This full ex paper was peer reviewed a he direcio of IEEE Couicaios Sociey subjec aer expers for publicaio i he IEEE Globeco proceedigs. A New Hybrid Nework Traffic Predicio Mehod Li Xiag, Xiao-Hu Ge, Chuag Liu, Lei Shu, Cheg-Xiag Wag 3 Dep. Elecroics & Iforaio Egieerig, Huazhog Uiversiy of Sciece & Techology, Wuha, P.R.Chia. Nishio Lab., Dep. Muliedia Egieerig, Graduae School of Iforaio Sciece & Techology, Osaka Uiversiy, Japa. 3 JRI-SIP, School of Egieerig & Physical Scieces, Herio-Wa Uiversiy, Ediburgh EH4 4AS, U.K. xhge@ail.hus.edu.c, lei.shu@is.osaka-u.ac.jp, 3 cheg-xiag.wag@hw.ac.uk Absrac How o predic he self-siilar ework raffic wih high bursiess is a grea challege for ework aagee. The covariaio orhogoal predicio could effecively capure he bursiess i he ework raffic, ad he arificial eural ework predicio could adap he ework raffic chage by self-learig. To iprove he predicio accuracy, we propose a ew hybrid ework raffic predicio ehod based o he cobiaio of he covariaio orhogoal predicio ad he arificial eural ework predicio. Through epirical sudy, he accuracy of he ew predicio ehod ca be effecively iproved see fro he ea ad he predicio error. Idex Ters Traffic Predicio; Covariaio Orhogoal (CO); Arificial Neural Neworks (ANNs); Self-siilariy; Bursiess; I. INTRODUCTION A uber of sudies have deosraed ha ework raffic is self-siilar i aure, showig high bursiess i a wide rage of ie scales, ad obeys i he heavy-ail disribuio []. Siilarly, Errors ecouered i wireless couicaio syses are bursy i aure ad he burs error saisics have bee well sudied i [],[3],[4]. The alpha-sable odel ca capure he self-siilariy ad heavy-ailess of ework raffic siulaeously [5], ad has played a icreasigly ipora role i raffic predicio. However, he ifiie variace of self-siilar raffic process, kow as he high variabiliy, will devaluae he classical leas ea square error crierio for alpha-sable odel based raffic predicors. To cope wih his challege, he iiu dispersio (MD) crierio ad he covariaio orhogoal (CO) crierio [6],[7],[8],[9],[],[] have bee applied isead. These predicio schees aage o explore he correlaios bewee alpha-sable raffic processes wih he dispersio or covariaio. The, he possible relaioship bewee he fuure raffic process ad he pas raffic process ca be developed usig esiaio echiques, which ca be applied for forecasig fuure ework raffic. The CO liear predicio [8] ca be effecive i predicig he bursy chages of he selfsiilar ework raffic. However, he ea of he prediced raffic uder his schee ofe goes below he acual level, resulig he liied predicio accuracy. Differe fro he alpha-sable ehod, he arificial eural eworks (ANNs) ca self-lear he raffic characerisics by followig a se of learig rules o adap is weigh coefficies ad ake predicios wihou ay prior kowledge of he characerisics of ework raffic. Differe fors of ANNs have bee applied for real raffic predicio. However, here is o sigle ANN for ha ca capure all he raffic characerisics []. I his paper, our work is o cobie he CO liear predicio schee wih he ANN approach so as o raise he predicio accuracy of he CO approach. As eioed above, he CO liear predicio ca capure he bursy chages of ework raffic while uder-predic he fuure raffic values; ad he ANN approaches are capable of predicig self-siilar raffic wih high precisio while eed cobiaio wih oher ehods. Cosiderig he pis ad falls of boh approaches, we propose a ew hybrid ework raffic predicio ehod o iprove he CO predicio ehod ad o raise he predicio accuracy. The ai coribuios of his paper are as follows: ) A siple hybrid predicio schee based o he CO crierio ad he ANNs is proposed for predicig selfsiilar ework raffic. ) Perforace of he proposed ehod is evaluaed hrough epirical sudy usig real raffic races, i ers of he self-siilar ad bursy characerisics of he prediced raffic ad he predicio error. 