Static Traffic Grooming in WDM mesh networks for Max-Connectivity nodes
using ILP
Partha Paul
Department of Computer Science Engg., Birla Institute of Technology, Mesra, Ranchi-835215,INDIA
Email Address: p_india@rediffmail.com
Mainak Basu
Department of Electronics and Communication Engg., Birla Institute of Technology, Mesra, Ranchi-835215,INDIA
Email Addresses: iaawe12@gmail.com
The Corresponding author : Partha Paul
Abstract
In this paper, we propose Max-Connectivity grooming in WDM mesh networks under static lightpath connection
requests. The grooming and wavelength conversion resources are placed at the nodes having maximum connections.
We propose, an Integer Linear Programming (ILP) approach to solve grooming, routing and wavelength (GRWA) in
6-nodes WDM mesh network using Max-Connectivity grooming. The Performance of Max-Connectivity grooming
has been compared with other grooming policies. Our simulation results demonstrate that deploying traffic grooming
resources on the Max-Connectivity nodes in optical networks is more cost effective and results in a similar blocking
performance. Results will be provided for a comparison between Integer Linear programme (ILP) and Genetic
Algorithm(GA) to determine the efficiency of Max-Connectivity grooming in small networks.
1. Introduction
Wavelength Division Multiplexing (WDM) in Optical Networks can meet the huge bandwidth requirements of
internet and telecommunications data and hence has emerged as an active area of research. In WDM multiple
wavelengths are transmitted through a single optical fiber, where each wavelength is capable of supporting a data rate
of several gigabits per second (e.g. OC-192, OC-768 etc). Under practical conditions, the request traffic of an
individual connection is of the order of a few megabits per second. Hence a significant portion of the transmission
capacity remains unutilized. Traffic grooming in a network allows one to multiplex the low speed traffic streams into
high speed wavelength channels [1]. This procedure allows an effective utilization of the channel bandwidth and also
minimizes the network cost by reducing the number of Add-Drop Multiplexers (ADM) and wavelengths used. In a
WDM network, a lightpath must first be established between the source and the destination nodes to carry traffic
using a wavelength and a proper route. The Routing and Wavelength Assignment (RWA) allows the minimization of
the b1locking probability cannot effectively utilize the network resources.
A combination of traffic grooming and RWA can solve the network bandwidth problem allocation more effectively.
The method multiplexes the connection requests of different bandwidth granularities on to a wavelength channel of
high bandwidth. Each grooming node can efficiently multiplex several low speed traffic streams on to high capacity
wavelength channels and also demultiplex them whenever required. The grooming node includes optical cross
connects (OXCs), demultiplexers (DMUX), multiplexers (MUX) and/or digital cross connects (DXCs) that perform
grooming as well as switching operations.
There has been several reported work, on the implementation of traffic grooming in ring networks [2 - 4] and in
WDM mesh networks [1, 5 - 7]. The operation in WDM mesh networks generates traffic scenarios that are static,
incremental or dynamic [8]. Thus to achieve cost-effective operation in a network, it is necessary to ensure grooming
devices are placed at proper positions. We propose the use of Max-Connectivity grooming, where grooming devices
are placed at the nodes having maximum number of connections. Other grooming policies like Edge-grooming and
All-grooming [9] have also been reported, that increases the network resources and hence the cost. Different
evolutionary algorithms (e.g. A multi-objective evolutionary algorithm [10]) have been proposed to maximize the
throughput while minimizing the required network resources. In the present paper, we have used Integer Linear
Programming (ILP) to solve the Grooming and Wavelength Assignment (GRWA) problem in 6-node WDM mesh
network using Max-Connectivity grooming. ILP works on a small solution set, that makes it easily applicable for
small networks. It is also more efficient than other heuristic approaches like Genetic Algorithms (GA), greedy
heuristics approach, most contiguous heuristic algorithms, allowing for reduced computational time and complexity.
The blocking probability has been investigated under different lightpath connections and the performance of MaxConnectivity grooming has been compared with other grooming policies. Our results indicate the improvement of
resource utilization while minimizing blocking probability.
2. Network Architecture and Max-Connectivity grooming
We have considered a 6-node WDM mesh network as shown in Fig. 1. The nodes 2 and 5 are considered with
maximum connections and the nodes 1, 3, 4 and 6 are considered as edge nodes for comparison.
1
2
3
6
5
4
Fig. 1: 6-Node WDM mesh network where(1,3,4 and 6) are edge nodes and (2 and 5 are maximum
connectivity nodes
In Fig. 1, the grooming devices are placed at the nodes having maximum number of connections (Max-Connectivity
grooming). There are two available wavelengths per link, all of which are considered bidirectional. For a given
number of connection requests for every source to destination lightpath, a wavelength has to be assigned. If all the
connections are satisfied, then there is no blocking of any request. In the event that the grooming devices are placed
randomly amongst the other nodes and all the connection requests cannot be met (i.e. a wavelength is unavailable for
a certain request), then the connection requests that cannot be met are said to be blocked. Another alternative, is to
increase the number of wavelengths used and the number of grooming devices, which will lead to an increase in the
total network cost. Thus it is important to properly place the grooming devices to minimize the blocking probability
while optimizing network cost. For effective operation, the GRWA problem must be solved for a given number of
grooming devices placed in the network. The following assumptions have been made for the solution of the GRWA
problem:
i.
