal 462051, India
a r t i c l e
i n f o
Article history: Received 31 December 2010 Accepted 28 May 2011
Keywords: WDM network Traffic grooming factor Blocking probability Routing and wavelength assignment
a b s t r a c t In this paper we carry out the performance analysis of traffic groomed multilayer optical networks. It is seen that the number of wavelength channels required decreases as the wavelength grooming factor increases. We have evaluated blocking probability for different load and grooming factor. The performance of the network has been evaluated for different conditions; first for fixed number of links with grooming factor set to 3 and subsequently with increase in grooming factor up to 18 in steps. The load on each link is selected as 2, 5, 9, 12, 15 and 20 Erlangs and the blocking probability as function of number of optical channels has been evaluated. In this work the effect of number of wavelength channels, traffic load and grooming factor on network blocking probability has been studied. The investigation reveals that the blocking probability decreases with increase in wavelength channels. Similarly we found that the blocking probability increases with increase in traffic load which is quite evident. Further it is shown that when the grooming factor is increased to significant value (16), the number of wavelengths requirement (8) becomes relatively stable. © 2011 Elsevier GmbH. All rights reserved.
1. Introduction The traffic grooming is use to efficiently groom low-speed traffic onto high capacity WDM channels. The generic grooming idea can be applied to any arbitrary optical network. The issue in transporting client calls using lightpaths is that client calls have data rates which are generally much smaller than the lightpath capacity. To address this issue traffic grooming techniques is used to combine low speed traffic stream on to high speed lightpaths. The traffic grooming is applied to groom low speed traffic to high speed lightpaths to share the resources in optical layer there by utilizing the network resources and reducing the overall cost of network. For each incoming call it is necessary to find a path consisting of logical links. The process of finding paths to consolidated client calls over logical topology is called traffic grooming. Efficiently grooming low-speed connections onto high capacity lightpaths will improve the network throughput and reduce the network cost. From the study of previous work reported so for, most of the work on traffic grooming has been confined to two layer architecture and was mainly concentrated on synchronous optical network (SONET) layer. Here we have extended the investigations to WDM apart from SONET. The details of the significant published work in the area of the traffic grooming can be elaborated as follow: Chen et al. have described the problem of traffic grooming in WDM ring networks
∗ Corresponding author. E-mail addresses: vitthal [email protected] (V.J. Gond), [email protected] (A. Goel). 0030-4026/$ – see front matter © 2011 Elsevier GmbH. All rights reserved. doi:10.1016/j.ijleo.2011.05.034
[1], authors have described how to minimize the cost at the node by minimizing no of electronics ports at the node. In [2] authors have described the framework for hierarchical traffic grooming in WDM networks of general topology. The author concentrated on solving the problem of constructing the logical topology and determines the routing of traffic components on it. Li et al. have considered the traffic grooming on general topology WDM networks with the objective of minimizing the number of wavelengths required in the networks [3]. Author discussed the fundamental problem of traffic grooming and shown that traffic grooming results in efficient utilization of the bandwidth. Banerjee and Mukherjee [4] have described that the number of wavelengths supported in the network determines the cost of the switching equipment where as number of transceiver per node determines the cost of the terminal equipments. Lardies et al. [5] have described methods for traffic grooming in a multi-layer network. In this paper authors have describes a combination of existing electrical network layer, SONET and an optical WDM layer to design more cost effective network. Ozdaglar and Bertsekas [6] have discussed that optical network employing WDM offers the promise of meeting the high bandwidth requirements. The design of virtual topology aiming at efficient utilization of the network resource such as the transceivers assign to each node, fiber that connect each node. Approaches to solve the routing problem can be broadly classified into four groups as fixed routing, fixed alternate routing, adaptive routing and least congested path routing. Among these approaches fixed routing is the simplest while adaptive routing is providing the best performance and alternate routing offers a trade off between complexity and performance. These approaches for routing and wavelength
V.J. Gond, A. Goel / Optik 123 (2012) 788–791
assignment in all optical networks are described in [5–9]. If there are multiple feasible wavelengths between a source node and a destination node, then a wavelength assignment is required to select a wavelength for a given lightpath, a review of wavelength requirement of all optical networks and wavelength assignment is described in [10]. Traffic grooming in different network topologies like path, star, ring and tree networks are described in [11]. Simulation methods for analysis of traffic patterns and study related to traffic growth are studied and reported in [12]. In this paper we mainly focus on traffic grooming in all-optical WDM network. In all optical WDM network in order to establish a connection between two nodes, a lightpath is established initially between source node and destination node. A lightpath is an optical communication channel established between a node pair in the network. In the absence of any wavelength conversion device, a lightpath is required to be on the same wavelength throughout the path it uses to connect the node pair in the network. A lightpath may hence span multiple fiber links, e.g., to provide a circuit-switched interconnection between two nodes which may have a heavy traffic flow between them and which may be located far from each other in the physical fiber network topology. Each intermediate node on the lightpath essentially provides an all-optical bypass facility to support the lightpath. In an N-node optical network, if each node is equipped with N − 1 transceivers (transmitters and receivers) and if there are enough wavelengths on all fiber-links, then every node pair could be connected by an all-optical lightpath, and there is no networking problem to solve. However, it should be noted that the network size (N) should be scalable; transceivers are expensive devices so that each node may be equipped with only a few of them, and technological constraints dictate that the number of WDM channels that can be supported in a fiber is limited. Thus, only a limited number of lightpaths should be set up on the network. The whole problem has been considered as network optimization problem with minimization of the blocking probability as the objective function. In the subsequent section traffic grooming techniques have also been discussed.