3) The effecs of boh pars i he hybrid predicio are aalyzed, icludig heir liiaios i predicig bursy ework raffic. The res of his paper is orgaized as follows: Secio II iroduces seleced work o raffic predicio; Secio III describes he syse odel ad priciples of each predicio par; Secio IV epirically sudies he predicio perforaces wih real raffic races colleced i wireless local area eworks; fially, Secio V cocludes he paper. II. RELATED WORK The research o alpha-sable odel based predicio has aily focused o he liear predicio for [6],[7],[8],[9],[],[]. However, he copuaio of he predicio coefficies is o sraighforward sice he secod order oes of alpha-sable process do o exis. Based o he MD crierio, Gallardo worked ou a ovel ehod o copue he coefficies [6] ad usually provide a robus perforace suggesed i [9]. However, his ehod resuls i a biased forecas wih o-uique closed-for predicio resuls. Therefore he iiizaio of dispersio is o opial []. To solve his proble, a opiizig approach usig seepes decede ehod has bee proposed o search he acual MD 978--444-5638-3//$6. IEEE
This full ex paper was peer reviewed a he direcio of IEEE Couicaios Sociey subjec aer expers for publicaio i he IEEE Globeco proceedigs. poi a a faser speed [] ad applied i dyaical resource allocaios []. Aoher work [7] cosiders he copoud predicio of wireless ework raffic usig he MD crierio. Workig fro a ew direcio, Ge proposed he ubiased CO liear predicio ehod i [8]. However, as previously eioed, he predicio accuracy of his ehod eeds o be iproved o adap he busy raffic. This is he ipora oivaio of our work i his paper. The ANN ehod predics ework raffic by perforig o-liear appigs bewee he fuure raffic values ad he pas ad prese raffic values. However, o sigle ANN for ca capure all he characerisics of ework raffic due o is coplexiy. Curre research has bee devoed o develop ore powerful ANN fors, such as he ovel BP eworks [3], or o cobie differe fors of ANNs for self-siilar raffic predicio [4]. I his paper, he CO crierio ad he o-liear ANN predicio approach are cobied o iprove he CO liear predicio ehod. The CO predicio ca capure he bursy chages while he ANN ca gai high predicio accuracy. The hybrid desig ais o raise he predicio accuracy by akig he rade-offs bewee hese wo ehods. III. SYSTEM MODEL Nework raffic predicio is he process of appig pas (ad prese) raffic values o fuure raffic values hrough liear or o-liear appig fucios as show i Eq.(), ˆX( + k) =F[X(),X( ),..., X( p + )] () where he fucio F aps he pas p raffic values X(),X( ),..., X( p +) io he k-sep-ahead raffic value ˆX( + k).the desig of raffic predicio schee aily cocers i cosrucig or devisig he proper appig fucios. The siple serial cobiaio of he CO liear predicio ad he ANN predicio ehods is cosidered here ad he syse odel is show i Fig.. The ipu of he CO par is he oralized ie series X i of ework raffic; afer he CO liear predicio, is oupu is he ie series Xc, which is he he ipu for he ANN predicio; ad he fial predicio resul is he oupu ie series Xo. The aheaical odel for he syse ca be siply represeed as: Xc =F (X i ) () Xo =F (Xc) =F (F (X i )) (3) where F ad F are predicio fucios, represeig he CO predicio ad he ANN predicio respecively. The priciples of boh predicio pars are covered i he followig pars. X i X c X o k M N L Fig.. Syse Model. A. The CO Liear Predicio The covariace fucio is a powerful ool i he sudy of Gaussia rado elees, bu i is o defied i he alpha-sable processes whe α <. Uder his codiio, he covariaio is desiged o replace he covariace ad is defiiio is as follows: Le X ad Y be sable rado vecors wih <α< ad specral easure Γ, ad (μ, ν) deoes he polar coordiaes of he joi process (X, Y ) o he R ui circle S, he covariaio of X o Y is deoed as: [X, Y ] α = μν <α > Γ(dμ, dν) (4) S Whe [X, Y ] α =, he vecor X is covariaio orhogoal o he vecor Y. Suppose X,X,..., X are he saple values of he ipu raffic series X i, he coefficie se is a,a,..., a are he. Referece [8] works ou he