Received: June 7, 207 98 IP Netwok Design by Modified Banch Method Kaiat Jaoenat Natchamol Sichumoenattana 2* Faculty of Engineeing at Kamphaeng Saen, Kasetsat Univesity, Thailand 2 Faculty of Management Science, Nakhon Pathom Rajabhat Univesity, Thailand * Coesponding autho s Email: k.natchamol@hotmail.com Abstact: One popula IP netwok outing potocol is OSPF (Open Shotest Path Fist), which uses algoithms to find its own path by calculating the path with the least weight fom souce to destination. As a esult, the design and outing of the data flow may not meet the equiements. To meet the efficiency of cable installation and outing, the Banch fo netwok design pocess was applied. With the ability to select the numbe of links to be exchanged with othes, we can tade-off between the design efficiency and the pocessing time. We used the ability of the Banch method to detemine a netwok with an efficient taffic flow distibution. We calculated the end-to-end delay time using the M/M/ model, then analyzed the netwok design efficiency of 8- and 9-node netwoks compaed to the Simplex method. Fo 8-, 9-, and 0-node netwoks, we compaed the MENTOR-II method to taffic flow and netwok complexity. The esults showed that the efficiency of the Banch method in tems of delay and cost closely align to the Simplex method but with faste calculation time. Howeve, moe exchange links () means a pocessing time close to the Simplex method. Keywods: Banch exchange, IP netwok design, Weight exchange. Intoduction The Intenet is a vey impotant technology and necessay fo connecting woldwide netwoks togethe. The devices that ae used to connect netwoks ae called outes. The cuent widely popula outing potocol is OSPF (Open Shotest Path Fist), which has many embedded advantages, such as using Dijksta s algoithm to find the shotest oute by itself, ecognizing change in the topology patten, and quickly updating the netwok s oute. Howeve, because OSPF outes use this algoithm to find thei own paths with the shotest outes, the taffic flow may not match the oveall needs of some flow paths. In addition, the efficiency and cost of netwok cable installation ae the most impotant factos to be consideed. Most netwok design algoithms ae faily complex, such as the Simplex linea pogamming method and the Banch method. The simple Banch method [] equies a complexity of O(N 5 ), whee N is the numbe of nodes, which is pohibitive fo modeating to lage netwoks. Howeve, as the Intenet becomes the lifeline to business and commecial applications, one must be awae of seveal issues in designing lage data netwoks (i.e., Intenet Sevice Povides backbone). One of the most impotant is that the IP netwok is a datagam netwok in which the outing potocols oute taffic ove the path with the shotest distance that is, the sum of link weights. Howeve, the link weight setting fo an optimum outing patten is a complex poblem that is possibly unfeasible [2-3]. Sidhaan, Gúein, and Diot [4] exploed the tade-off that exists between pefomance and the ovehead associated with the additional configuation steps fo IP netwoks. Sqalli, Sait, and Asadullah [5] engineeed a Tabu Seach Iteative heuistic using two diffeent implementation stategies to solve the OSPF weight setting poblem fo link failue scenaios. But these conventional techniques ae only the IP taffic assignment algoithms fo existed netwoks which cannot be used to design IP netwoks. Intenational Jounal of Intelligent Engineeing and Systems, Vol.0, No.6, 207
Received: June 7, 207 99 The least complex and high-speed heuistic netwok design algoithm is MENTOR (Mesh Netwok Topological Optimization and Routing [6], which selects a link to be installed as assigned taffic flows ove it. MENTOR is often used to design vitual cicuit packet switching netwoks, such as Fame Relay, ATM, and MPLS. Afte that, Cahn [7] poposed a modified vesion of MENTOR called MENTOR-II in which appopiate link weights ae assigned to the installed links such that the taffic always outes to the path with minimum distance and can be applied to IP netwoks. Howeve, both MENTOR and MENTOR-II give a good pefomance by using some value of the design paametes [8-9]. Banch [0] is a distibuted design method which consists of adding, dopping, o exchanging links to achieve bette pefomance. In ode to detemine the efficiency and costeffectiveness of cable installation and taffic outing, we applied ou modified Banch method fo IP netwok design to get the advantage of the ability to adjust between the design efficiency and the pocessing time of the design pocess. 