2. Traffic grooming techniques The need for traffic grooming is driven by the fact that it is much more economical to transmit data at higher rates over a single fiber than to transmit at lower rate on multiple fibers. There are fundamentally two ways of increasing the transmission capacity on a fiber. The first is to increase the bit rate. This requires higher-speed electronics processing circuits. Many lower-speed data streams are multiplexed into a higher-speed stream at the transmission bit rate by means of multiplexing techniques; the multiplexer typically interleaves the lower-speed streams to obtain the higher-speed stream. The highest transmission rate is limited due the processing speed of electronics processing circuits, which is known as electronic bottle neck. Another way is to increase the capacity by using Wavelength Division Multiplexing (WDM). WDM technology can significantly increase the capacity of fiber by allowing simultaneous transmission of multiple wavelengths or channels. In WDM network architecture, a WDM wavelength channel can either carry a high-speed traffic stream or a number of low speed traffic streams. In communication system, most of the connection have small bandwidth requirement. Without grooming each connection would occupy a dedicated wavelength. Since wavelength is a limited resource in a WDM network, it is necessary to allow multiple low bandwidth connections to share the same wavelength. Traffic grooming can significantly increase the utilization of the bandwidth of wavelength channels. Traffic grooming can be carried out at two different levels – first at electrical layer by using different multiplexing techniques in electrical layer with transmission through
789
Fig. 1. Multilayer network approach for traffic grooming.
SONET/SDH and second at optical level by using different multiplexing technique in optical layer. The traffic grooming problem based on static traffic demands is essentially an optimization problem. It can be seen as a dual problem from different perspectives. One perspective is that, for a given traffic demand, satisfy all traffic requests as well as minimize the total network cost. The dual problem is that, for given resource limitation and traffic demands, minimize blocking probability. To solve the problem we proposed the multilayer architecture of the network as shown in Fig. 1. The two layers are electrical layer and optical layer. The traffic grooming techniques at electrical layer and optical layer are described below. 2.1. Traffic grooming at electrical layer The individual user’s requirement is of the order of few Mbps, where each wavelength is capable of carrying the information of the order of few Gbps. Thus to utilize the available bandwidth efficiently the multiple users are multiplexed together and transmitted on one carrier. While multiplexing signals, different techniques are used at electrical layer. These techniques are time division multiplexing (TDM), frequency division multiplexing (FDM), etc. FDM is also known as sub carrier multiplexing (SCM). In TDM each user has an assign time slot, if we consider a limited speed of 1 Gbps and user requirement is of 100 Mbps, the multiplexing level is of the order of 10. Grooming factor is nothing but the multiplexing level itself, thus the grooming factor is 10 for above example. This is illustrated more clearly in Fig. 2. Due to the limitation on maximum switching frequency for electronics switching circuits, using these multiplexing techniques maximum data rate achieved is of the order of Mbps, this creates the electronics bottleneck. To overcome the limitations of electronics bottleneck WDM multiplexing at optical layer is used, which uses non-overlapping wavelength channels with each wavelength supporting a single communication channel operating at peak electronic speed. 2.2. Traffic grooming at optical layer Different multiplexing techniques can be used for traffic grooming in optical networks. These are space division multiplexing (SDM), time division multiplexing (TDM), statistical time division multiplexing (STDM) and wavelength division multiplexing
Fig. 2. Traffic grooming at electrical layer.
790
V.J. Gond, A. Goel / Optik 123 (2012) 788–791 Channel Separation
W1
W2
W3
W4
Wavelength
Fig. 3. Wavelength partitioning.
