Jora of Theoretca ad Apped Iformato Techoogy 10 th Febrary 2013. Vo. 48 o.1 2005-2013 JATIT & LLS. A rght reered. ISS: 1992-8645 www.att.org E-ISS: 1817-3195 HIDDE HOPS AWARE LOAD BALACIG BASED O GREEDY APPROACH 1 BI-BI HUAG, 2 ROG-HEG LI, 3 HOG-XIA ZHAG, 4 HUA ZOU, 5 FAG-CHU YAG State Key Laboratory of etworkg ad Swtchg Techoogy, Beg Uerty of Pot ad Teecommcato, Beg 100876 Cha Ema: { hagbb 1, rh 2, zoha 4, fcyag 5 }@bpt.ed.c, zhaghx103@gma.com ABSTRACT Vrta etwork mappg oe of the ma probem etwork rtazato. At preet, rta etworkg mappg am at mma reorce compto at btrate etwork, bt gore the reorce demaded by the hdde hop, makg botteeck de to the reorce hortage at the hdde hop. Th paper am at the mtaeo oadg baace of the btrate ode ad the btrate k, mathematcay formate the rta etworkg mappg probem cotraed by hop, ad oe t by g greedy agorthm. Or expermet how that th agorthm emate reorce botteeck effcety, prode a more baaced btrate etwork for the reqet of the coeqeta rta etwork reqet, th mprog the cotrctg cce rate of rta etwork, the aaabty of etwork reorce ad the proft of the fratrctre proder. Keyword: Vrta etwork appg, Hdde Hop, Load Baacg, Greedy Agorthm. 1. ITRODUCTIO Vrtazato of etwork reorce ha bee detfed a a key techoogy for Ftre Iteret reearch [1] ad actey ed crret reearch tetbed [2][3]. By rtazg both ode ad k reorce of a btrate etwork, mtpe rta etwork topooge wth wdey aryg charactertc ca be created ad cohoted o the ame phyca hardware. It make cod proder to ga ecoomca reee from dertzed phyca reorce [4]. Howeer, appyg rtazato of etwork reorce ead to the probem of mappg rta reorce to phyca reorce, kow a rta etwork mappg. The o-caed rta etwork mappg ca be ewed a the agmet of the reorce from a rta etwork to the compoet of a phyca etwork. Extg reearche [5-12] cafy t a a cotrat optmzato probem wth the obecte of mmzg mappg cot. Bt they egect the reorce compto of a hdde hop o the path, whch ret botteeck becae of ffcet hdde hop reorce. Becae mappg a rta k to a path the Sbtrate oboy e reorce of the btrate k o the path. Howeer, there are ao phyca ode o the path that w be traered by the rta k. Thee are caed Hdde Hop here. The rta k w ao come reorce of a Hdde Hop o the path. Frthermore, eera rta k ca e the ame phyca k. The botteeck fece the performace of the whoe btrate etwork ad the reqet cce rate of the coeqeta rta etwork. I preo work [13], the mportat ad reatc cocept of hdde hop trodced rta etwork mappg. The reqred demad of the hdde hop hep to carry ot a more reatc rta etwork mappg, becae more rta etwork ca be mapped takg to accot the CPU demad of hdde hop. Howeer, th work codere the offe ero of the agorthm, ad the rta ode mappg ot codered. I [14], the obecte to baace the oad of btrate k. Th paper formate t to be a tcommodty-fow probem ad propoe a agorthm to oe the rta etwork mappg probem baed o optmzato theory. Bt th paper egect the CPU reorce that mt be aged to a termedate ode ad doe t foc o the ode oad baacg. I [15], baaced k oad ad baaced ode oad rta etwork cotrcto agorthm are ge, repectey. Baed o thee, two agorthm 582
