NETWORK TRAFFIC FORECASTING USING MACHINE LEARNING AND STATISTICAL REGRESSION METHODS COMBINED WITH DIFFERENT TIME LAGS

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1 NETWORK TRAFFIC FORECASTING USING MACHINE LEARNING AND STATISTICAL REGRESSION METHODS COMBINED WITH DIFFERENT TIME LAGS 1 DERMAN AKGOL, 2 MEHMET FATIH AKAY 1 Compuer Engineering Deparmen, Osmaniye Korku Aa Universiy, Osmaniye, Turkey 2 Compuer Engineering Deparmen, Çukurova Universiy, Adana, Turkey 1 dermanakgol@gmail.com, 2 mfakay@cu.edu.r Absrac- In his sudy, differen machine learning mehods including Suppor Vecor Machines (SVM), Radial Basis Funcion (RBF) Neural Nework, Mulilayer Percperon (MLP), M5P (a decision ree wih linear regression funcions a he nodes), Random Fores (RF), Random Tree (RT), and Reduced Error Pruning Error (REPTree), and a saisical regression called Hol-Winers have been used o forecas he amoun of nework raffic in Transmission Conrol Proocol/Inerne Proocol (TCP/IP) -based neworks. Two differen Inerne Service Providers' (ISPs) raffic daa have been uilized o develop raffic forecasing models. By using differen ime lags along wih he aforemenioned mehods on he daa ses, several Inerne raffic forecasing models have been buil. The performance of he forecasing models for he daa ses has been assessed using Mean Absolue Percenage Error (MAPE). The resuls show ha SVM and M5P based models usually perform beer han oher models. Keywords- Machine Learning, Time Series, Traffic Engineering, Time Lags. I. INTRODUCTION Inerne raffic is he ransfer of daa across he Inerne. Amoun of Inerne raffic is rising, and several and large number of packes are sen horough all over he world [1]. Inerne/nework raffic analysis and modeling is an effecive srucure o characerize nework performance; herefore, i has been a crucial poin in many sudies [2]. Laely, since communicaion and nework echnologies have developed quickly, raffic characerisic is alering exremely. The research abou Inerne raffic analysis and modeling has varied from he large ime scale o he small ime scale. The researches have indicaed ha he raffic characerisics of he small ime scale reaced differenly from he large ime scale s one [2]. Since he characerisic of Inerne raffic is geing more and more sophisicaed, his creaes new difficulies o he managemen of he nework. In order o overcome hese problems, developmen of Inerne/nework raffic forecasing models have become one of he mos acive research areas. A raffic forecasing model needs o be able o express he characerisics of he nework in he pas and also, needs o be forecas he developmen of his nework in he near fuure [3]. The predicabiliy of Inerne raffic is subsanial poin in many fields such as adapive applicaion, admission conrol, and wireless and nework managemen [4]. To predic Inerne raffic is very imporan o undersand communicaion neworks, opimize resources and have a beer qualiy of service. As well, by comparing he real raffic wih he forecas, anomalies (such as securiy aacks, viruses, ec.) can be deeced wih he help of raffic forecasing [5]. Also, he prediced resuls can be used as a significan reference for he bandwidh allocaion of Inerne raffic and error conrol in managemen [6]. In lieraure, o he bes of our knowledge, alhough here exis several sudies which predic he nework raffic wih he help of saisical as well as machine learning regression mehods, only a few sudies exis ha compare he performance of differen machine learning mehods for predicion of nework raffic on differen daa ses using several ime lags. In [7], SVM, MLP, RBF, and RT have been applied o forecas nework raffic. I has been repored ha SVM based Inerne raffic forecasing models yield lower MAPE s han he ones obained by he oher mehods. In [8], SVM, MLP, RBF, RF, RT, and REPTree have been used o develop Inerne raffic forecasing models. I has been concluded ha SVM based Inerne raffic forecasing models give he lowes MAPE s while RBF based Inerne raffic forecasing models yield he highes MAPE s. Table 1 gives he some recen sudies on Inerne raffic forecasing. The aim of his sudy is o exend he work of [7], [8] and [9] and forecas/predic he amoun of raffic in TCP/IP-based neworks by using various machine learning mehods including SVM, MLP, RBF, M5P, RF, RT, and REPTree, and a saisical regression mehod called Hol-Winers. In [7] and [8], differen machine learning mehods have been used o forecas Inerne raffic; however, M5P has been employed for he firs ime in his sudy o forecas Inerne raffic. In addiion, he heurisic rules discussed in [16] have been 68