2.2.1. Grooming factor Traffic grooming is a technique which aggregates the traffic of multiple connections into a single wavelength channel; this can increase the utilization of the bandwidth of a wavelength channels. It is illustrated with an example, as shown in Fig. 4, if bandwidth of wavelength channel is OC-12 (422.08 Mbps) and the base channel bandwidth is OC-3 (155.52 Mbps), then four OC-3 connection can be groomed and supported by one OC-12 channel, here the grooming factor is 4. The grooming factor is defined as ratio of wavelength channel capacity to basic wavelength channel capacity i.e. OC-1/OC-3 corresponding to SONET/SDH respectively. If ‘C’ is carrier wavelength capacity and ‘c’ is basic wavelength capacity, then grooming factor is defined as GF =
C c
(1)
2.3. Formulation of traffic grooming problem Our aim is to groom traffic while serving all traffic requests between pairs of optical nodes in an optical WDM mesh network, the performance of the network is evaluated. A lightpath is established between nodes by setting up the OXCs along the route between nodes. Each lightpath needs a dedicated OXC port when traversing an intermediate node along the path. In addition, a transmitter–receiver pair is required at the ingress and egress nodes of the lightpath. It is well known that the RWA optimization
Fig. 5. Illustration of connection request.
1 Load=2 Erlangs Load=5 Erlangs Load=9 Erlangs Load=12 Erlangs Load=15 Erlangs Load=20 Erlangs
Blocking probability
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1
2
3
4
5
6
7
8
9
Number of channels per link
Fig. 6. Blocking probability as function of number of channels per links, GF = 3.
problem is NP-complete. In small network topology it is possible to obtain the results with integer linear programming methodology. In order to find the results for large network topology a heuristic approach is adopted. Here we use the heuristic approach. Here we aim to analyze the general mesh network so as to serve traffic requests between pairs of optical nodes. How the traffic requests are provided the connections is demonstrated in Fig. 5. The physical topology of the WDM network under consideration is modeled as an undirected graph with ‘N’ nodes and number of links between the nodes are ‘E’. We assume that the numbers of wavelength per link are same for all the links in the network. The network consists of nodes and links interconnected in an arbitrary mesh interconnection pattern. There are N nodes in the network labeled 1, 2, N. And the number of undirected links are 1, 2, E. A lightpath connection request is denoted by a (s, d) pair. Where ‘s’ is the source node and ‘d’ is the destination node. Call for node pair arrives according to a Poisson process and the holding time for call is exponentially distributed. The traffic (load) means the rate of calls per unit time. The inputs required for the analysis are – The Physical Network Topology, The Traffic Matrix, The Routing Scheme and Wavelength Assignment Method. In the simulations we generate random topology. The topology generator generates the physical topology with a connectivity
1
Blocking Probability as Function of Traffic Load No. Of Channels C=5 No. Of Channels C=6
0.9
Blocking probability
(WDM). In space division multiplexing technique many fibers are bundled into the single cable, partitions the physical space to increase the transport bandwidth. This is achieved by either bundling a set of fibers into a single cable, or using several cables within a network link. TDM divides the time into time-slots of fixed length. Using TDM multiple signals can share a given wavelength if they are non-overlapping in time. Statistical time division multiplexing allocates the available time slots as per need. Statistical time division multiplexing does the efficient utilization of the available time slots as compared to TDM. Basically in WDM technique the available wavelength spectrum is partitioned into a set of independent channels. This enables a given fiber to carry traffic on many distinct wavelengths. It is necessary to have sufficient spacing between any two wavelengths to make it possible to separate adjacent signals at the receiver end. WDM with multiplexing levels up to 100 wavelengths are in used. Partitioned wavelength spectrum is demonstrated in Fig. 3.
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0
2
5
9
12
15
Traffic Load in Erlangs
Fig. 4. Traffic grooming principle (GF = 4).
Fig. 7. Blocking probability as a function of traffic load.
20
V.J. Gond, A. Goel / Optik 123 (2012) 788–791
791
3. Results and discussion Blocking probability as function of number of optical channels is constructed. The observations show that the blocking probability decreases with the increase in number of optical channels. The relation between blocking probability and number of channels per link are plotted in Fig. 6. It is observed that the blocking probability increases with the traffic load in the network, which is quite obvious. The above observations have also been compared in tabular form in Table 1. Fig. 8. Number of wavelengths as a function of grooming factor.
4. Conclusion
Table 1 Blocking probability as function of traffic load (C* = number of channels). S.No.