Jora of Theoretca ad Apped Iformato Techoogy 10 th Febrary 2013. Vo. 48 o.1 2005-2013 JATIT & LLS. A rght reered. ISS: 1992-8645 www.att.org E-ISS: 1817-3195 Baaced Adapte rta etwork Cotrcto Agorthm (BACA) propoed. Bt, th paper, there are two e a foow: frty, the rta ode mappg the rta etwork reqet determed adace, whch mpfe the rta etwork mappg probem to the rta k mappg probem; Secody, th paper doe ot coder the CPU reorce that mt be aged to a termedate ode o the path that w be traered by the rta k. Addreg ch a probem oe cearo, we coder the CPU reorce that mt be aged to a termedate ode. To remoe effcety the reorce botteeck de to the ffcet hdde hop reorce, we am at the mtaeo oadg baace of the btrate ode ad the btrate k, formate the rta etworkg mappg probem cotraed by hop, ad propoe a Load baacg Greedy (LB-Greedy) agorthm. oreoer, we codct a merca comparo betwee or agorthm ad BACA. The mato expermet how that there are effcece abot LB-Greedy a foow: frt, after gettg rd of the reorce expee of a termedate ode, t abe to remoe effcety the reorce botteeck wth the goa of baaced k oad ad baaced ode oad. It w prode a more baaced btrate etwork for the coeqeta rta etwork reqet, thereby mprog the cotrctg cce rate of rta etwork, the aaabty of etwork reorce ad the proft of the fratrctre proder. Secod, mtg the hop cot o the path that w be traered by the rta k w e a e btrate reorce a pobe. So, t ca map a may rta etwork reqet a pobe the mted btrate etwork ad maxmze the proft of fratrctre proder. The ret of th paper orgazed a foow. Foowg that, ecto 2 formaze the rta etwork mappg probem ad preet the performace metrc. I Secto 3, we preet the LB-Greedy agorthm. I ecto 4 we decrbe the mato ettg ad preet mato ret that eaate the propoed agorthm, ad we cocde ad detfyg ftre reearch drecto ecto 5. 2. VIRTUAL ETWORK APPIG AD PERFORACE ETRICS 2.1 Vrta etwork appg ode For coeece, we abtract the rta etwork mappg probem to be the graph theory probem, ad e a weghted drected graph G (, E) to preet the btrate etwork. The whoe CPU reorce of the phyca ode deoted C, ad the aaabe reorce deoted by by ( ) c( ) ( e, ) E deoted by ( ( B e, )) aaabe badwdth deoted by ( (, )). The whoe badwdth of the btrate k, ad the b e. Smary, a weghted drected graph G (, E) preet the rta etwork whch a b-graph of the btrate etwork. The CPU reorce demad of rta ode deoted c, the badwdth demad of rta k by ( ) deoted by ( ( b e, )). appg a rta k to a path the Sbtrate oboy e reorce of the btrate k o the path, bt the rta k w ao come reorce of a Hdde Hop o the path. Here we deote the CPU reorce expee of a termedate ode by m (, ), whch make the rta etwork mappg more reaoabe. 2.1.1 Reorce compto mode of hdde hop The termedate ode o the btrate path eed to be cofgred ad correcty forward the packet pag the rta k, thereby they w hae a CPU expedtre. Ad how mch CPU reorce w be expeded deped o the badwdth demad ( ( b e, )) of rta k ad charactertc (ke freqecy of ode, etc) of the btrate ode. The, we w formate the CPU reorce demad of a termedate ode a foow: Sppoe Φ Gbp100 BW t, Γ GHz100 CPU t, the packet ze PS byte, CPU cyce whch eeded to forward ch ze packet ω Cyce. The CPU reorce expee of a termedate ode ca be cacated a foow: 9 ( e( )) Φ b, 10 m 8 100 PS (1) 9 Γ 10 ω Sbect to: 583