2 Table1: Summary of recen sudies on Inerne raffic forecasing SVRCACO, Suppor Vecor Regression wih Coninuous An Colony Opimizaion; SARIMA, Seasonal Auoregressive Inegraed Moving Average; CTSA, Chaoic Time Series Analysis; SVM, Suppor Vecor Machine; TLFN, Time-Lagged FeedForward Neworks; ANN, Arificial Neural Nework; ARIMA, Auoregressive Inegraed Moving Average; MLP, Mulilayer Percepron; SAE, Sacked Auoencoder; LR, Linear Regression; RBF, Radial Basis Funcion Neural Nework; FFNN, Feed Forward Neural Nework; FARIMA, Auoregressive Fracionally Inegraed Moving Average; GARCH, Generalized Auoregressive Condiional Heeroscedasiciy; RT, Random Tree, RF, Random Fores; REPTree, Reduced Error Pruning. applied o generae forecasing models while in [7] and [8], he ime lags used o developed forecasing models have been chosen randomly. In his paper, o develop forecasing models, hree differen ime lags for each daa se were used. The MAPE values of he models have been compued o deermine he performance of he Inerne raffic forecasing models. The resuls show ha he MAPE s of SVM and M5P based Inerne raffic forecasing models are comparable. Besides, he resuls indicae ha SVM and M5P based models perform beer han he ones obained by he oher mehods while RBF based forecasing models yield he highes MAPE s. The res of he paper is organized as follows. Secion 2 gives deails of raffic forecasing models. Secion 3 presens resuls and discussion. Finally, Secion 4 concludes he paper. II. TRAFFIC FORECASTING MODELS SVM is a machine learning mehod ha analyzes daa and recognizes paerns for classificaion and regression problems. The value of cos (C), kernel ypes, and kernel funcions parameers are he major componens ha affec he qualiy and performance of SVM based models [17]. MLP is a feed-forward arificial neural nework model describes a map from ses of inpu daa o a se of oupus. Muliple layers of nodes consiue MLP in a direced graph where exacly each layer is conneced o he nex one [18]. The parameers ha affec he performance of MLP models are he ype of acivaion funcions, learning rae, momenum, and number of neurons in he hidden layers. In RBF, he neurons in he hidden layer conain Gaussian ransfer funcions. RBF uses he K-means clusering algorihm o provide he basis funcions and learns eiher a logisic regression or linear regression on op of ha. Symmeric mulivariae Gaussians are fi o he daa from each cluser [19]. The number of clusers and he clusering seed value are he main componens ha affec he performance of an RBF model. M5P is a reconsrucion of M5 wih some improvemen. M5P inegraes a convenional decision ree wih he possibiliy of linear regression funcions a he nodes. The M5 rules algorihm uses separaeand-conquer echnique o produce a decision lis for regression problems. Separae-and-conquer echnique is a rule ha includes insances in he class, hen separaes hem ou, and proceeds on hose ha are lef [20]. The minimum number of insance o allow a a leaf node is he only parameer ha affecs he performance of an M5P model. RF is an ensemble learning algorihm using many decision ree models in order o improve he error rae for classificaion and regression analysis. There are many advanages of RF mehod such as generaing a highly accurae classifier, running efficienly on large daabases, idenifying he variables ha are imporan in he classificaion, being an effecive mehod for esimaing missing