Traffic load in Erlangs
1 2 3 4 5 6
2 5 9 12 15 20
Blocking probability C* = 5
C* = 6
0.04 0.29 0.52 0.63 0.69 0.78
0.01 0.19 0.43 0.56 0.63 0.71
defined by incidence nodes matrix, which is to be defined by the user. When the number of incidence nodes are increased the topology moves toward full mesh topology. The numbers of bidirectional link required in full mesh topology for ‘N’ nodes can be given by Number of Links =
N(N − 1) 2
(2)
The numbers of unidirectional links can be expressed as Number of Links = N(N − 1)
(3)
Since in large networks the numbers of links required in full mesh topology for ‘N’ nodes are too many which is not feasible in real network and therefore the partial topology is used. The number of input parameters required for creating physical topology using proposed algorithm are – number of nodes in the network and number of incidence nodes (Less than No. of Nodes). The randomly generated network topology generated using proposed algorithm presents an imitation of actual Wide-Area-Network (WAN). The network is evaluated for different conditions; first we evaluate it for fixed number of links with grooming factor set to 3 and subsequently the grooming factor increase in steps to 18. The load on each link is selected as 2, 5, 9, 12, 15 & 20 Erlangs. And the blocking probability as function of number of optical channels is evaluated. The blocking probability ‘Pb ’, as calculated using Erlang’s loss formula [13] is given by
Pb (L, (i), c) =
Li i!
×
C
1
i=0
Li /i!
(4)
where L is the traffic intensity (Traffic load) in Erlangs and C is the number of channels per link.
We have considered here the traffic grooming problem on general topology WDM mesh networks. The objective of the simulation work is to establish the relationship between the grooming factor and the number of wavelengths on a fiber, and to investigate the effect of blocking probability for different load conditions (Figs. 7 and 8). The research problem can be formulated as: for a given network topology with a set of connections, find the corresponding lightpaths by considering the wavelength capacity, grooming factor, etc. and assigning the wavelengths to respective lightpaths. We observed that as the wavelength capacity increases the requirement of the number of wavelength channels decreases. The simulation results show that increase in the grooming factor (wavelength channel capacity) considerably decrease the number of wavelengths required in the system. When the grooming factor is increased to significant value (16), the number of wavelengths requirement (8) becomes relatively stable. References [1] B. Chen, G.N. Rouskas, R. Dutta, Traffic grooming in WDM ring networks to minimize the maximum electronic port cost, in: Optical Switching and Networking, Elsevier, 2005, pp. 1–18. [2] B. Chen, G.N. Rouskas, R. Dutta, On hierarchical traffic grooming in WDM networks, IEEE/ACM Trans. Netw. 16 (3) (2008) 1226–1238. [3] D. Li, Z. Sun, X. Jai, K. Makki, Traffic grooming on general topology WDM networks, IEE Proc. Commun. 150 (3) (2003) 197–201. [4] D. Banerjee, B. Mukherjee, Wavelength routed optical network: linear formulation, resource budgeting tradeoffs, and a reconfiguration study, IEEE/ACM Trans. Netw. 8 (5) (2000) 598–607. [5] A. Lardies, R. Gupta, R.A. Patterson, Traffic grooming in a multi-layer network, Opt. Netw. Mag. (2001) 91–94. [6] A.E. Ozdaglar, D.P. Bertsekas, Routing and wavelength assignment in optical networks, IEEE/ACM Trans. Netw. 11 (2) (2003) 259–272. [7] J.F. Labourdette, et al., Fast approximate dimensioning and performance analysis of mesh optical networks, IEEE/ACM Trans. Netw. 13 (4) (2005) 906–917. [8] J. Prat, P. Chanclou, R. Davey, J.M. Finochietto, G. Franzl, A.M.J. Koonen, S. Walter, Long-Term Evolution of Passive Optical Networks, ACM AccessNets’06, 2006. [9] R. Ramamurthy, B. Mukherjee, Fixed-alternate routing and wavelength conversion in wavelength-routed optical networks, IEEE/ACM Trans. Netw. 10 (2002) 3. [10] H.Q. Ngo, D. Pan, Y. Yang, Optical switching networks with minimum number of limited-range wavelength converters, IEEE/ACM Trans. Netw. 15 (4) (2007) 969–979. [11] R. Dutta, S. Huang, G. Rouskas, Traffic Grooming in Path, Star and Tree Networks: Complexity, Bounds and Algorithms, SIFMETRICS’03, 2003, pp. 298–299. [12] K.Y. Jo, C. Munk, Simulation method for analysis of traffic processes in ATM networks, in: Proceedings of Winter Simulation Conference, 2000, pp. 983–989. [13] P. Rajalakshmi, J. Ashok, Analytical performance computation for all optical networks with wavelength conversion, IETE J. Res. 54 (2008) 1.