Jora of Theoretca ad Apped Iformato Techoogy 10 th Febrary 2013. Vo. 48 o.1 2005-2013 JATIT & LLS. A rght reered. ISS: 1992-8645 www.att.org E-ISS: 1817-3195 ( ) c m m > x c m 1 + e E δ ( ) (,, ) m(, ) ( ( )) ( ( )) (2) mt m t m f R p,,, b e, > 0 (3) ( ) ( ) δ,, m, > c( ) (4) (,, ) δ a bary arabe. It 0 f the btrate ode a termedate ode of the path that w be traered by the rta k ( e, ). It 0 eewhere. p( m, t,, ) preet the btrate path that w be traered by m t e,. Ad the reda the rta k ( ) badwdth of ( m, t,, ) ( ( m, t,, )) p deoted by R p. Cotra et (2) ad (3) cota the CPU capacty for btrate ode ad the badwdth capabty for btrate path p( m, t,, ). They are the m of the CPU ad the badwdth aged to each rta ode ad k, ad t w ot exceed btrate ode or k capacty. Cotra (4) cotra the CPU reorce of a termedate ode of a path that w be traered by a rta k. 2.1.2 Load formato for btrate ode ad btrate k Accordg to the tattc ad aay, t ca be draw that a more baaced btrate etwork ca mproe the cotrctg cce rate for the coeqeta rta etwork reqet, whch ca creae reorce tzato for btrate etwork. So, drg the mappg proce, t eed to are the baaced etwork oad amog btrate k, ad ao the baaced CPU oad amog btrate ode, whch ca mproe the cotrctg cce rate for the coeqeta rta etwork reqet ad make effcet e of the deryg reorce. The btrate ode act both the work ode performg er tak ad a hdde hop. A hdde hop w hae a CPU expedtre becae t ha to be cofgred ad t w hae to correcty forward the packet pag throgh th rta k. We deote the btrate ode CPU oad a foow: ( ) m m m 1 e, E ( ) ( ) x c( ) + δ,, m, ( ) c ( ) (5) The mea ae amog the btrate ode CPU oad deoted by : ag 1 ( ) ag (6) I the ame way, we deote the etwork oad amog btrate k a foow: ( ) L e ( ) mt m t f b e m t (, ) be (, ) e E ( ) (7) The mea ae for the etwork oad amog btrate k deoted by L ag : (8) L ag e E ( (, )) L e E The tadard deato for the CPU oad amog btrate ode deoted by : ( ( ) ) 2 ag 1 (9) The tadard deato for the etwork oad amog btrate k deoted by L : L (10) e E ( L( e(, )) Lag ) E To aod hot pot ad mproe the coeqeta rta etwork reqet acceptace rato, the obecte of the rta etwork mappg probem to mata baaced tre amog a btrate ode ad btrate k: mm α + βl (11) Where α ad β are ed to adt the weght of k ad ode oad baacg, repectey. 2.2 Vrta etwork appg ode To eaate the tre baacg performace, we may defe three performace metrc a foow: Defto 1: The rta etwork reqet acceptace rato of the btrate etwork ca be defed by 2 584
Jora of Theoretca ad Apped Iformato Techoogy 10 th Febrary 2013. Vo. 48 o.1 2005-2013 JATIT & LLS. A rght reered. ISS: 1992-8645 www.att.org E-ISS: 1817-3195 Rq cce _ rato Rq cce tota (12) Where Rq cce the mber of rta etwork reqet ccefy accepted by the btrate etwork Rq tota the tota mber of rta etwork reqet. Defto 2: The oadg baace degree amog btrate etwork ca be deoted by: D α + βl (13) Defto 3: The aerage of ode oad ad the aerage of k oad ca be deoted, repectey, a foow: 1 µ ode µ k ( ) e E (14) ( (, )) L e E (15) 3. PROPOSAL: LOAD BALACIG GREEDY ALGORITH Sce the rta etwork mappg wth the cotrat ha bee proed to be a P [5]. Ad fdg a optma rta etwork mappg for oadg baace by g mxed teger ear programmg (ILP) comptatoay