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Procedía Technology 10 (2013) 900 - 909
International Conference on Computational Intelligence: Modeling, Techniques and Applications
(CIMTA-2013)
Multicast Traffic Grooming based Light-Tree in WDM Mesh
Networks
Ashok Kumar Pradhana *, Tanmay Dea
aNational Institute of Technology (NIT), Computer Science and Engineering Department, India
Abstract
Multicast applications such as video conferencing, weather forecasting and on-line multi player gaming are major areas of Internet traffic growth. The disparity between bandwidth offered by a wavelength and the bandwidth requirement of a multicast connection can be purposefully solved by grooming low bandwidth connection requests into a high bandwidth wavelength channel in an optical network. In this paper, we discuss multicast traffic grooming problem using light-tree approach with static multicast connection requests. As higher layer electronic ports such as transmitters and receivers are dominant cost factors in a WDM mesh networks, it is critical to reduce their number when grooming multicast traffic into high bandwidth trees. This paper propose a heuristic algorithm called Saturated-Light-Tree based Multicast Traffic Grooming (SLTMTG) that solves grooming, routing and wavelength assignment problems. SLTMTG algorithm is based on grooming of multicast traffic to constrained light-trees in which traffic is groomed for better resource utilizations. This approach is used to minimize the grooming cost as well as wavelength requirement. Here, proposed approach tries to satisfy all connection requests. The performance of proposed algorithm has compared with existing Multicast Traffic Grooming (MTG) algorithm. The results are compared on several standard networks to measure cost and wavelength utilization.
© 2013 The Authors.PublishedbyElsevierLtd.
Selectionandpeer-reviewunderresponsibility of theUniversity of Kalyani,DepartmentofComputerScience&Engineering
Keywords: Grooming, Light-tree, Multicast, Multicast Routing and Wavelength Assignment (MRWA), Wavelength Division Multiplexing (WDM)
1. Introduction
Multicasting is a technique in which source sends a message to multiple destinations. Multicas applications such as weather forecasting, on-line video conferencing, distance learning etc. are expected to be major areas of Internet traffic growth and become key network application in near future. In Wavelength Division Multiplexing (WDM) technology, multiple wavelengths are transmitted through a single fiber and transmission capacity can be very large Terabits/second. Capacity of each wavelength channel is in the range of several Gigabits/second (e.g., OC-48, OC-192, OC-768 etc.). However, traffic requested by individual connection request in a network is in the order of
* Corresponding author. Tel.: +91-9832780560 E-mail address: pradhan.mtech@gmail.com
2212-0173 © 2013 The Authors. Published by Elsevier Ltd.
Selection and peer-review under responsibility of the University of Kalyani, Department of Computer Science & Engineering doi: 10.1016/j.protcy.2013.12.436
Megabits/second. Hence, significant portion of a transmission capacity of a wavelength channel will be wasted if bandwidth is not effectively utilized. Therefore, to properly utilize the wavelength channel several bandwidth granularities are to be groomed or multiplexed into a single high speed wavelength channel. This technique is known as Traffic Grooming, which minimizes the network cost by reducing the number of higher layer electronic ports and wavelengths required in a network.
In WDM network a lightpath [1,2] must be established to carry traffic between a single source and destination. A lightpath connects two ends without Optical-Electrical-Optical (OEO) conversion at the intermediate nodes. Although routing and wavelength assignment problem (RWA) minimizes the connection blocking, but it cannot utilizes the network resources efficiently. Due to this, for effective utilization of network resources, a natural extension of lightpath called light-tree [3,4] concept is used which supports one to many connection in one single logical hop tree. This can substantially reduce the average packet hop distance and the total number of transceivers used. In the logical layer a light-tree is presented as a set of direct links from source to the destination set of light-tree. Since, the transmission from source to all destinations takes only one hop and is done all optically, this is called logical one hop tree (LOHT) [4]. These light-trees act as the conduits for upper layer traffic. Low bandwidth connections are routed by combining several light-trees and forming a large tree to reach all the destinations. Hence, by using the light-tree concept with grooming the mismatch between the bandwidth and wavelength capacity can be overcome. Since, a tree topology is natural for supporting multicast applications, considerable research has been studied on approaches for light-tree based multicast traffic grooming.