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Performance analysis of traffic groomed optical network Vithal J. Gond ∗ , Aditya Goel Department of Electronics and Communication, Maulana Azad National Institute of Technology, Bhopal 462051, India
a r t i c l e
i n f o
Article history: Received 31 December 2010 Accepted 28 May 2011
Keywords: WDM network Traffic grooming factor Blocking probability Routing and wavelength assignment
a b s t r a c t In this paper we carry out the performance analysis of traffic groomed multilayer optical networks. It is seen that the number of wavelength channels required decreases as the wavelength grooming factor increases. We have evaluated blocking probability for different load and grooming factor. The performance of the network has been evaluated for different conditions; first for fixed number of links with grooming factor set to 3 and subsequently with increase in grooming factor up to 18 in steps. The load on each link is selected as 2, 5, 9, 12, 15 and 20 Erlangs and the blocking probability as function of number of optical channels has been evaluated. In this work the effect of number of wavelength channels, traffic load and grooming factor on network blocking probability has been studied. The investigation reveals that the blocking probability decreases with increase in wavelength channels. Similarly we found that the blocking probability increases with increase in traffic load which is quite evident. Further it is shown that when the grooming factor is increased to significant value (16), the number of wavelengths requirement (8) becomes relatively stable. © 2011 Elsevier GmbH. All rights reserved.
1. Introduction The traffic grooming is use to efficiently groom low-speed traffic onto high capacity WDM channels. The generic grooming idea can be applied to any arbitrary optical network. The issue in transporting client calls using lightpaths is that client calls have data rates which are generally much smaller than the lightpath capacity. To address this issue traffic grooming techniques is used to combine low speed traffic stream on to high speed lightpaths. The traffic grooming is applied to groom low speed traffic to high speed lightpaths to share the resources in optical layer there by utilizing the network resources and reducing the overall cost of network. For each incoming call it is necessary to find a path consisting of logical links. The process of finding paths to consolidated client calls over logical topology is called traffic grooming. Efficiently grooming low-speed connections onto high capacity lightpaths will improve the network throughput and reduce the network cost. From the study of previous work reported so for, most of the work on traffic grooming has been confined to two layer architecture and was mainly concentrated on synchronous optical network (SONET) layer. Here we have extended the investigations to WDM apart from SONET. The details of the significant published work in the area of the traffic grooming can be elaborated as follow: Chen et al. have described the problem of traffic grooming in WDM ring networks
∗ Corresponding author. E-mail addresses: vitthal [email protected] (V.J. Gond), [email protected] (A. Goel). 0030-4026/$ – see front matter © 2011 Elsevier GmbH. All rights reserved. doi:10.1016/j.ijleo.2011.05.034
[1], authors have described how to minimize the cost at the node by minimizing no of electronics ports at the node. In [2] authors have described the framework for hierarchical traffic grooming in WDM networks of general topology. The author concentrated on solving the problem of constructing the logical topology and determines the routing of traffic components on it. Li et al. have considered the traffic grooming on general topology WDM networks with the objective of minimizing the number of wavelengths required in the networks [3]. Author discussed the fundamental problem of traffic grooming and shown that traffic grooming results in efficient utilization of the bandwidth. Banerjee and Mukherjee [4] have described that the number of wavelengths supported in the network determines the cost of the switching equipment where as number of transceiver per node determines the cost of the terminal equipments. Lardies et al. [5] have described methods for traffic grooming in a multi-layer network. In this paper authors have describes a combination of existing electrical network layer, SONET and an optical WDM layer to design more cost effective network. Ozdaglar and Bertsekas [6] have discussed that optical network employing WDM offers the promise of meeting the high bandwidth requirements. The design of virtual topology aiming at efficient utilization of the network resource such as the transceivers assign to each node, fiber that connect each node. Approaches to solve the routing problem can be broadly classified into four groups as fixed routing, fixed alternate routing, adaptive routing and least congested path routing. Among these approaches fixed routing is the simplest while adaptive routing is providing the best performance and alternate routing offers a trade off between complexity and performance. These approaches for routing and wavelength
V.J. Gond, A. Goel / Optik 123 (2012) 788–791
assignment in all optical networks are described in [5–9]. If there are multiple feasible wavelengths between a source node and a destination node, then a wavelength assignment is required to select a wavelength for a given lightpath, a review of wavelength requirement of all optical networks and wavelength assignment is described in [10]. Traffic grooming in different network topologies like path, star, ring and tree networks are described in [11]. Simulation methods for analysis of traffic patterns and study related to traffic growth are studied and reported in [12]. In this paper we mainly focus on traffic grooming in all-optical WDM network. In all optical WDM network in order to establish a connection between two nodes, a lightpath is established initially between source node and destination node. A lightpath is an optical communication channel established between a node pair in the network. In the absence of any wavelength conversion device, a lightpath is required to be on the same wavelength throughout the path it uses to connect the node pair in the network. A lightpath may hence span multiple fiber links, e.g., to provide a circuit-switched interconnection between two nodes which may have a heavy traffic flow between them and which may be located far from each other in the physical fiber network topology. Each intermediate node on the lightpath essentially provides an all-optical bypass facility to support the lightpath. In an N-node optical network, if each node is equipped with N − 1 transceivers (transmitters and receivers) and if there are enough wavelengths on all fiber-links, then every node pair could be connected by an all-optical lightpath, and there is no networking problem to solve. However, it should be noted that the network size (N) should be scalable; transceivers are expensive devices so that each node may be equipped with only a few of them, and technological constraints dictate that the number of WDM channels that can be supported in a fiber is limited. Thus, only a limited number of lightpaths should be set up on the network. The whole problem has been considered as network optimization problem with minimization of the blocking probability as the objective function. In the subsequent section traffic grooming techniques have also been discussed.