k-sep-ahead liear predicio schee: F : ˆX+k = a ix + i (5) i= where ˆX +k is he prediced values, ad he coefficies are calculaed accordig o Eq. (6). This approach is oed as a (,, k) CO liear predicor, eaig a k-sep-ahead liear predicio wih coefficies ad saple values. a a = a X X X+ X = = + + + X X X X + + X X + + + X X + + k+ k+ k+ k k + k (6) B. The ANN Predicio A (M,N,L) 3-layer coo back-propagaio (BP) eural eworks are chose for raffic predicio, where M, N, L represes he uber of euros a each layer. Differe fro he CO approach, he predicio fucio F of he ANN approach is o explicily copued, bu self-leared. Specifically, each layer follows he specific learig rules ad adjuss he weighs uil he ea square error bewee he expeced oupu ad he acual oupu becoes lower ha a pre-deeried value. The, he BP eural ework ca be used for raffic predicio. I he syse odel, fracioal saples of he ie series Xc are used for raiig he BP eural ework. IV. THE PROPOSED HYBRID SCHEME Based o he syse odel, he deailed hybrid predicio process is desiged as follows, divided io wo periods: Predicio seup: i his period, he syse is iiialized ad he he BP eural eworks are raied o fi he real raffic uil he pre-deeried accuracy is achieved. 978--444-5638-3//$6. IEEE
This full ex paper was peer reviewed a he direcio of IEEE Couicaios Sociey subjec aer expers for publicaio i he IEEE Globeco proceedigs. Sep : Decide he archiecure ad paraeers for he BP eural eworks, such as he riple (M,N,L) represeig he uber of odes a each layer ad he ea square error bewee he expeced ad he acual oupu,i.e, he predefied predicio accuracy. Besides, decide he paraeer riple (,, k) for he CO predicio par, where is he uber of he predicio coefficies, is he or of he saple space {X,X,..., X } ad k is he predicio sep. Sep : Iiialize he weighs radoly. Sep 3: Trai he BP eural ework ad sop raiig uil he pre-defied accuracy is achieved. Predicio: i his period, he well-raied BP eural eworks ca be used for raffic predicio. This process ca be furher divided io wo sages-he CO predicio sage ad he ANN predicio sage, wih each coaiig several seps. Sep 4: The firs saples are picked up fro he ipu raffic series X i o calculae he predicio coefficies accordig o Equ. (6). Sep 5: The k-sep-ahead predicio resul are calculaed uder he CO crierio by Equ. (5). Sep 6: The ( +) saples are picked up for aoher predicio. Go o o Sep 5 ad his process coiues. This is he firs sage of he hybrid predicio ad he predicio resuls are he ie series Xc. Sep 7: The M saples of he ie series Xc are ipu o he BP eural eworks for he secod sage predicio. The shif o aoher M saples ad coiue he ANN predicio. The fial predicio resuls are he ie series Xo. By cobiig hese wo ehods, our proposed schee ais o raise he predicio abiliy. Specifically, he CO predicio par is used as a coarse predicio ad ais o capure he variaio red of he self-siilar raffic; while he NN par is used as a fie predicio so as o raise he predicio accuracy. The predicio accuracy is evaluaed i he followig secio. V. SIMULATION EXPERIMENTATION I his par, he predicio perforace of he hybrid schee is evaluaed by wo raffic races ad copared wih he CO liear predicio schee. The races are colleced fro a real wireless local area ework (WLAN) deployed durig he 6d IETF Pleary Sessio [5] o March, 5. The previous sudy has revealed he self-siilariy of he colleced raffic [6]. Boh races, wih differe degrees of flucuaios or bursiess, are aggregaed a.s ie scale ad he oralized o he ierval [,]. Durig he siulaio, he specific paraeer seig for he (,,k) CO liear predicio par is (5,,); ad for he ANN predicio par, a (,4,) BP eural ework is ipleeed wih pre-defied accuracy 4. Figure ad 3 give he oesep-ahead predicio resuls of he cobied approach for each race, where he prediced raffic follows he acual raffic visually. The he prediced ie series are furher quaiively aalyzed i he followig wo subsecios. Nework Traffic