Literature Survey of nonblocking network topologies

Literature Survey of nonblocking network topologies S.UMARANI 1, S.PAVAI MADHESWARI 2, N.NAGARAJAN 3 Department of Computer Applications 1 Department of Computer Science and Engineering 2,3 Sakthi Mariamman Engineering College 1 Thandalam,Tamilnadu. R.M.K.Engineering College 2 Kavaraipettai,Tamilnadu. Coimbatore Institute of Engineering and Technology 3 Coimbatore,Tamilnadu. INDIA swekalnag@rediffmail.com, ravania@gmail.com Abstract: - The performance of a parallel computer greatly depends upon how, the different processors are capable of exchanging data. This, thus require an arbitrary permutation (nonblocking) to be done by the connection networks. A nonblocking network is capable of providing N parallel paths between a pair of nodes forming any arbitrary permutation. In this paper, we present three different simple nonblocking schemes in WDM switching networks such as Crossbar, Clos-network, Benes-network and also select the best scheme among them. Key-Words: WDM, Multicast WDM switching networks, Nonblocking, Crossbar, Benes and Clos. 1. Introduction The explosive growth of the Internet has fueled intensive research on high-speed optical networks based on Wavelength-Division Multiplexing (WDM) technology. WDM technology harnesses the large bandwidth of the optical fiber, which is of the order of several Terabit/s into a few tens of wavelengths, each of which can be operated at electronic rates of a few Gb/s. Point-to-Point WDM links with several tens of wavelengths have been deployed by carrier networks. Efficient support for multicast communication in various networks has been the subject of much study in recent years. In this paper, we consider supporting multicast in switching networks (also called switches in some literature). Switching networks that can realize all possible multicast assignments are referred to as multicast switching networks. The WDM switching network consists of N input ports and N output ports. Each port connects to the switching network via a fiber link carrying k wavelengths. It realizes all possible multicast assignments. A multicast assignment is a mapping from a subset of network source nodes to a subset of network destination nodes, with no overlapping allowed among the destination of different sources. Multicast is an operation to transmit information from single source to multiple destinations [9]. Source Destination Source Destination Source Destination Fig.1. Examples of multicast assignment in an eight-node network. ISSN: 1790-5117 336 ISBN: 978-960-474-162-5

A multicast assignment is called a full-multicast-assignment if no new multicast connection can be added to this multicast assignment to form a new multicast assignment otherwise, it is called a partial-multicast-assignment. In general, a multicast assignment, full or partial, is called an any-multicastassignment Fig.1 gives several examples of multicast assignments in an 8-node network[3], [4]. In a multicast assignment, the number of destination from the same source is referred to as the fan-out of the source. Clearly, a permutation is a special case of a multicast assignment where the fan-out of each source is exactly one. Networks that can realize all possible multicast assignments are referred to as multicast networks. Moreover, a multicast network can be either nonblocking or rearrangeable. In a nonblocking multicast network, any new multicast connection from a source to its destinations can be realized without any disturbance to existing connections in the network, while in a rearrangeable multicast network, rearrangements of on-going connections in the network may be needed. Apparently, a nonblocking network can provide more powerful connecting capability than a rearrangeable network, but it usually has higher hardware complexity as well [1]. This paper is organized as follows. In section 2, we will first describe different multicast nonblocking switching networks. Furthermore, derive how the network cost to be reduced. In section 3, we compare the three different multicast nonblocking switching networks and select the best topology for the research work. In section 4, conclude the paper. 2. Multicast WDM switching networks As shown in Fig 2, the WDM switching network consists of N input ports and N output ports. Thereby, the non blocking network of N nodes can communicate simultaneously such that it allows any node to communicate with any other node and therefore, each port connects to the switching network via a fiber link carrying N wavelengths, denoted as {1,2,3,4.,N-1}. Also, each input port is equipped with N fixed-tuned optical transmitters, and each output port is equipped with N fixed tuned optical receivers [4], [6]. Fig. 2. An N N WDM network 2.1 Crossbar A switching network which consists of one or more stages of switches can be used to provide various connections between inputs and outputs. The Crossbar network is the simplest type of switching network and can be used to implement any permutation thereby provides full connectivity. The N M Crossbar is illustrate in Fig 3a., which is implemented as a rectangular array with N inputs(rows) and M outputs(columns),as shown in Fig 3b. Fig.3a) NxM crossbar network, where input 1 connect to output 3 and input 2 connect to output 2. Fig.3b) Rectangular array switch connections. It is simple in that the addresses of the nodes taking part in the permutations themselves lead to the control directly. In a crossbar, any cross point could be in one of the two states, ON (denoted as black dot in the Fig. ISSN: 1790-5117 337 ISBN: 978-960-474-162-5