daa, ec. [21]. The imporan parameers ha affec he performance of an RF model are he number of aribues o be used in random selecion, he number of rees, and he random number seed. RT is a ree ha is formed randomly by using a cluser of rees having N random feaures a every node [21]. The number of folds (i.e. he amoun of daa used for back-fiing), he minimum oal weigh of he insances in a leaf, and he random number seed used for selecing aribues affec he performance of an RT model. REPTree is a fas decision ree. Informaion gain as he spliing crierion is used o build a decision/regression ree and reduced-error pruning is used o prune he decision/regression ree. I only sors values for numeric aribues once [22]. The 69

3 number of folds (i.e. he amoun of daa used for pruning), he minimum oal weigh of he insance in a leaf, and he seed used for randomizing he daa are he parameers ha affec he performance of an REPTree model. Hol-Winers is a crucial forecasing mehod. In Hol- Winers, he predicive model consiss of rended and seasonable paerns ha are chosen from noise by averaging hisorical values. I has some advanages like easiness of using i, having less compuaion, and accuracy for seasonal series [9]. The imporan parameers ha affec performance of a Hol-Winers model are he lengh of he seasonal cycle and he smoohing facor. Ranges for he values of parameers for SVM-based, MLP-based, RBF-based, M5P-based, RF-based, RTbased, REPTree-based and Hol-Winers-based Inerne raffic forecasing models are given in Table 2. Table2: Values of he uilized parameers for raffic predicion models Mehods Parameers Values C [1-30] SVM Kernel ype Polynomial Epsilon ( ) [0 1] Learning rae [0 1] MLP Momenum [0 1] Number of neurons in he [3 6] hidden layers RBF Number of cluser [13-22] Clusering seed [0-11] M5P Minimum number of insances [4 21] Number of feaures [0 17] RF Max number of ree [ ] Random number seed [1 12] Number of folds [2 5] RT Minimum oal weigh of he [1 17] insances Random number seed [1 11] Number of clusers [0-12] REPTree Minimum oal weigh of he [3-6] insances Seed [1-19] Seasonal cycle lengh [1-3] Hol- Seasonal smoohing facor [0, 1] Winers Trend smoohing facor [0-1] Value smoohing facor [0-1] In his paper, wo differen daa ses have been uilized. One of he daa ses (referred o as DS1) was provided from a privae ISP wih ceners in eleven European ciies beween he daes of and The oher one (referred o as DS2) was provided from Unied Kingdom Educaion Research Neworking Associaion beween he daes of and Each daa se was formed wih a 5 minue ime scale. In his paper, he heurisic rules discussed in [16] have been uilized o build forecasing models. The rules of sliding windows are given below: 1. Use all ime lags from 1 o a given maximum m: <1, 2,, m> Use all lags, he auocorrelaion values of which are above a given hreshold 3. Use he four ime lags wih he highes auocorrelaions. The auocorrelaion coefficien is a saisic which evaluaes he correlaion among a series and iself wih lagged of k periods: r k T 1 k y y y k y T y y 1 (1) such ha y,..., 1 y T implies he ime series and y shows he average of he series. Auocorrelaions help o deec seasonal componens [9]. The auocorrelaions for DS1 and DS2 is given by Fig. 1 and Fig.2, respecively. By using he rules for ime lag selecion, discussed above, 3 differen sliding windows have been generaed for each daa se. DS1-lag1 and DS2-lag1 have been buil by seing m as 25 in he firs rule. DS1-lag2 and DS2-lag2 have been generaed by selecing all lags whose auocorrelaion values are above 0.9. DS1-lag3 and DS2-lag3 have been generaed by selecing four of he highes auocorrelaions. Table 3 gives he ime lags used for each daa se. Fig.1. The auocorrelaions for DS1 Fig.2. The auocorrelaions for DS2