Nework Traffic Nework Traffic Nework Traffic.8.6 Acual Traffic.4 Arrival Tie(Ui ie=.s)..8.6.4 Prediced Traffic. Arrival Tie(Ui ie=.s).8.6 Fig.. Oe-sep-ahead Predicio Resuls for Daa I..4 Acual Traffic. Arrival Tie(Ui ie=.s)..8.4 Prediced Traffic.4 Arrival Tie(Ui ie=.s) Fig. 3. Oe-sep-ahead Predicio Resuls for Daa II. A. Characerisics Aalysis of Prediced Traffic The self-siilariy ad he bursiess of prediced raffic are evaluaed hrough he Hurs paraeer (H) ad he heavyail idex (α). The Hurs paraeer is he uique easure of he self-siilariy degree ad H (.5, ); For a selfsiilar process, he larger Hurs value iplies he higher degree of self-siilariy ha he process exhibis. Besides, he characerisics of bursiess ca be refleced by he heavy-ail idex ad α (, ). Asα decreases, he degree of bursiess icreases. Furherore, he ea raffic level is sudied due o he lack of secod order oes for self-siilar processes. Table I ad II show he resuls of he above aalyses, fro which he followig resuls could be go: () The CO liear predicio par ca effecively capure he self-siilar ad bursy characerisics of ework raffic. Fro Table I ad II, he Hurs paraeer ad he heavy-ail idex of he prediced raffic i he firs sage (he CO predicio sage) are icreased oderaely (less ha %). Thus, he characerisics of he acual ework raffic are aiaied i boh ess hough. However, he characerisics of he fial prediced raffic (uder he hybrid predicio) for boh ess are deeper affeced ha i he CO predicio. For he firs race, H ad α boh decrease ore ha %, iplyig ha he selfsiilariy ad he bursiess are seeigly chaged. Ad for 978--444-5638-3//$6. IEEE
This full ex paper was peer reviewed a he direcio of IEEE Couicaios Sociey subjec aer expers for publicaio i he IEEE Globeco proceedigs. TABLE I COMPARISONS OF TRAFFIC CHARACTERISTICS FOR DATA I Origial CO Cobied Hurs.733.87.54 alpha.873.88.54 ea.95.78.94 TABLE II COMPARISONS OF TRAFFIC CHARACTERISTICS FOR DATA II Origial CO Cobied Hurs.86.88.83 alpha.53.79.7 ea.64.53.633 Cuulaive Error 3 4 5 6 CO Liear Predicio Cobied Predicio 7 The Nuber of Prediced Daa Fig. 4. Cuulaive Error for Daa I. he secod race, H decreases while α icreases, boh wih a larger aou ha i he CO predicio. By coparisos, his is due o he effec of he ANN predicio par. Thus he ANN adaped here shows he liiaio of fiig he self-siilar ad bursy dyaics of ework raffic i boh ess. () The cobied predicio could aiai he ea level of he acual ework raffic. The ea of he prediced raffic decreased 4% ad 8% for each raffic race respecively, which leads a seeig degradaio i he predicio accuracy uder he CO predicio. However, he ea of he prediced raffic varies slighly (approxiae %) uder he cobied predicio. This is gaied a he cos of he icreased syse coplexiy uder he cobied predicio. Through coparisos, he ANN predicio par accous for he aiaiig of he ea raffic level. I addiio, his is aily due o he self-learig capabiliy of ANNs. Fro he above aalyses, he CO predicio par acs as a coarse predicio ad could capure he dyaical behaviors of self-siilar ad bursy ework raffic; ad he ANN predicio par could aiai he ea raffic level ad ac as a fie predicio; however, he ANNs could affec he self-siilariy ad bursiess of he prediced raffic. B. Predicio Error Aalysis To furher copare he predicio accuracy, he Cuulaive Error (CE) ad he Absolue Cuulaive Error (ACE) are used as perforace erics for predicio error aalysis. The wo erics are defied as follows: CE(N) = N = ACE(N) = N = [y( + k) x( + k)] (7) y( + k) x( + k) (8) where y( + k) is he prediced raffic value, x( + k) is he acual raffic value, ad N is he uber of prediced daa. Figures 4 ad 5 illusrae he CE versus he uber of prediced daa N for boh he CO ad he cobied approaches. Fro hese wo figures, he CEs of boh races decrease i a approxiaely liear way uder he CO liear predicio while reai basically a zero for hose of he cobied approach, idepede of he icrease of N, for boh