tractabe. We propoe effcet hertc to oe the probem. LB-Greedy a greedy agorthm wth hertc for mappg the rta etwork reqet to the btrate etwork, whe tryg to baace the oad of the whoe btrate etwork after gettg rd of the reorce expee of a termedate ode. Ge beow the deta of LB-Greedy. Before decrbg the deta of LB-Greedy, the reorce demad of a rta ode ad a rta k w be frty defed. Defto 4: The reorce demad of a rta ode ca be defed a foow: H( ) c ( ) b ( ) L ( ) L Where, for a rta etwork reqet, ( ) the et of a the mapped otgog k of, b ( ) the badwdth demad of the rta k c the CPU demad of whch mapped. ( ). Accordg to the defto aboe, we defe the reorce demad of a rta k (, ) foow: e a ( (, )) ( ) ( ) + ( ) ( ) H e c b c b L ( ) L ( ) LB-Greedy a rta etwork mappg agorthm coordatg ode ad k. The trategy for rta k mappg ee the Agorthm 1: Agorthm 1 LB-Greedy 1: Parameter Itazato: taze the parameter ad ~. ad ~ are the et of mapped k ad mapped k G, repectey. 2: Whe ~ do 3: Chooe the rta k wth the arget H e, ~ reorce demad ( ( )) 4: If both the orce ode Sode ad the detato ode Eode of the rta k are mapped, they w be mapped a foow: 4.1: For Sode, fd the aocated btrate ode wth the arget aaabe reorce H( ) for t. 4.2: Fd a bet of caddate btrate ode for Eode. The caddate btrate ode mt meet wth the codto a foow: a) The btrate ode aocated b) The btrate ode wth the hop cot mt. c) The aaabe reorce of the btrate ode meet wth the cotrat (2). d) There at eat a path whoe badwdth meet wth (3). Ad the cotrat o each hdde hop o the path mt meet wth (4). 4.3: Ag the caddate ode wth mmm mappg cot (ee (11)) to Eode. 5: Ee f ether of Sode ad Eode mapped, the mapped ode w be mapped a foow: 5.1 Fd a bet of caddate btrate ode for the mapped ode wth the hop cot mt of the 585
Jora of Theoretca ad Apped Iformato Techoogy 10 th Febrary 2013. Vo. 48 o.1 2005-2013 JATIT & LLS. A rght reered. ISS: 1992-8645 www.att.org E-ISS: 1817-3195 mapped ode. Ad the caddate btrate ode mt be meet wth the codto a foow: a) The aaabe reorce of the aocated btrate ode meet wth (2). b) There at eat a path whoe badwdth meet wth (3). Ad the cotrat o each hdde hop o the path mt meet wth (4). 5.2 Ag the caddate ode wth mmm mappg cot (ee (11)) to the mapped ode. 6: Ee f both of them are mapped, there at eat a path whoe badwdth mt meet wth (3), ad the cotrat o each hdde hop o the path mt meet wth (4). 7: If t cceed, pt the mapped rta k to, ad remoe t from ~. Or chooe a rta k radomy, remoe th rta k ad the oe to reate to t from to ~. 8: If ~, pt ot the mappg cheme, or go back to 2. 4. PERFORACE EVALUATIO I th ecto, we w tdy the effcecy of or propoa. To achee th, we w frt decrbe the mato eromet, ad the preet or mato ret. The expermet foc prmary o the performace comparo of LB-Greedy wth the BACA [15]. 