All links are bidirectional links.
ii.
Grooming and wavelength conversion resources should be placed on the nodes having maximum
connectivity.
iii.
Capacity of one wavelength on one fiber is constant ‘C’ (OC-48).
iv.
Traffic demand is static. Connection requests (R) are known in advance.
v.
Number of wavelengths available per fiber is limited (we have used 2 wavelengths per fiber).
vi.
Traffic requests may be through any one of speeds: OC-1, OC-3, OC-12 and OC-48.
In the present work, the GRWA problem has been resolved for a 6-node WDM mesh network using Integer Linear
Programming. This is a method used to determine a way to achieve the best outcome in a given mathematical model
for some list of requirements represented as linear relationships. Linear programming is a specific case of
mathematical programming. Given a polytope and real-valued affine function defined on this polytope, a linear
programming method will find a point on the polytope where this function has the smallest (or largest) value if such a
point exists, by searching through the polytope vertices. In this optimization technique ,the objective function and the
constraint functions are linear functions of the design variables. It consists of linear programs in which some or all the
variables are restricted to integer values. Linear programs are problems that can be expressed in canonical form:
Maximize f(x)= cT x
Subject to Ax ≤ b
And, x ≥ 0
In our ILP approach to solve the GRWA problem, the grooming devices are increased additively and the resultant
blocking probability is examined.
3. Network Cost formulation
The major cost of the optical networks is due to the wavelengths used in connections establishment, and grooming
and wavelength conversion devices deployed on the nodes. The connection requests are considered as static i.e. all
the requests are known in advance. Assuming the wavelength conversion devices are used with the grooming devices,
the objective function for the network cost can be written as:
where,
: is the number of grooming devices used at the ith node,
resources used at the ith node,
: is the number of wavelength conversion
: is the number of hops used by the ith connection request, N is the number of nodes
in the mesh network in which grooming and wavelength conversion resources are placed, L is the number of
requested connections, CG is the grooming cost and CW is the wavelength conversion cost. Eq. (1a) is subject to the
following constraints:
i.
At most one lightpath can be setup between two nodes using a single wavelength,
where, w : is the particular wavelength used between node i and node j,
implies that wavelength w has been
assigned to the lightpath from node i to node j, variable b(i, j) signifies whether lightpath from node i to node j exists
or not.
ii.
Grooming and wavelength conversion capability of each node is limited to the number of grooming devices
placed on that node.
iii.
Grooming state of each grooming device is limited to the maximum capacity of the fiber link i.e.
where, r
L, c = [1, 3, 12.... Cmax], Cmax is the maximum capacity of the fiber link,
is the lightpath request
between node i and j with bandwidth c.
In our present work, we have minimized the objective function given by Eq. (1a). The minimization has been
achieved by minimizing the number of Hop counts Hi and then minimizing the number of devices used (Grooming
and wavelength conversion devices).
4. Results and Discussion
The performance of the ILP procedure to solve GRWA problem has been demonstrated in a WDM optical 6-node
network topologies as illustrated in Fig 1. The flowchart for the procedure is shown in Fig. 2. We have compared our
results with edge grooming and all grooming. We have found that it is efficient and cost effective to deploy grooming
and wavelength resources on the nodes having maximum connectivity instead of placing resources randomly over the
network.
Fig. 2: Flowchart of ILP formulation for static traffic grooming in optical networks
The results of the grooming policies are compared in Fig. 3 to Fig. 5. For Max-Connectivity grooming in a 6-node
mesh network, we have used nodes 2 and 5 having maximum connectivity and for edge grooming, we have assumed
that only nodes 1, 3, 4 and 6 would be equipped with the grooming and wavelength conversion resources. Fig. 3
shows the estimation of the blocking probability with the number of grooming devices, using the ILP formulation
stated above.
Fig 3: Blocking probability vs. traffic grooming and wavelength conversion resources using 50 lightpath requests
Fig.4 enunciates the cost for three different grooming policies using 6 node network architectures. The network cost
is measured by the wavelength link cost, grooming and wavelength conversion devices cost used in the network. The
cost shown in Fig. 4 is the normalized cost depending upon the objective function given by Eq. (1a).
Fig 4: Total cost vs. number of connections
The traffic load is represented as:
where, L = Offered load in unit Erlangs, λ= Number of lightpath requests per unit time, H = Average call holding
time; where holding time is exponentially distributed with mean
considered to be Poisson distributed with mean
. All the arrival requests to the nodes have been
.