2. Modified banch exchange method Banch is a distibuted design method that can be applied to IP netwok design. It stats by connecting the station with any topology and then adding, dopping, o exchanging links to achieve bette pefomance though a link exchange called pemutation. Thus, the default link weights ae assigned and exchanged to achieve bette pefomance, as shown in Fig.. An oveview of the modified Banch method is shown in Fig.. It stats with the following use s equiements: () The numbe of netwok nodes. (2) The node degee, which is the atio of the numbe of signal lines to the numbe of nodes. (3) Taffic equiement to flow between the two nodes. (4) Umax, which is the maximum acceptable taffic utilization of links. (5) Umin, which is the minimum acceptable taffic utilization of links. The initial netwok with default weight links is ceated with the node degee equied fom the use. The netwok links ae then exchanged to get the best netwok delay. Finally, the link weights ae exchanged to get the best netwok with the best link weights. The initial netwok ceation pocess begins by installing links between node pais with the most taffic equiements in ode to meet the equied node degee. Then the links load, suitable bandwidth, and delay cost ae calculated. If thee is any beach of utilization conditions, links with beach of conditions must be dopped and the link with the next lagest taffic equiement will be added instead until the netwok meets the use s node degee. The links bandwidth exchange pocess stats by calculating each link s netwok load and exchanging each link s bandwidth, which has the -ank highest taffic load with othe links. When each new netwok is ceated by the links bandwidth exchange pocess, then the new delay cost and the links netwok load is calculated. But if thee is any link with beach of utilization conditions, this netwok will be dopped. Afte calculating all foms of exchange, the netwok with the least delay cost is selected; if thee is not an acceptable netwok, a netwok with minimal condition violations is chosen to be the solution. Stat Requiements and design paametes Ceate an initial netwok links link weights Optimized netwok End Figue. Oveview of the Banch method Intenational Jounal of Intelligent Engineeing and Systems, Vol.0, No.6, 207
Received: June 7, 207 00 Afte the solution netwok is ceated by the links bandwidth exchange pocess, a default weight is assigned to each link. But if the default weight is not suitable fo the solution netwok, then we used a link s weight exchange pocess to poduce a suitable link weight fo each link. We begin by calculating each link s netwok load and exchanging each link s weight, which has the -ank highest taffic load with the othe links. When each new netwok is ceated by the links weight exchange pocess, then the new delay cost and the links netwok load is calculated. But if thee is any beach of utilization conditions, this netwok will be dopped. Afte calculating all foms of exchange, the netwok with the least delay cost is selected; if thee is not an acceptable netwok, a netwok with minimal condition violations is chosen to be the final solution. Finally, the output netwok consists of the following: () Good link connections and bandwidths among nodes. (2) Link weights, which allow fo efficient OSPF outing. (3) Total delay cost of the netwok. (4) Oveall time involved in the pocess. (5) Installation cost of the netwok. 3. Expeimental design We conducted an expeiment to compae the taffic flow pefomance of netwoks designed by the modified Banch method with the same equiement netwoks designed by the Simplex method and the MENTOR-II algoithm. The expeiment was conducted with thee node numbes 8, 9, and 0 and six node degee values,.0,.2,.4,.6,.8, and 2.0. We used DELITE [7] to geneate thee diffeent data sets fo each node numbe and taffic equiement, with total inbound and outbound taffic fo each data set equal to 00 Mbps, 50 Mbps, and 200 Mbps. A total of 62 data sets wee used in this expeiment. In pats of the MENTOR-II algoithm, we used the design paametes [9] of α (0, 0.5, ), ρ (0.6, 0.7, 