4.1 Smato Setp A tated [15], we et the btrate etwork topoogy wth 100 ode. The aerage btrate etwork coectty fxed at 0.02. The CPU ad badwdth reorce of the btrate ode ad k are rea mber formy dtrbted betwee 50 ad 100. We mode the arra of rta etwork reqet by a Poo Proce wth rate 0.05;ad each oe ha a expoetay dtrbted fetme wth a aerage of 400 tme t. Frthermore, we et the rta etwork ze accordg to a dcrete form dtrbto, g the ae ge [2, 10]. The aerage rta etwork coectty fxed at 0.5. The CPU ad badwdth demad of rta ode ad rta k are rea mber formy dtrbted betwee 0 ad 50. A tated [14], we et the hop cot wth [4,8]. The expee of Hdde hop o the path that w be traered by the rta k ee [16], we et a btrate etwork traportg packet ze PS 1500 byte, the btrate ode CPU capabty Γ 2.66 GHz, the btrate ode badwdth capacty Φ 1Gbp, the mber of cyce ed to proce a packet the ode ω 40000 Cyce. Accordg to thee parameter ettg, the CPU reorce that mt be aged to a termedate ode o the path that w be traered by the rta k 1.2 tme the badwdth. The rage of the weght coeffcet α ad β or obecte fcto (13) are both [0.2-0.8], ad they meet wth the cotrat α + β 1. 4.2 Eaato Ret Or eaato ret qatfy the effcecy of LB-Greedy we propoed. Seera performace metrc for eaato prpoe are ed, cdg the rta etwork reqet acceptace rato defed by Eqato (12), the oad baacg degree defed by Eqato (13), the aerage of ode oad defed by Eqato (14), the aerage of k oad defed by Eqato (15). We mmarze the key oberato from or mato a foow. Fg. 1 how a comparo of the acceptace rato of rta etwork reqet obtaed by the mappg tratege LB-Greedy ad BACA. We ca ee frt of a that both of the two agorthm prodce hgh acceptace rato whch achee to 100%. Or propoa cotety hgher tha BACA whe the mber of rta etwork reqet grow. A mportat factor that BACA prodce arger reda reorce fragmetato o the btrate etwork tha LB- Greedy, whch fece the acceptace rato of comg rta etwork reqet. Fg. 1 The Vrta etwork Reqet Acceptace Rato Comparo. Fg.2 eaate the oad baacg degree of LB- Greedy ad BACA whe the mber of rta etwork reqet creae. The e the ae of oad baacg degree, the more baaced the btrate etwork. So we ca oboy fd the LB-Greedy ca prodce a more baaced btrate etwork tha BACA. The reao that LB-Greedy cheme aocate the reorce to the rta etwork reqet 586
Jora of Theoretca ad Apped Iformato Techoogy 10 th Febrary 2013. Vo. 48 o.1 2005-2013 JATIT & LLS. A rght reered. ISS: 1992-8645 www.att.org E-ISS: 1817-3195 wth mmm mappg cot (ee (11)), whch cotrct a more baaced btrate etwork. Fg. 2 The Loadg Baace Degree Comparo. Fg. 3 The Aerage Of ode Load Comparo. ffcet hdde hop reorce, th paper am at the mtaeo oadg baace of the btrate ode ad the btrate k, formate the rta etworkg mappg probem cotraed by hop. ote that t P-hard ad comptatoay tractabe. I repoe, we propoed a LB-Greedy agorthm. Baed o extee mato, after gettg rd of the reorce expee of a termedate ode, t abe to remoe effcety the reorce botteeck wth the goa of baaced k oad ad baaced ode oad. It w prode a more baaced btrate etwork for the coeqeta rta etwork reqet, thereby mprog the cotrctg cce rate of rta etwork, the aaabty of etwork reorce ad the proft of the fratrctre proder. Frthermore, mtg the hop cot o the path that w be traered by the rta k w e a tte btrate reorce a pobe. So, t ca map a may rta etwork reqet a pobe the mted btrate etwork ad maxmze the proft of fratrctre proder. ACKOWLEDGETS Th work pported by the atoa atra Scece Fd Cha der Grat o. 2009CB320406, the atoa 863 Hgh-tech Proect of Cha der Grat o. 2011AA01A102, Fd for Create Reearch Grop of Cha (60821001) ad State Key Lab of etworkg ad Swtchg Techoogy. REFERECES Fg. 4 The Aerage Of Lk Load Comparo. Fg. 3 ad Fg. 4 how that LB-Greedy ca prodce e aerage of ode oad ad k oad tha BACA for the ame rta etwork reqet. To accept a rta etwork reqet, LB-Greedy wth hop cot mt come e btrate reorce tha BACA. Ad ao LB-Greedy cotrct a more baaced btrate etwork wth mmm mappg cot (ee (11)) tha BACA. A thee effort make LB-Greedy to prodce e ode oad ad k oad tha BACA btrate etwork. 