In the early days of WDM, the wavelength was consider as the dominant cost factor of the network. Due to this, it was important to reduce the number of wavelengths to meet the traffic requests. However, given recent advance in WDM technology, the dominant cost factor is no longer wavelengths, but the number of higher layer electronic ports, such as IP router ports (transmitter and receivers). Transmitter and receivers are used to transmit and receive the optical signals, so that the number of transmitters and receivers used is equal to the number of IP router ports. In this work, a heuristic approach is used to solve grooming, routing and wavelength assignment (GRWA) problem in WDM mesh networks. This approach is simple to handle for larger networks. In this approach edges are groomed based on the traffic requests generated. It also works on static traffic request, i.e., all traffic request must be known in advance. In this paper, we aim to design cost-effective WDM networks with multicast traffic grooming by reducing both number of transmitters and receivers as well as the number of required wavelengths.
The rest of this paper is organized as follows. In Section 2, previous work related to grooming, routing and wavelength assignment of traffic request is presented. In Section 3, the mathematical formulation of light-tree based multicast traffic grooming is explained. In Section 4, the proposed approach of multicast traffic grooming, routing and wavelength assignment problem is presented. Section 5 describes the experimental results of applying this heuristic on standard networks and evaluate their performances based on simulation results. Finally, conclusion is drawn in Section 6.
2. Previous Work
Achieving efficient traffic grooming in WDM networks has been a challenging research area in recent years. Based on whether or not the connection requests are known a priori, the traffic grooming can be categorized as static or dynamic traffic grooming. In static traffic grooming traffic requests are known priori. Optimal solution [1] can be achieved through optimization in static traffic grooming, usually by using Integer Linear Programming (ILP) method, with the objective of minimizing the resource used, such as wavelengths, wave-links or add/drop ports and maximize the network throughput. An optimal ILP formulation of multicast traffic grooming [3,5] is suggested to minimize the cost of the network in terms of the number of SONET Add/Drop Multiplexers (ADM). The formulation also minimizes the number of wavelength channels used in the network. A light-tree based ILP formulation [4] is proposed to minimize the network cost associated with network resources such as higher layer electronic ports and number of wavelengths used. They have also proposed a heuristic algorithm, called sub-light-tree saturated grooming (SLTSG) to achieve scalability. An ILP optimization problem [6] is formulated for multicast traffic grooming to design a light-tree based logical topology with delay bounds. BWA algorithm proposed by Billah et al. [7] efficiently constructs multicast routing trees and using First-Fit algorithm for traffic grooming, considering wavelength conversion capability in the network nodes. The objective of their work is to minimize the wavelengths channels used in a link. Authors in
[8] suggested a heuristic algorithm to solve the sparse splitting problem. It reduced the link cost by constructing a minimal cost tree with multicast capable nodes to increase the traffic grooming effect based on relationship of multicast sessions. A tripartite graph model and an ILP formulation is proposed [9] to solve the multicast traffic grooming problem based on light-tree merging method.
However, some studies assumed a dynamic traffic model in which traffic demands arrive randomly over a period of time, and decisions are taken without waiting for future traffic demands. These models are more suited to the operational mode of WDM networks, and hence factors like network utilization or blocking probability are optimized. Light-tree division adjacent node component based grooming scheme (LTD-ANCG) proposed in [10,11] improves the efficiency of resource utilization and lowers the OEO conversion overhead. The authors in [12] proposed an on-line multicast traffic grooming algorithm called multicast dynamic light-tree grooming (MTDGA), which adopts dynamically changing light-trees as the building block and is implemented by using an auxiliary-graph model. Compared with the lightpath algorithm for the problem, the light-tree algorithm has much better performance in terms of blocking probability, with only a slight increase in delay. Guo et al. [13] proposed a new multicast multi-granular grooming approach to perform the hierarchical sequential grooming to improve the joint performance of increasing bandwidth utilization efficiency, reducing blocking probability and saving ports of multicast requests in optical networks. The authors in [14] suggested a new multicast green grooming (MGG) approach to save the energy consumption by using the energy-efficient optical bypass technology in green optical networks.
3. Problem Formulation
In this section we will mathematically formulate the problem of multicast traffic grooming, routing and wavelength assignment problem as shown below: Given:
\N|: number of vertices (nodes) in the network. W: maximum number of wavelengths available per fiber. A: wavelength index starting from 1 and ending at W. Am: wavelength assigned to multicast request m. C: capacity of a wavelength channel.
a : relative cost of higher layer electronic ports (transmitters and receivers).
P : relative cost of wavelength channel.
M: total number of multicast requests.
Q : a very large integer number.
cm: bandwidth request by a multicast request m.
t(sm; Dm; cm): a tuple of the elements sm, Dm, cm representing a multicast request m. s: source of the multicast request m.