4 Table3: Lis of he lags used for each daa se Lags Name Chosen Lags DS1-lag1 {1, 2,, 25} DS1-lag2 {1, 2,, 18} DS1-lag3 {1, 2, 3, 4} DS2-lag1 {1, 2,, 25} DS2-lag2 {1, 2,, 21} DS2-lag3 {1, 2, 3, 4} 1 1 n A F MAPE (2) n A where n is he number of forecas samples, A is he acual value, and F is he forecas value [23]. III. RESULTS AND DISCUSSION For model esing, he firs 2/3 of each daa se has been uilized as a raining se and he res has been used as a es se. The performance of he forecasing models has been evaluaed by compuing MAPE s, which is a meric used commonly in forecasing applicaions. The formula of MAPE is given in Eq. (2) The compued MAPE s for each raffic forecasing model on he DS1 and DS2 are shown in Table 4 and Table 5. Fig.3. and Fig.4. show he bar graphs of he average MAPE s of differen lags for all mehods for he 5- minue daa ses, respecively. Time Lags Table4: MAPE s for each raffic forecasing models on he DS1 Regression Mehods SVM MLP RBF M5P RF RT REPTree Hol-Winers MAPE MAPE MAPE MAPE MAPE MAPE MAPE MAPE DS1-lag DS1-lag DS1-lag Time Lags Table5: MAPE s for each raffic forecasing models on he DS2 Regression Mehods SVM MLP RBF M5P RF RT REPTree Hol-Winers MAPE MAPE MAPE MAPE MAPE MAPE MAPE MAPE DS2-lag DS2-lag DS2-lag Fig.3. The average MAPE s of differen lags for all mehods for DS1 Fig.4. The average MAPE s of differen lags for all mehods for DS2 Based on he resuls obained, he following discussions can be saed: The smalles and highes MAPE s vary in he range of % and % for DS1 and DS2, respecively. Predicion models for DS2 give 37.72% lower MAPE s on he average han he MAPE s of he predicion models for DS1. The general ranking of he mehods in erms of heir predicion performance based on MAPE s is SVM, MLP, M5P, RF, Hol-Winers, REPTree, RT, and RBF for DS1 while M5P, SVM, RF, Hol-Winers, MLP, REPTree, RT, and RBF for DS2. Paricularly, SVM gives 16.24% lower MAPE s on he average han he MAPE s of oher models for DS1 while M5P yields 18.16% lower MAPE s on he average han he MAPE s of oher models for DS2. When he lenghs of ime lags for DS1 are examined, he forecasing model developed by seing m as 25 in he firs rule given in heurisic rules yields lower MAPE s. More specifically, he forecasing model developed by using DS1- lag1 gives 2.49% and 0.34% lower MAPE s on he average han he MAPE s of he models 71

5 developed by using DS1-lag2 and DS1-lag3, respecively. When he lenghs of ime lags for DS2 are examined, he forecasing model developed by using he ime lags generaed by selecing all auocorrelaions above 0.9 gives lower MAPE s. Paricularly, he forecasing model developed by using DS2-lag2 yields 2.51% and 7.09% lower MAPE s on he average han he MAPE s of he forecasing models developed by using DS2-lag1 and DS2-lag3, respecively. CONCLUSION In his sudy; SVM, MLP, RBF, M5P, RF, RT, REPTree, and Hol-Winers have been used o develop Inerne raffic forecasing models by using differen lags for DS1 and DS2. The resuls show ha in general, he lags buil by using auocorrelaions give lower MAPE s. Addiionally, i is observed ha SVM and M5P based models perform beer han he ones obained by he oher mehods and can be used as a viable ool for forecasing he amoun of raffic in TCP/IP-based neworks. In he fuure, differen machine learning mehods wih differen ime lags will be applied o forecas he amoun of raffic in TCP/IP-based neworks, since his can help managemen operaions performed by ISPs. ACKNOWLEDGEMENTS This work is suppored by Çukurova Universiy Scienific Research Projec Coordinaion Deparmen (Projec No: FYL ). REFERENCES [1] M. Hasegawa, W. Gang, Applicaion of nonlinear predicion mehods o he Inerne raffic, The 2001 IEE Inernaional Symposium on Curcius and Sysems (ISCAS 2001), Sydney, NSW, pp , [2] Y. Chen, B. Yang, and Q. Meng, Small-ime scale nework raffic predicion based on flexible neural ree, Applied Sof Compuing, vol.12 no.1, pp , [3] C. Wang, X. Zhang, H. Yan, and L. Zheng, An Inerne Traffic Forecasing Model Adoping Radical Based on Funcion Neural Nework Opimized by Geneic Algorihm, Firs Inernaional Workshop on Knowledge Discovery and Daa Mining (WKDD), Adelaide, SA, pp , [4] G. Ruka, and G. 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