races. Cuulaive Error 3 4 5 CO Liear Predicor Cobied Predicio 6 The Nuber of Prediced Daa Fig. 5. Cuulaive Error for Daa II. Besides, Figures 6 ad 7 illusrae he ACE versus he uber of prediced daa N for boh he CO ad he cobied approaches. For he firs race, he ACE of he cobied approach grows slower ha ha of he CO approach; while he case goes opposie for he secod race. Cosiderig ha he secod race flucuaes ore widely ha he firs race, he capabiliy of ANNs o fi his raffic race is furher liied. Thus, he ACE of he prediced raffic uder he cobied approach grows faser ha uder he CO predicio for he secod race. Absolue Cuulaive Error 7 6 5 4 3 CO Liear Predicio Cobied Predicio The Nuber of Prediced Daa Fig. 6. Absolue Cuulaive Error for Daa I. Based o he above aalysis, whe he real raffic flucuaes i a sall rage, or becoes less bursy, he cobied 978--444-5638-3//$6. IEEE
This full ex paper was peer reviewed a he direcio of IEEE Couicaios Sociey subjec aer expers for publicaio i he IEEE Globeco proceedigs. Absolue Cuulaive Error 9 8 7 6 5 4 3 CO Liear Predicio Cobied Predicio The Nuber of Prediced Daa Fig. 7. Absolue Cuulaive Error for Daa II. predicio could aiai he ea level of ework raffic ad he predicio error ca be reduced see fro he CEs ad he ACEs. Thus, he predicio accuracy ca be effecively raised copared wih he CO liear predicio. Cosiderig he effecs of boh predicio pars, he CO predicio ca capure he characerisics of self-siilar raffic i he firs sage, revealed fro he chages of self-siilariy ad bursiess paraeers; besides, he BP eural eworks ca fiely adjus he predicio accuracy i he secod sage, paricularly aiaiig he ea level wih reduced predicio errors. This is aily due o he self-learig capabiliy of ANNs i he cobied approach. However, he iprovee of he predicio accuracy is liied whe he real raffic flucuaes widely, or becoes bursy eough. I par A, he ANNs are foud o affec he self-siilariy ad bursiess of he prediced raffic, showig liied capabiliy i fiig real raffic. This effec is seeigly see whe he real raffic flucuaes widely eough. Moreover, i resuls he faser icrease i he ACE of he prediced raffic for he secod race. Thus he ANNs affec he furher iprovee of predicio accuracy. VI. CONCLUSION A ew hybrid predicio ehod cobiig he CO crierio ad he ANNs is proposed o predic he bursy ad self-siilar ework raffic. Through he copariso sudy usig he real colleced raffic races, he cobied predicio ouperfors he CO ehod i he predicio accuracy, see fro he ea value level of ework raffic ad he predicio error. Meawhile, he ANNs ca affec he self-siilariy ad bursiess of he prediced ework raffic. Ad hus he iprovee i predicio accuracy becoes liied especially whe he real raffic flucuaes widely eough. I he fuure work, we would furher ivesigae he effec of ANNs o characerisics of he prediced ework raffic ad he opiize he cobied predicio schee. Besides, oher fors of cobiaio will be explored ad evaluaed, e.g., he igh couplig of he CO crierio i he desig of he ANNs, like he cobiaio of he CO crierio wih he self-learig process. ACKNOWLEDGMENT The auhors ackowledge he suppor fro he Naioal Naural Sciece Foudaio of Chia (NSFC), corac/gra uber: 6877; Naioal 863 High Techology Progra of Chia, corac/gra uber: 9AAZ39; The Miisry of Sciece ad Techology (MOST), Ieraioal Sciece ad Techology Collaboraio Progra, corac/gra uber: 93; ad he RCUK for he UK-Chia Sciece Bridges Projec: R&D o (B)4G Wireless Mobile Couicaios. L. Shu s research i his paper was suppored by Gra-i-Aid for Scieific Research (S)() of he Miisry of Educaio, Culure, Spors, Sciece ad Techology, Japa. C.-X. Wag also ackowledges he suppor fro he Scoish Fudig Coucil for he Joi Research Isiue i Sigal ad Iage Processig wih he Uiversiy of Ediburgh, as par of he Ediburgh Research Parership i Egieerig ad Maheaics (EPRe). REFERENCES [] W. Lelad, M. Taqqu, W. Williger, ad D. 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