Performance Metrics Analysis of Torus Embedded Hypercube Interconnection Network

N. Gopalakris hna Kini et al /Internati onal Journal on Com puter Science and Engineeri ng Vol.1(2 ), 2009, 78-80 78 Performance Metrics Analysis of Torus Embedded Hypercube Interconnection Network N. Gopalakrishna Kini Dept of CSE, Manipal Institute of Technolog y (Manipal University), Manipal, I ndia ng.kini@manipal.edu M. Sathish Kumar School of EECS, Seoul National University, South Korea mskuin@yahoo.com Mruthyun jaya H.S. Dept. of E&C, Manipal Institute of Te chnology (Manipal University), Manipal , India mruthyu.hs@manipal.edu Abstract —Advantages of hypercube network and torus topology ar e used to derive an embedded architecture for product network known as torus embedded hyperc ube scalable inter connection netw ork. This paper an alyzes torus embedded hypercube networ k pertinent to parallel architecture. The network metr ics are used to show how good embedded network can be de signed for parallel computation. Network parameter analysis an d comparison of embedded net work with basic net works is presented. Keywords-Concurrent torus network , Emb edded networ k , Hypercube network , Torus networ k , Network paramete rs , Scalability , Reliability. I. I NTRODUCTION The interconnecti on network is an im portant com ponent in a parallel com puter. A good intercon nection networ k is expected to have l east number of li nks, topological network cost and more reli able [1]. The inte rconnection network must be able to scale up with a few buildin g blocks and with minimum redesign. The hypercube is a n etwork with hi gh connectivity and si mple rout ing but the node degree g rows logarithmi cally with number of ve rtices making i t difficult t o build scalable architecture [2], [3], [10]. Torus is a netw ork with constant node degree a nd is highly scalabl e architecture but has larger n etwork diam eter [2], [4], [9] . The advantages of hypercube and torus network can be superposed on t o an embedded archit ecture [4]-[8] call ed torus embedded hypercube scal able interconnectio n network. II. A RCHITECTURAL PROPERTIES Let l × m be the size of se veral concurrent torus networks with l number of rows an d m number of columns and N be ing the number of n odes connected in t he hypercube, the t orus embedded hypercube net work can be designed with t he size of ( l , m , N ). Nodes with id entical positio ns in the toru s networks will be a grou p of N number of nod es connected in the hypercube configuration a nd can be add ressed with three components such as row nu mber i , column num ber j of torus and address of node k in hypercube where t he addressed node is residing. He nce, a ( l , m , N )–torus embedde d hypercube network will have l × m × N number of nodes and a n ode with address as ( i , j , k ) whe re 0 ≤ i < l , 0 ≤ j < m a nd 0 ≤ k < N . The data routing functions of torus em bedded hypercube network could be anal yzed [6]-[8] as in (1)- (5). T h 1 ( i , j , k ) = ( i , ( j+ 1) mod m , k ) (1) T h 2 ( i , j , k ) = ( i , ( m+j- 1) mod m , k ) (2) T h 3 ( i , j , k ) = (( i+ 1) mod l , j , k ) (3) T h 4 ( i , j , k ) = (( l+i- 1) mo d l , j , k ) (4) T Cd ( k n- 1 .....k d+ 1 k d k d- 1 .....k 0 ) =( k n- 1 ...k d+ 1 d k k d- 1 .....k 0 ) (5) Figure 1. A (2,2,8)-t orus em bedded hypercu be network The end to end connections of row and column of each torus are not shown in Fi gure1 for simplicity. A wraparound connection is done alon g each row or colum n if they have same label as a complet ion of (2, 2, 8)-tor us embedded hype rcube network. The proposed netw ork is a highly scalable netw ork. Scalability is achieved in either ways. Firstly, the dimension of the hypercube can be increas ed by keeping t he size of concurrent torus sam e but increasing the num ber of concurrent torus accordingly. Secondly, dimens ion of torus is expanded by keeping the size o f the hypercube co nstant. Scaling up th e system using l atter method i n which expandi ng the size of torus without affecti ng the nod e degree of existing nodes is preferred than the case in former m ethod of hypercube expansion [4], [5]. ISSN : 0975-3397 N. Gopalakris hna Kini et al /Internati onal Journal on Com puter Science and Engineeri ng Vol.1(2 ), 2009, 78-80 79 The total number of lin ks, topolo gical netwo rk cost, the scalability and th e reliability are the parameters co nsidered in evaluating the perf ormance of this networ k. The result obta ined shows that the torus embedded hypercube favors the scal ability of interconnecti on network. III. R ESULTS AND D ISCUSSION A. To tal number of lin ks For an interconnecti on network the total number of links is expected to be as low as possibl e. Because this parameter that reflects link compl exity and ultimat ely the economical cost. Table I shows the number of link s with respect to the scalin g of the parallel architect ure for the basic and e mbedded networks considered. It is observed that the total n umber of links for torus embedded hypercu be network lies in between n-cube hypercube and torus netwo rk. It is to be noted that the torus embedded hype rcube offers larger number of li nks than torus network as shown in Figure 2. Thi s is because of the n ode degree of hypercube that gr ows logarithmically as the network is scaled up. TABLE I. C OMPARISON RESULTS OF T OTAL NUMBE R OF L INKS OF BASIC A ND EMBEDDED NET WORKS Figure 2. Graphical analysis of number of links of basic and em bedded network s B. Topological network co st Network cost is the main parameter for measuring and comparing different topologies. Topolog ical cost of the