2. Traffic grooming techniques The need for traffic grooming is driven by the fact that it is much more economical to transmit data at higher rates over a single fiber than to transmit at lower rate on multiple fibers. There are fundamentally two ways of increasing the transmission capacity on a fiber. The first is to increase the bit rate. This requires higher-speed electronics processing circuits. Many lower-speed data streams are multiplexed into a higher-speed stream at the transmission bit rate by means of multiplexing techniques; the multiplexer typically interleaves the lower-speed streams to obtain the higher-speed stream. The highest transmission rate is limited due the processing speed of electronics processing circuits, which is known as electronic bottle neck. Another way is to increase the capacity by using Wavelength Division Multiplexing (WDM). WDM technology can significantly increase the capacity of fiber by allowing simultaneous transmission of multiple wavelengths or channels. In WDM network architecture, a WDM wavelength channel can either carry a high-speed traffic stream or a number of low speed traffic streams. In communication system, most of the connection have small bandwidth requirement. Without grooming each connection would occupy a dedicated wavelength. Since wavelength is a limited resource in a WDM network, it is necessary to allow multiple low bandwidth connections to share the same wavelength. Traffic grooming can significantly increase the utilization of the bandwidth of wavelength channels. Traffic grooming can be carried out at two different levels – first at electrical layer by using different multiplexing techniques in electrical layer with transmission through
789
Fig. 1. Multilayer network approach for traffic grooming.
SONET/SDH and second at optical level by using different multiplexing technique in optical layer. The traffic grooming problem based on static traffic demands is essentially an optimization problem. It can be seen as a dual problem from different perspectives. One perspective is that, for a given traffic demand, satisfy all traffic requests as well as minimize the total network cost. The dual problem is that, for given resource limitation and traffic demands, minimize blocking probability. To solve the problem we proposed the multilayer architecture of the network as shown in Fig. 1. The two layers are electrical layer and optical layer. The traffic grooming techniques at electrical layer and optical layer are described below. 2.1. Traffic grooming at electrical layer The individual user’s requirement is of the order of few Mbps, where each wavelength is capable of carrying the information of the order of few Gbps. Thus to utilize the available bandwidth efficiently the multiple users are multiplexed together and transmitted on one carrier. While multiplexing signals, different techniques are used at electrical layer. These techniques are time division multiplexing (TDM), frequency division multiplexing (FDM), etc. FDM is also known as sub carrier multiplexing (SCM). In TDM each user has an assign time slot, if we consider a limited speed of 1 Gbps and user requirement is of 100 Mbps, the multiplexing level is of the order of 10. Grooming factor is nothing but the multiplexing level itself, thus the grooming factor is 10 for above example. This is illustrated more clearly in Fig. 2. Due to the limitation on maximum switching frequency for electronics switching circuits, using these multiplexing techniques maximum data rate achieved is of the order of Mbps, this creates the electronics bottleneck. To overcome the limitations of electronics bottleneck WDM multiplexing at optical layer is used, which uses non-overlapping wavelength channels with each wavelength supporting a single communication channel operating at peak electronic speed. 2.2. Traffic grooming at optical layer Different multiplexing techniques can be used for traffic grooming in optical networks. These are space division multiplexing (SDM), time division multiplexing (TDM), statistical time division multiplexing (STDM) and wavelength division multiplexing
Fig. 2. Traffic grooming at electrical layer.
790
V.J. Gond, A. Goel / Optik 123 (2012) 788–791 Channel Separation
W1
W2
W3
W4
Wavelength
Fig. 3. Wavelength partitioning.