3b.) and OFF. For an example, consider 4 4 crossbar and the permutation P as P = 1 2 3 4 4 2 1 3 bars, each cross bar of size n 1 m. Similarly the output lines are grouped into r 2 groups and each group has n 2 lines. The output stage has r 2 cross bars each of size m n 2, where m is some integer. The middle stage has m cross bars of size r 1 r 2. It is obvious that m should be greater than or equal to n 1 and n 2 (otherwise some of the input or output lines shall not have the switches for connection)[9]. Fig.4, 4 x 4 crossbar and permutation p. As shown in Fig4.The given permutation requires that an input node from the first row to be connected to the corresponding node in the second row. The permutations itself tell us the addresses of the switches to be closed. In the above example, switches to be closed are given by the row and column number as (1,4) (2,2) (3,1) (4,3). In general, the number of crosspoints is used as a representative measure of the hardware complexity of switching circuits. It is easy to see that an N M crossbar network has N 2 crosspoints (Assume N=M).Thus, it has O(N 2 ) hardware cost, which is expensive for a large N[7],[5]. The hardware cost can be reduced by using a multistage interconnection network. 2.2 Clos Network The good example of multistage interconnection network is Clos network. The Clos network reduces the number of switches significantly compared to the crossbar for large values of N. A N M Clos network is shown in Fig.5. The architecture of Clos network is derived as follows. The numbers N and M are assumed to be composite. The number N is factored as a product of two integers n 1 and r 1 (N=n 1.r 1 ), while the number M is factored as a product of n 2 and r 2 (M=n 2.r 2 ). In the Clos network N inputs lines are grouped into r 1 groups. Each group has n 1 lines. The first stage of the network consists of r 1 cross Fig.5.Clos Network The first to second stage connections are as follows. The output line no.1 of all the cross bars in the first stage (r 1 in numbers) are connected to the input lines 1,2,..r 1 of the first cross bar in the middle stage. On similar lines output lines with numbers 2 of all the cross bars in the first stage are connected to lines 1,2, r 1 of the second cross bar in the middle stage. In general the output lines of all the first stage cross bars with line no. k are connected to the input lines of k th cross bar lines 1,2,..r 1 in the middle stage.the hardware cost of the network in terms of the number of cross points. r 1.(n 1.m)+m.(r 1.r 2 )+r 2.(m.n 2 ) (1) m(r 1.n 1 +r 1.r 2 +r 2.n 2 ) (2) Assuming M=N with n 1 =n 2 =r 1 =r 2 =sqrt(n) m(n 2 +n 2 +n 2 ) m(3n 2 ) 3 n 3 (since n=m) 3 N 1.5 (3) ISSN: 1790-5117 338 ISBN: 978-960-474-162-5

2.3 Benes Network A special case of NxN Clos network, where the number N(typically assumed to be power of 2) is factored into factors n 1,n 2 =2 and r 1,r 2 =N/2, is shown in Fig. 6. for N=16 as a three stage network Clos network. The first stage has N/2 cross bars are also used in the last stage, while the middle stage has two cross bars of N/2 N/2 size each[8]. The 2 2 cell may be connected to form a 4 4 Benes network, it is similar to 4 4 Clos network. Once we have 4 4 Benes network it could be used in the central stage to form a 8 8 network. The 8 8 network could be used in the central stage to form a 16 16 network. The network controls the switch settings directly by using the cross bar routing. Benes network is an extension of cross network. Recursively, the middle stage cross bar are decomposed into smaller cross bars. E.g.: P= 0 1 2 3 4 5 6 7 5 2 4 6 1 7 0 3 Fig.6. 16x 16 Benes Network Further decomposition of these two N/2 N/2 cross bars using N/4 N/4 cross can be done, and in general the idea can be applied recursively. The recursion terminates when trivial cross bars of size 2 2 are reached. The networks designed using this decomposition principle is called Benes binary networks. The 2 2 cross bars could be implemented using four switches. Such a cross bar implements only two permutations, viz., identity and an exchange permutation for two inputs as shown in Fig.7. A 2 input and 2 output cell can be defined to implement these two functions. The cell can be controlled by one bit control indicating the desired permutation on two inputs (straight or cross i.e., exchange). This binary decomposition was suggested by Benes [Benes 1965] therefore these networks are called Benes networks. Fig.7. 2 2 cell with two routing functions where P = permutation The cells are grouped and the subnetworks are numbered as 0 and 1 where 0 represents the upper subnetwork, 1 represents the lower subnetwork. Input lines are characterized by rows and output lines are characterized by columns. Setting depends upon the first and last stage of input and output lines. 0 1 2 3 4 5 6 7 0 x 0 1 x 1 2 x 1 3 x 0 4 x 0 5 X 1 6 x 1 7 x 0 Fig.8. Dividing the connection into two groups 0 and 1. The above Fig.8. illustrates that an input from the 4 th row and output from the 2 nd column represented as x 0, routed through the submit 0(i.e. the upper subnet). Through the middle stage, the lines from the input stage to the output stage may either straight or cross. So that we can identify in which subnetwork it was routed. Decomposing of the middle stage continues and grouping up of the entries and outgoings are routed accordingly. E.g. Grouping of rows and columns with ISSN: 1790-5117 339 ISBN: 978-960-474-162-5