5. COCLUSIOS I th paper, we aayze the e of extg reearche, ad coder the CPU reorce that mt be aged to a termedate ode. To remoe effcety the reorce botteeck de to the [1] A. Ber, A. Fcher, ad H. de eer, Vrtaerg m ftre teret, Iformatk- Spektrm, o. 33, o. 2, pp. 186 194, 2010. [2] J. Carapha ad J. Jméez, etwork rtazato: a ew from the bottom, Proceedg of the 1t AC workhop o Vrtazed fratrctre ytem ad archtectre, 2009, pp. 73 80. [3] D. Schwerde, D. Güther, R. Hee, B. Rether, ad P. üer, Germa-ab expermeta facty, Ftre Iteret-FIS 2010, pp. 1 10, 2010. [4] A. Lek,. Kem, J. m, S. Ta, ad T. Sadhom, What de the Cod? A archtectra map of the Cod adcape, Proceedg of the 2009 ICSE Workhop o Software Egeerg Chaege of Cod Comptg, 2009, pp. 23 31. 587
Jora of Theoretca ad Apped Iformato Techoogy 10 th Febrary 2013. Vo. 48 o.1 2005-2013 JATIT & LLS. A rght reered. ISS: 1992-8645 www.att.org E-ISS: 1817-3195 [5]... K. Chowdhry,. R. Rahma, ad R. Botaba, Vrta etwork embeddg wth coordated ode ad k mappg, IFOCO 2009, IEEE, 2009, pp. 783 791. [6]. Zhag, C. W,. Jag, ad Q. Yag, appg mtcat erce-oreted rta etwork wth deay ad deay arato cotrat, GLOBECO 2010, 2010 IEEE Goba Teecommcato Coferece, 2010, pp. 1 5. [7] S. ZHAG ad X. QIU, A oe rta etwork mappg agorthm for cot mmzg, Cyber Jora: Jora of Seected Area Teecommcato (JSAT), 2011. [8] H. Y, C. Qao, V. Aad, X. L, H. D, ad G. S, Srabe Vrta Ifratrctre appg a Federated Comptg ad etworkg Sytem der Sge Regoa fare, GLOBECO 2010, 2010 IEEE Goba Teecommcato Coferece, 2010, pp. 1 6. [9] G. S, H. Y, L. L, V. Aad, H. D, ad X. Gao, Effcet agorthm for rabe rta etwork embeddg, Aa Commcato ad Photoc Coferece ad Exhbto, 2010. [10] I. Faar,. Ataad, G. Poe, ad H. Zmmerma, VE-AC: Vrta etwork embeddg agorthm baed o at cooy metahertc, Commcato (ICC), 2011 IEEE Iteratoa Coferece o, 2011, pp. 1 6. [11] Y. Zh ad. Ammar, Agorthm for agg btrate etwork reorce to rta etwork compoet, Proc. IEEE IFOCO, 2006, o. 2. [12]. Y, Y. Y, J. Rexford, ad. Chag, Rethkg rta etwork embeddg: btrate pport for path pttg ad mgrato, AC SIGCO Compter Commcato Reew, o. 38, o. 2, pp. 17 29, 2008. [13] J. F. Botero, X. Heebach, A. Fcher, ad H. De eer, Optma mappg of rta etwork wth hdde hop, Teecommcato Sytem, pp. 1 10, 2011. [14] JIAG g, WAG Bao-, WU Chmg,KOG Xag-qg, I Xao ad ZHAG. Reearch o etwork Vrtazato ad Vrta etwork appg Agorthm[J]. Acta Eectroca Sca, 2011, 39(6): 1315-1320. [15] Q g, Wag Bao-, Wag B-qag ad Zhag Dog. Reearch o Baaced Cotrcto Agorthm of Vrta etwork[j]. Joa of Eectroc & Iformato Techoogy, 2011, 33(6): 1301-1306. [16] A. Fcher, J. F. Botero Vega,. De, D. Schoer, X. Heebach Serra, ad H. De eer, ALEVI-A framework to deeop, compare, ad aayze rta etwork embeddg agorthm, 2011. 588