0.8), and s (0.3, 0.4, 0.5) and then calculated the pefomance in the following aeas. 3. Delay efficiency Conside a diected netwok gaph G = (N, A) with a capacity c a fo each a A and, as defined in pevious section, d st denotes the amount of taffic st flow between s and t. Let f a indicate how much taffic flow fom s to t ove ac a, taffic load l a ove link a A is the sum of all f st a. It is suggested by Fotz et al. [3] to measue the netwok pefomance by delay cost function in Eq. (). Φ = a A a(l a, c a), () whee a(l a, c a) is an M/M/ queuing theoy style link cost function given by Eq. (2). a(l a, c a) = l a / (c a - l a) (2) With this function, it is moe expensive to send flow along acs whose loads appoach capacity, which is what we want. Howeve, the function does not deal with oveloaded links that is, l a c a. To ovecome this poblem, l a /(c a - l a) is appoximated by a piece-wise linea function [3] a(0) = 0 and deivative in Eq. (3). a(l a, c a) = fo 0 l a / c a < /3, 3 fo /3 l a / c a < 2/3, 0 fo 2/3 l a / c a < 9/0, 70 fo 9/0 l a / c a<, 500 fo l a / c a< /0, 5000 fo /0 l a / c a <. (3) Then we can calculate the delay efficiency as a diffeence between the total netwok delay [3] of the oiginal method and the new method fom Eq. (4). Delay Efficiency = D L o M D B 00 % (4) When delay efficiency is a pefomance in tems of total link delay in the netwok, D L o M is a total links netwok delay designed by the Simplex o MENTOR-II method and D B is a total links netwok delay designed by the Banch method. 3.2 Pocessing time efficiency We can calculate the efficiency of the time spent in the netwok design pocess as shown in Eq. (5). Times = T B T L o M (5) When Times is a pocessing time efficiency of the netwok, T L o M is the time spent on the design pocess of the Simplex o MENTOR-II method and T B is the time spent on the design pocess of the Banch method. Intenational Jounal of Intelligent Engineeing and Systems, Vol.0, No.6, 207
Received: June 7, 207 0 3.3 Installation cost efficiency When it is necessay to conside the cost of installing cables, then we can calculate the installation cost efficiency [] of the design pocess as shown in Eq. (6): Cost Efficiency = C L o M C B 00 % (6) When Cost Efficiency is an installation cost efficiency of the netwok, C B is the total netwok installation cost that was designed by the Banch method and C L o M is the netwok installation cost that was designed by the Simplex o MENTOR-II method. 4. Expeiment esults and analysis 4. Expeiment esults We analyzed the pefomance among the netwoks designed by the Banch, Simplex, and MENTOR-II methods in the thee aeas of delay, pocessing time, and installation cost []. The esults ae shown in Tables 9. Tables 3 show the aveage delay cost of the netwoks designed by the Banch, Simplex, and MENTOR-II methods. The esults fo each method wee aveaged fom the esults of 62 netwoks, except fo Banch, which ae sepaated fo each value of. Tables 4 6 show the aveage pocessing time of netwoks designed by the Banch, Simplex, and MENTOR-II methods. The esults fo each method wee aveaged fom the esults of 62 netwoks. As with the delay cost, the Banch esults ae sepaated fo each value of. Table. Aveage delay cost of 8-node netwoks Delay Cost Banch 679.8 2 652.54 3 640.7 4 622.6 463.48 895.67 5 608.69 6 589.23 7 582.77 Table 2. Aveage delay cost of 9-node netwoks Delay Cost Banch 206.04 2 204.7 3 2079.83 4 2067.54 899.43 2485 5 2062.04 6 2058.63 7 2058.63 Table 3. Aveage delay cost of 0-node netwoks Delay Cost Banch MENTOR-II 3642.9 2 3424.09 3 3272.63 4 342.57 3849.75 5 3085.29 6 3047.43 7 2377.33 Table 4. Aveage pocessing time fo designing 8-node netwoks Pocessing Time Banch 0.0 2 0.08 3 0.32 4 5.4 5558.03 0.02 5 2.02 6 203.32 7 880.79 Table 5. Aveage pocessing time fo designing 9-node netwoks Pocessing Time Banch 0.03 2 0. 3 0.53 4 5.8 338283.55 0.024 5 89.26 6 956.67 7 7208.6 Intenational Jounal of Intelligent Engineeing and Systems, Vol.0, No.6, 207