2,4,8,16.rows/columns of the original matrix for every successive step. So that the idea behind the Benes network control is that the relevant input and output lines corresponding to the permutation in the middle stage could be directly setup. The Hardware cost of a Benes binary network can be worked out as follows: Assume that N=2 n, then the total number of cells in the network. N/2.(2n-1) (4) N/2.(2log 2 N-1) (5) (N log N N/2) (6) 3.0 Comparison of Multicast WDM Switching Networks We now determine the number of switches required for crossbar, Clos, Benes network in various node systems are shown in table 1. Consider the table given below; the crossbar is cost effective up to 8 nodes systems. The Clos network is cost effective for 16 nodes systems. The Benes network is cost effective than the other two networks when the number of node is high. N Crossbar Clos Network Benes Network 2 4 9 4 4 16 24 16 8 64 69 80 16 256 192 224 32 1024 543 576 64 4096 1536 1408 128 16384 4344 3328 Table 1. Number of Switches in various networks as a function of N. The main advantage of Benes network reduces the number of switches in the middle stage when compared to other networks. 4. Conclusion In this survey paper, we have discussed various multicast WDM switching networks and highlighted the advantages of Benes network which is considered as the best network for nonblocking scheme when the number of nodes is high. As a future work, we suggest to carry out the performance analysis of two fold network for maximum requests. References: 1. Y.yang and G.M. Masson, Nonblocking Broadcast Switching Networks, IEEE Trans. Computers, vol. 40,no. 9, pp. 1005-1015,1991. 2. C.Clos, A Study of Non-Blocking switching Networks, The Bell System Technical J., vol. 32, pp. 406-424,1953. 3. Y. Yang and J. Wang, Nonblocking k-fold multicast networks, IEEE Trans. Parallel Distrib, syst., vol, 14, pp. 131-141, Feb 2003. 4. Y.Yang J.Wang, and C.Qiao, Nonblocking WDM multicast switching networks, IEEE Trans. Parallel Distrib, Syst., vol. 11,pp. 1274-1287, Dec 2000. 5. Yuanyuan Yang, Senior Member, IEEE, and Jianchao Wang, A New Design for Wide-sense Nonblocking Multicast Switching Networks, IEEE Transactions On Communications, VOL 53, NO.3, MARCH 2005. 6. B.Chidhambararajan, K.Kalamani, N.Nagarajan,S.K.Srivatsa, Multicast Connection Capacity Of WDM Switching Networks Without Wavelength Conversion, wseas transactions on circuits and systems issue 11, ISSN: 1790-5117 340 ISBN: 978-960-474-162-5

vol.4,november 2005. ISSN 1109-2734. 7. Yuanyuan Yang, Senior Member, IEEE, and Jianchao Wang, Member, IEEE Computer Society, A Fault-Tolerant Rearrangeable Permutation Network, IEEE transactions on computers, vol 53, no.4, April 2004. 8. Yun Deng, Student Member, IEEE, Tony T.LEE, Fellow, IEEE, Crosstalk-Free Conjugate Networks For Optical Multicast Switching, arxiv:cs/0610040v1 [cs.ni] 9 Oct 2006. 9. Zhenghao Zhang and Yuanyuan Yang, Senior Member, IEEE, Performance Analysis of K-Fold Multicast Networks, IEEE transactions on communications, vol 53, No.2, February 2005. ISSN: 1790-5117 341 ISBN: 978-960-474-162-5