Cyber Journals: Multidisciplinary Journals in Science and Technology, Journal of Selected Areas in Telecommunications (JSAT), January Edition, 2011

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1 Cyber Jourals: Multdscplary Jourals cece ad Techology, Joural of elected Areas Telecommucatos (JAT), Jauary dto, 2011 A ovel rtual etwork Mappg Algorthm for Cost Mmzg ZHAG hu-l, QIU Xue-sog tate Key Laboratory of etworkg ad wtchg Techology Beg Uversty of Posts ad Telecommucatos Beg , Cha, -mal: zhagshul@bupteduc Abstract-Resources assged to vrtual etwork are ot optmal resources, whch are caused by some scarce resources To solve ths problem, ths paper proposes a ovel vrtual etwork mappg algorthm that ca realze mappg cost mmzg, called CMMA, based o two characterstcs of etwork vrtualzato evromet, that s vrtual etwork has lfecycle ad substrate etwork resources are creased or decreased perodcally CMM cludes vrtual etwork mappg sub-algorthm (MsA) that ca label vrtual odes ad vrtual lks whch are ot allocated optmal resources, ad heurstc mgrato sub-algorthm (HMsA) that ca realze saved substrate resources maxmzato ad mgrato cost mmzato mulato results show that CMMA ca save aroud 15% substrate etwork resources, ad HMsA ca use ltter tme to save the most substrate etwork resources tha greedy mgrato algorthm (GMA) ad radom mgrato algorthm (RMA) Keywords-mgrato, etwork vrtualzato, vrtual etwork mappg, vrtual etwork resource allocato 1 ITRODUCTIO etwork vrtualzato s a mportat method to solve rgd ssue of the curret etwork [1,2] Uder the etwork vrtualzato evromet, etwork Provder (P) s dved to ubstrate etwork Provder (P) ad rtual etwork Provder (P) [2,3] The duty of P s to buld the ubstrate etwork () The duty of P s to create rtual etwork () through ret resources ad provde professoal servces for users eeds to share the substrate ode resources ad substrate lk resources to acheve the commucato uder the etwork vrtualzato evromet o, vrtual etwork resource allocato s oe of the key problems ad the latest research achevemets clude [4-8] (I ths paper, mappg, allocato ad assgmet are used alterately) But, substrate resource utlzato rate s stll ot hgh The ma reaso s that some vrtual etwork resources do ot obta optmal substrate etwork resources, because parts of substrate etwork resources are scarce Fortuately, etwork vrtualzato evromet has two mportat characterstcs: (1) rtual etwork wll release occupacy resources whe ts lfecycle s ed; (2) P creases or decreases substrate etwork resources perodcally accordg to the resource utlzato rate of substrate etwork Based o these two characterstcs, ths paper presets a ovel vrtual etwork mappg algorthm that ca realze mappg cost mmzg, called CMMA CMM cludes vrtual etwork mappg sub-algorthm (MsA) that ca label vrtual odes ad vrtual lks whch do ot obta optmal resources, ad heurstc mgrato sub-algorthm (HMsA) that ca realze saved resources maxmzato ad mgrato cost mmzato mulato results show that CMMA ca save aroud 15% resources of substrate odes ad substrate lks tha exstg vrtual etwork mappg algorthm, ad HMsA ca use ltter tme to save the most substrate etwork resources tha greedy mgrato algorthm (GMA) ad radom mgrato algorthm (RMA) 2 RLATD WORK About vrtual etwork resource allocato, there have bee may researches ad the typcal latest researches clude [4-8] The path splttg ad mgrato methods were used to mprove the success rate of vrtual etwork mappg [4] I order to coordate two phases betwee the ode mappg ad lk mappg, [5] formulated the embeddg problem as a mxed teger program through augmetato ad smulato expermets show that the proposed algorthms crease the acceptace rato ad the reveue whle decreasg the cost tha algorthm [4] [6] proposed dstrbuted autoomc resources maagemet framework ad mgrated 1