Received: June 7, 207 02 Table 6. Aveage pocessing time fo designing 0-node netwoks Pocessing Time Banch MENTOR-II 0.07 2 0.26 3 3.39 4 6.37 0.025 5 252.02 6 6990.53 7 4925.95 Table 7. Aveage installation cost of 8-node netwoks Installation Cost Banch 2476.42 2 2476.42 3 2476.42 4 2476.42 289.96 2243.6 5 2476.42 6 2476.42 7 2476.42 netwoks. As with the delay cost and pocessing time, the Banch exchange esults ae sepaated fo each value of. 5. Results analysis This section analyzes the total delay cost, pocessing time, and installation cost of 8-, 9-, and 0-node netwoks. Figs. 2 4 show the delay cost compaison of the modified Banch method to the Simplex and MENTOR-II methods. By selecting links to be exchanged in the Banch method, we found that the delay efficiency of the Banch method will fluctuate based on the numbe of selected links (). The geate the value of, the less netwok delay, which makes this method bette than the MENTOR- II method and moe closely aligned to the Simplex method. As shown in Tables 3, with equal to, we can see that the aveage delay cost of 8-, 9-, and 0-node netwoks is,679.8, 2,06.04, and 3,642.9, espectively, but when equals 7, the aveage delay cost of 8-, 9-, and 0-node netwoks is educed to,582.77, 2,058.63, and 2,377.33, espectively. Table 8. Aveage installation cost of 9-node netwoks Installation Cost Banch 3226 2 3226 3 3226 4 3226 2825.38 2902 5 3226 6 3226 7 3226 Delay cost 2000 500 500 0 Banch Simplex Figue.2 Aveage delay cost in 8-node netwoks Table 9. Aveage installation cost of 0-node netwoks Installation Cost Banch MENTOR-II 563.56 2 563.56 3 563.56 4 563.56 376.67 5 563.56 6 563.56 7 563.56 Tables 7 9 show the aveage netwok installation cost designed by the Banch, Simplex, and MENTOR-II methods. The esults fo each method wee aveaged fom the esults of 62 Delay cost 3000 2500 2000 500 Intenational Jounal of Intelligent Engineeing and Systems, Vol.0, No.6, 207 500 0 Banch Simplex Figue.3 Aveage delay cost in 9-node netwoks
Received: June 7, 207 03 Delay cost 5000 4000 3000 2000 0 Banch Mento-II Figue.4 Aveage delay cost in 0-node netwoks Times (S) 0 00 0 0. 0.0 Banch Simplex Figue.5 Aveage pocessing time of 8-node netwoks Figs. 5 7 show the pocessing time compaison of the modified Banch method to the Simplex and MENTOR-II methods. By selecting links to be exchanged in the Banch method, we found that the pocessing time of the Banch method will also fluctuate based on the numbe of selected links (). The geate the value of, the moe pocessing time needed by the Banch method, which makes it wose than the MENTOR-II method and moe closely aligned to the Simplex method. As shown in Tables 4 6, with equal to, the aveage pocessing time of 8-, 9-, and 0-node netwoks is 0.0, 0.03, and 0.07 seconds, espectively, but when equals 7, the aveage pocessing time of 8-, 9-, and 0-node netwoks is inceased to 880.79, 7,208.6, and 49,25.95 seconds, espectively. Figs. 8 0 show the installation cost compaison of the modified Banch method to the Simplex and MENTOR-II methods. By selecting links to be exchanged in the Banch method, we found that the installation cost of the Banch method did not fluctuate based on the numbe of selected links (). As shown in Tables 7 9, the aveage installation cost of 8-, 9-, and 0- node netwoks is 2,476.42, 3,226, and 5,63.56, espectively. Times (S) 000 00 0 00 0 0. 0.0 Banch Simplex Figue.6 Aveage pocessing time of 9-node netwoks Times (S) 00 0 00 0 0. 0.0 Banch Mento-II Figue.7 Aveage pocessing time of 0-node netwoks Installation cost 2500 2450 2400 2350 2300 2250 2200 250 Banch Simplex Figue.8 Aveage installation cost in 8-node netwoks Installation cost 3300 3200 300 3000 2900 2800 Banch Simplex Figue.9 Aveage installation cost in 9-node netwoks Intenational Jounal of Intelligent Engineeing and Systems, Vol.0, No.6, 207
Received: June 7, 207 04 Installation cost 6000 5000 4000 3000 2000 0 Banch Mento-II Figue.0 Aveage installation cost in 0-node netwoks Pocessing time (s) 000 00 0 00 0 0. 0.0 4 5 6 7 8 9 Numbe of nodes Figue. Simplex method pocessing time Pocessing time (s) 0 00 0 0. 0.0 0.00 4 5 6 7 8 9 Numbe of nodes = Figue.2 Banch method pocessing time The Simplex method netwok design and outing pocess takes a vey long time, especially fo lage netwoks. Fig. shows the elationship between the numbe of nodes and the pocessing time, which can be appoximated to an exponential equation of y = 0.0003e 3.3572x when x and y ae the numbe of nodes and the pocessing time, espectively. The Banch netwok design and outing pocess takes less time than the Simplex method. Fig. 2 shows the elationship between the numbe of nodes and the pocessing time fo each. These elationships can be appoximated to exponential equations of y = 0.0026e 0.4584x, y = 0.0055e 0.543x, y = 0.0098e 0.877x, y = 0.033e 0.9469x, y = 0.0527e.2992x, y = 0.2684e.3965x, and y = 0.7678e.5465x, fo equals to 7, espectively. Fom these estimated elationships, we can conclude that the Simplex method is not suitable fo lage netwoks. Using the example of a -month pocessing time, the Simplex method could povide only a 7-node netwok, while the Banch method could povide a maximum 45-node netwok with =. 