The blocking probability for three different grooming policies (i.e. all grooming, edge grooming, max-connectivity
grooming) is plotted with static traffic load (Erlang) in Fig. 5. Simulation results have been shown for 6-node
networks depicted in Figure 5. In this evaluation, the resources placed on the nodes are fixed and then for each
grooming policy the results are compared. Also, we have assumed that all the nodes in the network will have
wavelength conversion capability and each fiber supports 2 wavelengths. We have placed 4 grooming devices in all
the grooming schemes. Our results show that placing the grooming resources on the nodes having maximum
connectivity is more efficient than placing the grooming resources on the edges or on randomly chosen nodes.
Fig. 5: Comparison of Blocking Probability Vs Traffic Load using 4 traffic grooming resources
Figure 6.depicted that the blocking probability versus the number of traffic grooming and wavelength conversion
resources installed in the network 10, 30, and 50 static lightpath requests, for Genetic Algorithm(GA) and ILP
respectively. This figure shows that for both the approaches the best blocking performance is achieved when
wavelength conversion and grooming devices are used on all nodes whereas maximum blocking occurs when
wavelength conversion and traffic grooming devices are used at the edges. However, the blocking performance of the
ILP approach is better than that of the Genetic based approach (GA) for small networks. This may be attributed to the
condition that ILP can solve the problem for different traffic demand distributions (which is prevalent for the case of
Max-Connectivity grooming), but GA requires traffic demand to be uniformly distributed over all the nodes.
However, the resources (Grooming Devices) required for achieving similar performance is more in the case of
Genetic Approach, which is expected, since the ILP optimizes the objective function for given resources.
Fig. 6: Comparison of Blocking Probability Vs Traffic grooming and Wavelength Conversion
resources between ILP and GA
Fig. 7 compares the total cost of traffic grooming and wavelength conversion resources used in GA and ILP for a 6nodes network with various degree of traffic grooming and wavelength conversion capability. In figure .1 we have
used 6-nodes topology where maximum connection size is OC-48 and each WDM link has two wavelengths. This
study shows that the total cost of traffic grooming and wavelength conversion resources used in our proposed ILP is
lower than the same used by genetic-based heuristic without hindering the blocking performance of the network.
Fig. 7: Total Cost Vs No of Connection using 6-nodes mesh networks
Fig. 8 depicts that increasing the number of grooming and conversion devices can significantly reduce the blocking
probability for ILP and GA, especially when the network is heavily loaded. But for a given number of grooming
devices, ILP provides a lower blocking probability than GA, as shown in the Figure. Also the blocking probability for
a traffic load of 20 Erlangs is the same when the average number of traffic grooming and wavelength conversion
resources is increased from 2 to 12. This indicates that a network designer can reduce the network cost without
affecting the network performance by deploying a limited number of traffic grooming and wavelength resources in
the network.
Fig. 8: Comparison of blocking probability vs traffic load
Fig. 9 shows the failure rate comparison between the different grooming policies and the bars in the graph represent
the blocked connections. In all grooming ,all the 6 nodes will be equipped with grooming capability where as maxconnectivity grooming only nodes 2 and 5 will have grooming capability and edge grooming only nodes 1,3,4,6 will
have grooming capability. All the plots shows nth connection failure for different traffic grooming techniques for 50
lightpath requests. It can be observed that most of the initial connection requests are established due to the availability
of resources. As the resources are limited, more blocking is observed when lightpath request increases. In all
grooming, the number of failed connections is less as compared to max-connectivity and edge grooming, but the cost
is very high due to the placement of grooming devices in all the nodes. The max-connectivity and edge grooming
shows quite similar performance as compared to all grooming using less number of resources
Fig. 9(a)
(b)
(c)
Fig. 9: The failure rate comparison between (a) All-grooming, (b) Edge grooming and (c) MaxConnectivity grooming.
5. Conclusions
We have demonstrated Max-Connectivity traffic grooming, routing and wavelength assignment in a 6-node WDM
mesh network where grooming and wavelength conversion resources are deployed in the nodes having maximum
connectivity. An ILP model has been used to solve the traffic grooming under static lightpath requests. It has been
seen that the Max-Connectivity grooming improves the blocking probability compared to other grooming policies for
a fixed number of lightpath requests. Also it is more cost effective for a given number of connections. We have also
compared the performance of ILP with the same of GA for small networks and have found that ILP gives a better
result than GA for the given circumstances. For large networks, there will be a significant increase in the number of
variables to be introduced into the method used to solve the GRWA problem for the network. The use of ILP under
such circumstances is not advised since GA would provide a better result, albeit at the cost of processing time. But
for small networks, ILP provides a better result than GA and with significantly reduced time required for the
processing. Our work can be extended for dynamic traffic grooming in WDM mesh networks, where traffic matrices
change with time. It needs the proper modification of the objective function which is to be minimized under certain
traffic conditions.
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