2.2.1. Grooming factor Traffic grooming is a technique which aggregates the traffic of multiple connections into a single wavelength channel; this can increase the utilization of the bandwidth of a wavelength channels. It is illustrated with an example, as shown in Fig. 4, if bandwidth of wavelength channel is OC-12 (422.08 Mbps) and the base channel bandwidth is OC-3 (155.52 Mbps), then four OC-3 connection can be groomed and supported by one OC-12 channel, here the grooming factor is 4. The grooming factor is defined as ratio of wavelength channel capacity to basic wavelength channel capacity i.e. OC-1/OC-3 corresponding to SONET/SDH respectively. If ‘C’ is carrier wavelength capacity and ‘c’ is basic wavelength capacity, then grooming factor is defined as GF =
C c
(1)
2.3. Formulation of traffic grooming problem Our aim is to groom traffic while serving all traffic requests between pairs of optical nodes in an optical WDM mesh network, the performance of the network is evaluated. A lightpath is established between nodes by setting up the OXCs along the route between nodes. Each lightpath needs a dedicated OXC port when traversing an intermediate node along the path. In addition, a transmitter–receiver pair is required at the ingress and egress nodes of the lightpath. It is well known that the RWA optimization
Fig. 5. Illustration of connection request.
1 Load=2 Erlangs Load=5 Erlangs Load=9 Erlangs Load=12 Erlangs Load=15 Erlangs Load=20 Erlangs
Blocking probability
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1
2
3
4
5
6
7
8
9
Number of channels per link
Fig. 6. Blocking probability as function of number of channels per links, GF = 3.
problem is NP-complete. In small network topology it is possible to obtain the results with integer linear programming methodology. In order to find the results for large network topology a heuristic approach is adopted. Here we use the heuristic approach. Here we aim to analyze the general mesh network so as to serve traffic requests between pairs of optical nodes. How the traffic requests are provided the connections is demonstrated in Fig. 5. The physical topology of the WDM network under consideration is modeled as an undirected graph with ‘N’ nodes and number of links between the nodes are ‘E’. We assume that the numbers of wavelength per link are same for all the links in the network. The network consists of nodes and links interconnected in an arbitrary mesh interconnection pattern. There are N nodes in the network labeled 1, 2, N. And the number of undirected links are 1, 2, E. A lightpath connection request is denoted by a (s, d) pair. Where ‘s’ is the source node and ‘d’ is the destination node. Call for node pair arrives according to a Poisson process and the holding time for call is exponentially distributed. The traffic (load) means the rate of calls per unit time. The inputs required for the analysis are – The Physical Network Topology, The Traffic Matrix, The Routing Scheme and Wavelength Assignment Method. In the simulations we generate random topology. The topology generator generates the physical topology with a connectivity
1
Blocking Probability as Function of Traffic Load No. Of Channels C=5 No. Of Channels C=6
0.9
Blocking probability
(WDM). In space division multiplexing technique many fibers are bundled into the single cable, partitions the physical space to increase the transport bandwidth. This is achieved by either bundling a set of fibers into a single cable, or using several cables within a network link. TDM divides the time into time-slots of fixed length. Using TDM multiple signals can share a given wavelength if they are non-overlapping in time. Statistical time division multiplexing allocates the available time slots as per need. Statistical time division multiplexing does the efficient utilization of the available time slots as compared to TDM. Basically in WDM technique the available wavelength spectrum is partitioned into a set of independent channels. This enables a given fiber to carry traffic on many distinct wavelengths. It is necessary to have sufficient spacing between any two wavelengths to make it possible to separate adjacent signals at the receiver end. WDM with multiplexing levels up to 100 wavelengths are in used. Partitioned wavelength spectrum is demonstrated in Fig. 3.
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0
2
5
9
12
15
Traffic Load in Erlangs
Fig. 4. Traffic grooming principle (GF = 4).
Fig. 7. Blocking probability as a function of traffic load.
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V.J. Gond, A. Goel / Optik 123 (2012) 788–791
791
3. Results and discussion Blocking probability as function of number of optical channels is constructed. The observations show that the blocking probability decreases with the increase in number of optical channels. The relation between blocking probability and number of channels per link are plotted in Fig. 6. It is observed that the blocking probability increases with the traffic load in the network, which is quite obvious. The above observations have also been compared in tabular form in Table 1. Fig. 8. Number of wavelengths as a function of grooming factor.
4. Conclusion
Table 1 Blocking probability as function of traffic load (C* = number of channels). S.No.