Dm = {d1, d2,..., dk}: a set of destinations for request m, where \Dm\ = k. Variables:
TRf: number of transmitters required at node i. RR,: number of receivers required at node i.
highest index of wavelength channel used over all fiber links. YA: a binary variable. It is 1 when a wavelength is used in a light-tree, otherwise 0. LAd: number of light-trees from ith node to the destination node set D assigned with the wavelength A. LfD > 1 when there are multiple link disjoint light-trees from ith node to the destination node set D using the same wavelength A.
AmD: a binary variable. It is 1 if a multicast request m traverses from ith node to the destination node set D in the logical layer, Otherwise 0.
Objective: The main purpose of this work is to minimize the network costs in terms of number of transmitters and receivers requires as well as number of wavelengths. The following equation demonstrate the objective function.
Minimize(a * ^(TR + RR¡) + ¡.3 * ^ A¡
Where, a and ¡3 are constant parameters and M represents the number of multicast requests. Constraints:
The number of light-trees generated is constrained by the number of transmitters, receivers and wavelength used in the network.
f will be the index of the highest number of wavelengths used in the network illustrate in equation 2.
f > A * Yx VA (2)
Equation 3 demonstrate that YA is set to 1 if wavelength A is used by the any light-tree in the network.
Ya >XE LAd/Q VA (3)
i Dedi
Equation 4 states that number of transmitters must be less than or equal to the number of receivers used in the network.
J]TRi RRi (4)
i=1 i=1
Equation 5 ensures that bandwidth utilization of all multicast requests must be less than or equal to all the wavelength capacity of the network.
J^cm.AmD < LAd.C Vi, D e di (5)
4. Proposed Approach
In this section we proposed a heuristic algorithm called Saturated-Light-Tree based Multicast Traffic Grooming (SLTMTG). As we know that transmitters and receivers are the costly devices in an optical network. Hence, prime objective of this approach is to minimize the cost associated with electronic resources used in a network simultaneously minimizing the usage of wavelengths. Proposed approach works in three phases, such as, multicast routing, grooming and wavelength assignment.
In multicast routing phase, individual path is explored from single source to single destination using Dijkstra's shortest path algorithm. The process is repeated for all set of destination requests and all individual paths are combined to form a multicast tree. The session requests are ordered such that multicast sessions sharing common branches can be groomed into a single wavelength. The multicast requests are sorted in the descending order of their session size. We have given higher bandwidth requests greater priority than lower bandwidth requests. Those multicast sessions have common set of requests among multiple sessions will be groomed first than those sessions have less common set of requests. It then tries to find the combination with as large with a common requests size as possible to save transmitters. If the combination with the common request size r cannot be found, it will try to find out a combination with the common request size r - 1 and so on. The procedure of finding common request size is as follows: starting from each request from beginning of the sorted list, algorithm will check every request with rest of requests to be selected or not. If the requested downward have enough common set of requests and has sufficient bandwidth, then this multicast request will be groomed with the previous request. If the selected request can occupy the whole wavelength channel, a light-tree will be constructed to update the multicast requests as well as bandwidth capacity. In the same fashion, the process will be repeated untill all multicast requests are satisfied. Wavelength is assigned to the multicast trees which can fully utilize bandwidth to the wavelength capacity. If there are multiple such requests then the process could be done in any order. If the groomed multicast trees request is less than the maximum bandwidth capacity and there is no possible match left for that tree, then a single wavelength is to be assigned.
4.1. Complexity Analysis of SLTMTG:
Time complexity of generating paths having single source and single destinations using Dijasktra algorithm is O(N2), where, N is the number of nodes in the network. Union of all the paths generate multicast tree. Due to this,
Algorithm 1: Saturated-Light-Tree based Multicast Traffic Grooming (SLTMTG) Input : A network G(V, E) with capacity C of each wavelength and a set of multicast session requests
R = {m1, m2,..., mn} Output: Routing and wavelength assignment of groomed multicast trees
1 for i = 1 to |R| do
2 t = p /* let t be an empty set */
3 for k = 1 to |m,| do
4 pk = shortestPath(s(mi), dk)
5 t = t U pk
6 T = T U t /* set of multicast trees T */
7 return T
8 for i = 1 to T | do
for j = 1 to T | do
pi,j = Sort( ti, tj ) /* Sort multicast requests based on tree size and bandwidth */
Arrange the pair of trees according to their tree size and bandwidth for j = 1 to |T| do
if pi,j + p and fi + fj < C then
tj = tj — (ti n tj) /* removing common edges from tj as they are groomed with ti */ fi = fi + fj; /* since tj has changed, requests and bandwidth will be updated */
return T'; /* set of groomed trees T'*/
17 for i = 1 to |T'j do
20 21 22 23
l = p /* initially set l to be an empty set */ while |W | + ( do
if (A j free for all links oft'{) then l = (t< U Aj) /* t' eT */ L = L U l remove A; from L
24 return L /* set of wavelengths L*/
the order of complexity of m destination nodes is O(m * N2). When there are r number of requests are generated time complexity is O(r * (m * N2). Time complexity of grooming r requests and m destinations set is O(r2 * m2). In this approach First-Fit technique is used for wavelength assignment. The complexity of wavelength assignment is O(W ), where, W is the number of wavelengths available per fiber in the network. Hence, order of time complexity in worst case using SLTMTG is O(r * (m * N2)) + O(r2 * m2 * W).