network depends o n the number of links a nd its di ameter. From Table II it is observ ed that the toru s embedded hypercube network has a low net work cost. It i s also to be o bserved that the topological cost of ( l , m , 16) - net work is m ore than that of the n-cube hypercube. This is because of the network diameter of the torus net work that affects the t opological cost of ( l , m , 16) –torus em bedded hypercube net work. The grap hical analysis of network cost of basic and embedded networks is shown in Figur e 3. Even though the torus em bedd ed hypercube network do not reach to the level of prominent features of hypercube or torus network the results obtain ed shows tha t it gives be tter performance with respect to weaknesses of these basic networks. As far as network scalability of torus embedded h ypercube network is concerne d, selection of the ap propriate scaling up configuration i s most importa nt. The configurati on is selected in which the dim ension of torus is expan ded by keeping t he size of the hypercube constant and hence the node degree remains const ant. TABLE II. C OMPARISON RESULTS OF TOPOLOGICAL COST OF BASIC AND EMB EDDED NETWORKS Figure 3. Graphical analysis of network cost of basic and embedded networks ISSN : 0975-3397 N. Gopalakris hna Kini et al /Internati onal Journal on Com puter Science and Engineeri ng Vol.1(2 ), 2009, 78-80 80 C. Reliability of the network Reliability of a n etwork addresses the p robability that a given source-desti nation pair has at least one fault-free path between them. In th e reliability analys is the prob ability of nod e or link failure i n a scaled up network is considered . An analytical meth odology is used in find ing the reliability and prediction of availability of interconnection networks. This methodology takes into account the network topology, network size and the routing algori thm used. The reliability analysis presented here is with resp ect to the failure of th e neighboring nodes or links al ong a routing pat h. TABLE III. R ELIABILITY ANALYSIS FOR T ORUS EMBEDDED HYPERCUBE INTE RCONNECTION NETWORK The reliability analysis for th e torus embedded hypercu be interconnection network is show n in Table III. For a defined network configurati on, each and every node possesses equal link complexity. Acco rding to the analysis it is o bserved that the reliability of the torus em bedded hypercube interconnect ion network improves w ith respect to the scalabi lity of the netw ork. Larger the network better the reliab ility. Unreliability also gets minimized as the network is scaled up. IV. C ONCLUSION The proposed network i s a combination of hypercube and torus network t opologies. The analysi s results show that torus embedded hypercu be interconnection n etwork is highly scalable and configurat ion of the exis ting node is not requi red. Due to the existence of concurrent multiple to rus and hypercubes, this network pr ovides a great architectural support for parallel processing . The growth of the n etwork is more efficient in terms of communication. Further, an analysis on th e reliability of torus embedded hypercube intercon nection network has shown that as the interconnectio n network is scaled u p the network will be more reliable and also the unreliabi lity of th e interconnectio n network gets min imized. This is very desirable feature for the interconnection n etwork as the network remains operational for more failure of neighborin g nodes or links in parallel co mputer architecture. R EFERENCES [1] Zhaoyang Li, Yi Zhang, Yu Chen and Ruichun Tang, “Design and implem entation of a high-perform ance interconnection network,” Proceedings of the Fourth Intern ational Conference on Parallel and Distributed Computing, Appli cations and Technologies, 2003, PDCAT'2003, 27-29 Aug.200 3, pp.17-20. [2] K. Hwang, “Advanced Computer Architecture: Parallel ism, Scalability, Programmability,” NewYork McGraw-Hill, 1993. [3] Hesham El-Rewini and Mostafa Abd-El-Barr, “Advanced Co mputer Architecture and Parallel Processing,” John Wiley & Sons, Inc., Hoboken, New Jersey, 2005. [4] Ahmed Louri and Hongki Sung, “An Optical Multi-Mesh Hypercube: A Scalable Optical interconnection Network for Massively Parall el Computing,” Journal of Lightwave Technology, Vol.12, No.4, Apr.1994, pp.704- 716. [5] Ahmed Louri and Hongki Sung, “A scalable optical hypercube-based interconnection network for m assively parallel computing,” Applied optics, Vol.33, No.11, Nov.1994. [6] N. Gopalakrishna Kini, M. Sathish Kumar and Mruthyunjaya H. S., “A Torus Embedded Hypercube Scalable Inter connection Network for Parallel Architecture,” IEEE explor e conference publications, Mar.2009, pp.858-861. [7] N. Gopalakrishna Kini, M. Sathish Kumar and Mruthyunjaya H. S. , “Analysis and Comparison of Toru s Em bedded Hypercube Scalable Interconnection Network for Parallel Ar chitecture,” International journal of Computer Science and Network Security , Vol.9, No.1, Jan.2009, pp.242-247. [8] N. Gopalakrishna Kini, M. Sathish Kumar and Mruthyunjaya H.S., “Design and Comparison of Torus Em bedded Hypercube with Mesh Embedded Hypercube Interconnection Network,” International journal of Information Technology and Know ledge Management, Vol.2, No.1, Jun.2009, pp.87-9 0. [9] J.F.Fang, J.Y.Hsiao and C.Y.Tang, “Embedding Meshes and TORUS Networks onto degree-four chor dal rings,” IEE Proc.- Comput. Digit. Tech., Vol.145, No.2, Mar.1998. [10] Liu Youyao, Han Jungang and Du Huimin, “A Hypercube-based Scalable Interconnection Network fo r Massively Parallel Computing,” Journal of Com puters, Vol.3, No.10, Oct.2008, pp.5 8-65. ISSN : 0975-3397