Traffic load in Erlangs
1 2 3 4 5 6
2 5 9 12 15 20
Blocking probability C* = 5
C* = 6
0.04 0.29 0.52 0.63 0.69 0.78
0.01 0.19 0.43 0.56 0.63 0.71
defined by incidence nodes matrix, which is to be defined by the user. When the number of incidence nodes are increased the topology moves toward full mesh topology. The numbers of bidirectional link required in full mesh topology for ‘N’ nodes can be given by Number of Links =
N(N − 1) 2
(2)
The numbers of unidirectional links can be expressed as Number of Links = N(N − 1)
(3)
Since in large networks the numbers of links required in full mesh topology for ‘N’ nodes are too many which is not feasible in real network and therefore the partial topology is used. The number of input parameters required for creating physical topology using proposed algorithm are – number of nodes in the network and number of incidence nodes (Less than No. of Nodes). The randomly generated network topology generated using proposed algorithm presents an imitation of actual Wide-Area-Network (WAN). The network is evaluated for different conditions; first we evaluate it for fixed number of links with grooming factor set to 3 and subsequently the grooming factor increase in steps to 18. The load on each link is selected as 2, 5, 9, 12, 15 & 20 Erlangs. And the blocking probability as function of number of optical channels is evaluated. The blocking probability ‘Pb ’, as calculated using Erlang’s loss formula [13] is given by
Pb (L, (i), c) =
Li i!
×
C
1
i=0
Li /i!
(4)
where L is the traffic intensity (Traffic load) in Erlangs and C is the number of channels per link.
We have considered here the traffic grooming problem on general topology WDM mesh networks. The objective of the simulation work is to establish the relationship between the grooming factor and the number of wavelengths on a fiber, and to investigate the effect of blocking probability for different load conditions (Figs. 7 and 8). The research problem can be formulated as: for a given network topology with a set of connections, find the corresponding lightpaths by considering the wavelength capacity, grooming factor, etc. and assigning the wavelengths to respective lightpaths. We observed that as the wavelength capacity increases the requirement of the number of wavelength channels decreases. The simulation results show that increase in the grooming factor (wavelength channel capacity) considerably decrease the number of wavelengths required in the system. When the grooming factor is increased to significant value (16), the number of wavelengths requirement (8) becomes relatively stable. References [1] B. Chen, G.N. Rouskas, R. Dutta, Traffic grooming in WDM ring networks to minimize the maximum electronic port cost, in: Optical Switching and Networking, Elsevier, 2005, pp. 1–18. [2] B. Chen, G.N. Rouskas, R. Dutta, On hierarchical traffic grooming in WDM networks, IEEE/ACM Trans. Netw. 16 (3) (2008) 1226–1238. [3] D. Li, Z. Sun, X. Jai, K. Makki, Traffic grooming on general topology WDM networks, IEE Proc. Commun. 150 (3) (2003) 197–201. [4] D. Banerjee, B. Mukherjee, Wavelength routed optical network: linear formulation, resource budgeting tradeoffs, and a reconfiguration study, IEEE/ACM Trans. Netw. 8 (5) (2000) 598–607. [5] A. Lardies, R. Gupta, R.A. Patterson, Traffic grooming in a multi-layer network, Opt. Netw. Mag. (2001) 91–94. [6] A.E. Ozdaglar, D.P. Bertsekas, Routing and wavelength assignment in optical networks, IEEE/ACM Trans. Netw. 11 (2) (2003) 259–272. [7] J.F. Labourdette, et al., Fast approximate dimensioning and performance analysis of mesh optical networks, IEEE/ACM Trans. Netw. 13 (4) (2005) 906–917. [8] J. Prat, P. Chanclou, R. Davey, J.M. Finochietto, G. Franzl, A.M.J. Koonen, S. Walter, Long-Term Evolution of Passive Optical Networks, ACM AccessNets’06, 2006. [9] R. Ramamurthy, B. Mukherjee, Fixed-alternate routing and wavelength conversion in wavelength-routed optical networks, IEEE/ACM Trans. Netw. 10 (2002) 3. [10] H.Q. Ngo, D. Pan, Y. Yang, Optical switching networks with minimum number of limited-range wavelength converters, IEEE/ACM Trans. Netw. 15 (4) (2007) 969–979. [11] R. Dutta, S. Huang, G. Rouskas, Traffic Grooming in Path, Star and Tree Networks: Complexity, Bounds and Algorithms, SIFMETRICS’03, 2003, pp. 298–299. [12] K.Y. Jo, C. Munk, Simulation method for analysis of traffic processes in ATM networks, in: Proceedings of Winter Simulation Conference, 2000, pp. 983–989. [13] P. Rajalakshmi, J. Ashok, Analytical performance computation for all optical networks with wavelength conversion, IETE J. Res. 54 (2008) 1.