6. Conclusion Adopting the Banch method fo netwok design and outing is a highly flexible option. With the ability to select the numbe of links () to be exchanged with othes, we can tade-off between the design efficiency and the pocessing time. We used the ability of the Banch method to add, dop, and exchange links in ode to detemine a netwok with an efficient taffic flow distibution. We then analyzed the pefomance of netwok delay, pocessing time, and installation cost of the Banch method. The esults showed the aveage delay pefomance compaed to the Simplex method is equal to 9.77%, the aveage pocessing time compaed to the Simplex method is 337,03.4 seconds faste, and the efficiency of installation cost is equal to 89.72% compaed to the Simplex method. In compaison with the MENTOR- II method, the esults showed that the aveage delay pefomance is equal to 8.27%, the aveage pocessing time is,80.2 seconds slowe, and the efficiency of installation cost equals 74.42%. In addition, we found that given the geate the numbe of, the delay and time pefomance of the Banch method would be even bette. Howeve, given moe numbes of links (), the Banch method equied moe pocesso time than the MENTOR-II method and thus aligned moe closely to the Simplex method. In conclusion, the Banch method offes bette pocessing time but with slightly wose delay and installation cost efficiency compaed to the Simplex method. But, in compaison with the MENTOR-II method, the Banch method offes bette efficiency in netwok delay but with slightly wose pocessing time and highe installation cost. Thus moe eseach woks need to be done in the futue to find a suitable technique to be added in ou method fo deceasing the pocessing time and the installation cost. Intenational Jounal of Intelligent Engineeing and Systems, Vol.0, No.6, 207
Received: June 7, 207 05 Refeences [] A. Keshenbaum, Telecommunications netwok design algoithms, McGaw-Hill, New Yok, N.Y. 993. [2] W. Ben-Ameu, E. Goudin, B. Liau, and N. Michel, Dimensioning of Intenet netwoks, In: Poc. of the second intenational wokshop on the design of eliable communication netwoks, Munich, Gemany, pp. 56 6, 2000. [3] B. Fotz, J. Rexfod, and M. Thoup, Taffic engineeing with taditional IP outing potocols, IEEE Communications Magazine, Vol.40, No.0, pp. 8 24, 2002. [4] A. Sidhaan, R. A. Gúein, and C. Diot, Achieving nea-optimal taffic engineeing solutions fo cuent OSPF/IS-IS netwoks, IEEE/ACM Tansactions on Netwoking, Vol.3, No.2, pp. 234 247, 2005. [5] M. H. Sqalli, S. Sait, and S. Asadullah, OSPF weight setting optimization fo single link failues, Intenational Jounal of Compute Netwoks & Communications, Vol.3, No., pp. 68 83, 20. [6] A. Keshenbaum, P. Kemani, and G. A. Gove, MENTOR: An algoithm fo mesh netwok topological optimization and outing, IEEE Tansactions on Communications, Vol.39, No.4, pp. 503 53, 99. [7] R. S. Cahn, Wide aea netwok design: Concepts and tools fo optimization, Mogan Kaufmann, San Mateo, CA, 998. [8] K. Jaoenat, and P. Chankeitkong, On outing pefomance of MENTOR algoithm, WSEAS Tansaction on Communications, Vol.9, No.5, pp. 769 776, 2006. [9] P. Chankeitkong, K. Jaoenat and P. Keatthaleenglit, On IP Netwok Routing Pefomance of MENTOR-II Algoithm, In: Poc. of IT Towads Empowement Intenational Confeence, Bangkok, Thailand, pp.38-43, 2007. [0] C. Ababei, and R. G. Kavassei, Efficient netwok econfiguation using minimum cost maximum flow-based banch exchanges and andom walks-based loss estimations, IEEE Tansactions on Powe Systems, Vol.26, No., pp. 30 37, 20. [] K. Jaoenat, S. Chimmanee and P. Chankeitkong, Algoithms fo IP netwoks design with ECMP outing enable, In: Poc. of 7 th Intenational Confeence on Computing and Convegence Technology, Seoul, South Koea, pp. 420 425, 202. Intenational Jounal of Intelligent Engineeing and Systems, Vol.0, No.6, 207