4.2. Example:
We have considered a network having six nodes and eight edges as shown in Fig.1. By applying our approach SLTMTG in 6 node network we can generate ten random multicast requests as shown in Table.1. We assume that wavelength capacity C is OC-12, and bandwidth requirement of a multicast request can be one of OC-1, OC-3 or OC-12. Multicast trees are generated form these multicast requests is as shown in Fig.2. Multicast tree-3 generated from request R3 has bandwidth capacity OC-12, which has satisfied full bandwidth capacity, hence a single wavelength is assigned to it. The remaining requests are arranged in non-decreasing order of their session size (number of source and destinations) and requested bandwidth. Multicast session requests having larger common session size and bandwidth capacity will groom first. In a given example, multicast requests R1, R2, R4 and R6 all have common similar sub-multicast request as that of R1(2 ^ 3,6). Hence, all sub multicast requests are groomed with R1(2 ^ 3,6) to satisfy the full bandwidth capacity of that link. Now, sub-multicast requests R5, R6 and R9 have common sub-request which
Table 1. Ten multicast requests for the 6 nodes network
Requests Source Destinations Bandwidth (OC)
1 1 2, 3, 4, 6 3
2 4 1,2,3,6 3
3 2 3 12
4 4 2, 3,5, 6 3
5 1 2, 4, 5, 6 3
6 1 2, 3, 6 3
7 6 1,3,4,5 1
8 1 4, 5,6 3
9 4 1, 2, 3 3
10 1 4,5 3
Figure 2. Randomly generated Multicast trees
is groomed with R^1 ^ 2) that satisfies the full bandwidth capacity of that link . Remaining sub multicast request R1 (1 ^ 4) have common set of sub-request as that of R5, R8 and R10. Therefore, these three sub-multicast requests are groomed with R1 to fully satisfy the link capacity. In this way, R1(1 ^ 2,3,4,6) is groomed with these sub-multicast requests to satisfy full bandwidth capacity and a single wavelength is assigned to it. In the same fashion grooming and wavelength assignment take place for other sessions untill all requests are satisfied for all multicast sessions. As multicast grooming takes place either in the source or destination nodes, hence use of transceivers or receivers can also be minimized by using sub-multicast traffic grooming approach in an optical network.
5. Experimental Result Analysis
In this section, we compare the numerical results obtained from proposed algorithm saturated-Light-tree based multicast traffic grooming (SLTMTG) with existing algorithm multicast traffic grooming [MTG] [8]. The simulation results is obtained on standard networks such as 14 node NSF network and 17 node German network. Here, multi-
Figure 3. 14-node NSF Network
Figure 4. 17-node German Network
Maximum session size 8
MTG .....•■■■■
SLTMTG —■---
10 20 30 40 50 60 70 80 90 100 Number of sessions
35 30 Ü 25
Üä 10
Maximum session size 8
MTG -■■•-■ SLTMTG -J-—
10 20 30 40 50 60 70 80 90 100 Number of sessions
Figure 5. Number of Wavelengths per link vs Number of sessions for 14-node NSF Network
Figure 6. Number of Wavelengths per link vs Number of sessions for 17-node German Network
cast requests are randomly generated having single source and multiple destination. We assume that capacity C of wavelength is OC-48, and required bandwidth granularities are randomly chosen among one of OC-1, OC-3, OC-12 or OC-48. We set a to 3 and¡i to 1 as relative cost parameters. The average value of 100 iterations of simulation on various randomly generated multicast requests are resulted using SLTMTG is as shown in this section.
Figure.5 and 6 show results of wavelength requirement of the saturated-light-tree based multicast traffic (SLTMG) with existing algorithm called multicast traffic grooming (MTG) [8]. Here, number of session varies from [10,100], keeping maximum session size is 8 for both the networks. From the following figures it is clear that SLTMTG achieves lowest wavelength requirement than existing MTG algorithm. This is because SLTMTG has higher efficiency of grooming multicast requests than MTG. Those multicast requests has maximum matching and more bandwidth capacity than others will groom first. Due to this, bandwidth wastage will be less and grooming effect will be higher in SLTMTG algorithm which results minimizing the wavelength requirement in the network. Whereas, in case of MTG algorithm multicast requests are satisfied as per randomly generated requests. Multicast requests are not to be arranged in ascending/descending order as per their session size or bandwidth requirement. Due to this, mulicast requests having lesser tree size and bandwidth will groom earlier than larger tree size and bandwidth. This results, more wavelength requirement and less bandwidth utilization in MTG than proposed SLTMTG.
Cost comparison of the two algorithms, saturated-light-tree based multicast traffic grooming SLTMTG and multicast traffic grooming MTG is depicted in Fig.7 and 8. It is clear from the following figures that SLTMTG has a lower cost than MTG algorithm. This is because SLTMTG construct sub multicast trees which can be fully or partially groomed. Whereas, MTG multicast-trees are groomed one by one, and each multicast tree may not be shared by other multicast requests. Due to this, SLTMTG has lesser requirement of electronic equipments (transceivers and receivers) and wavelength than MTG algorithm. As cost of the network depends on number of electronic equipments and wavelengths used, therefore, SLTMTG gives better performance than MTG algorithm.
50 r-45 -40 -35 -30 -25 -20 15
Maximum session size 8
".......
MTG SLTMTG
10 20 30 40 50 60 70 80 90 100 Number of sessions
55 -50 -45 -40 -35 -30 -25 20
Maximum session size 8
MTG SLTMTG
10 20 30 40 50 60 70 80 90 100 Number of sessions
Figure 7. Cost per node vs Number of sessions for 14-node NSF Network
Figure 8. Cost per node vs Number of sessions for 17-node German Network
! 4 aj
1.5 it'''
Number of sessions 100
6 8 10 Number of destinations
........ e d o 5
er re 4.5
cx re 4
—- er 3.5
of 2.5
be um Nu 2 1.5
MTG SLTMTG
6 8 10 12 Number of destinations
Figure 9. Number of Receivers require per node vs Number of destinations for 14-node NSF Network
Figure 10. Number of Receivers require per node vs Number of destinations for 17-node German Network
Figure.9 and 10 compare the number of receivers needed by the two algorithms. Here destination size varies from [2,12] for NSF network and [2,14] for German network, keeping maximum session size 8. It is observed that number of receivers required by SLTMTG is less than MTG algorithm, because SLTMTG uses saturated grooming to increase the utilization of light-trees than MTG. Due to the same reason SLTMTG uses fewer transmitters than MTG algorithm as shown in Fig.11 and 12.
Comparison of the wavelength requirement with the number of destination nodes of both the networks is shown in Fig.13 and 14. Here, SLTMTG performs better than MTG with the increase of destination size. The reason is that SLTMTG grooms multicast requests as much as possible leading to higher utilization of sub-multicast trees. On the other hand, MTG groom the requests one by one and sharing of the multicast requests is also less compare with the SLTMTG.
6. Conclusion
In this paper, the design of WDM mesh networks with multicast traffic grooming is considered. We have proposed a heuristic algorithm called Saturated-Light-Tree based Multicast Traffic Grooming (SLTMTG) with the objective of minimizing the cost associated with higher layer electronic ports (transceivers and receivers) and the number of wavelengths used. The result reveals that in this heuristic approach, light-tree based sharing is more resource efficient than normal grooming of light-trees as explained in Multicast Traffic Grooming (MTG). Because saturated-light-tree multicast traffic grooming tries to construct light trees which are fully utilized by several multicast requests, whereas
Î 3 <5
<5 .û
1 0.5 f
Number of sessions 100
e d o 4.5
re 3.5
rs er 3
—A 2.5
CO ran 2
Tr of 1.5
er b um 1
Nu 0.5
6 8 10 Number of destinations
6 8 10 Number of destinations
Figure 11. Number of Transmitters require per node vs Number of destinations for 14-node NSF Network
Figure 12. Number of Transmitters require per node vs Number of destinations for 17-node German Network
Number of sessions 100
MTG SLTMTG
6 8 10 Number of destinations
Number of sessions 100.,,.''"'
MTG -■■•-SLTMTG -J--
6 8 10 12 Number of destinations
Figure 13. Number of Wavelengths per link vs Number of destinations for 14-node NSF Network
Figure 14. Number of Wavelengths per link vs Number of destinations for 17-node German Network
in case of MTG multicast requests are not to be shared properly. To demonstrate the performance of this heuristic approach we have considered well known network such as 14 node NSF and 17 node German network.
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