2 vrtual ode betwee adacet substrate ode to deduce substrate lk pressure ad save substrate lk resource [7] addressed the problem of optmally redeployg the exstg vrtual etwork frastructure as the substrate etwork resources evolves ad focused o mmzg the upgradg cost, wth satsfyg ode resource costrat ad path delay costrat [8] put forward a recofgurato method ad could realze etwork resources load equlbrum ad mprove the etwork beefts To sum up, the curret researches do ot cosder the problem that vrtual etwork resources are ot assged optmal resources, because parts of substrate resources are scarce Falg to desg optmzato algorthm to make vrtual odes ad vrtual lks obta the optmal substrate etwork resources whe substrate etwork evromet chages I vew of the above questo, ths paper desgs a ovel vrtual etwork mappg algorthm to optmze vrtual etwork resources ad mplemet saved resources maxmzato ad mgrato cost mmzato 3 PROBLM FORMULATIO 31 ubstrate etwork () over tme I order to cotue to provde resources for the ew request, P wll crease substrate etwork resources perodcally O the cotrary, f oe substrate etwork resource utlzato rate s too low, ths s closed Fg1 vrtual etwork resource allocato 32 rtual etwork Request (R) mlar to the, a weghted udrected graph G = (,, A, A ) s used to deote R We L express the R of vrtual odes ad vrtual lks terms of the attrbutes of the odes ad lks of the substrate etwork A weghted udrected graph G = (,, A, A ) s L ach attrbute a A of vrtual ode has a used to deote, where s the set of substrate odes assocated o-egatve value D a expressg how far a ad s the set of the substrate lks ach substrate ode has attrbute a capacty weght value c( ) A, whch clude CPU ad geographc locato loc( ) ach substrate lk e = lk(, ) has attrbute a L L A, whch clude badwdth capacty weght value b( e ) The substrate path s deoted by P, whch s the set of substrate lk For example, the path of source ode s to the destato ode t s expressed by P ( s, t ) I the rght of Fgure 1, there s a substrate etwork, whch the umbers over the lks represet avalable badwdths ad the umbers rectagles represet avalable CPU resources ome substrate etwork resources become scarce after P assgs substrate etwork resources to vrtual etwork request vrtual ode ca be placed from the locato specfed by loc( ) For example, there are two R the left of Fgure 1 As the descrpto [2, 5], each has a lfecycle I ths paper, the arrvals of R are modeled by a Posso process, ad the durato of the requests follows a expoetal dstrbuto 33 rtual etwork Resource Allocato (RA) Whe a R arrves, must to decde whether to allocate resources to R or ot The allocato of R to ca be decomposed to two maor compoets, whch are ode allocato ad lk allocato 1) ode allocato ach vrtual ode from the same R must be allocated to a dfferet substrate ode by a mappg F : from vrtual ode to substrate ode, whch s defed as: 2

3 F ( ), F ( ) = F ( ) (1) ubect to: f =,, c( ) c( F ( )) F ( )=, k ds( loc( ), loc( )) d, d k D (1a) (1b) Where ds(, ) measures the dstace betwee the locatos of two odes ad Costrat codto (1a) deotes that the CUP capacty of substrate odes allocated to vrtual ode must bgger tha CUP capacty of vrtual ode request Costrat codto (1b) deotes that the dstace betwee substrate ode ad vrtual ode must be the scope of vrtual ode request I Fgure 1, the frst R has the ode mappg {A1 A, B1 B, C1 } The secod R has the ode mappg {A2 C, B2 F, C2 G, D2 H} 2) Lk allocato Accordg to the locato of substrate odes whch hosted the source ode ad destato ode of vrtual lk, each vrtual lk s mappg to a substrate path It s defed as F : P from vrtual lks to substrate path for all e = lk(, ) ubect to: (2) F (, ) P ( F ( ), F ( )) b( P) b( e ), P F ( e ) (2a) Costrat codto (2a) deotes that the badwdth capacty of substrate path must bgger tha the badwdth capacty requested by vrtual etwork I Fgure 1, the frst R has bee assged the lk mappg {(A1, B1) {(A,B) }, (B1, C1) {(B,)}, (A1, C1) {(A,C), (C,D), (D,)} }, ad the secod R has the lk mappg{(a2, B2) {(C,D), (D,), (,F)}, (A2, C2) {(C,G)}, (C2, D2) {(G,H)}, (D2, B2) {(H,F)}} 3) Mappg reveue ubstrate etwork ca obta reveue through assgmet resource to R mlar to the prevous work [4,5], whe mappg a R G ( ) mappg reveue as: t at tme t, ths paper defes the (3) R ( G ( t )) = b ( e ) + ρ c ( ) map e where coeffcet ρ s used to tradeoff the reveue betwee badwdth ad CPU 4) Mappg cost Whe substrate etwork hosted a R, some substrate etwork resources were cosumed by vrtual odes ad vrtual lks Whe mappg a R G ( ) defes the cost of mappg a R as: e e e t at tme t, ths paper C ( G ( t e )) = b + c ( ) map where b e e cosumed by e 5) Mappg obectve deote the sum of substrate lk (4) e badwdth The mappg obectve s that more Rs ca be accepted by over tme T Ths paper defes the mappg obectve as: (5) T T T 0 map t= T t= 0 map max(lm R ( G ( t))/ T lm C ( G ( t))/ T) 34 rtual etwork Mgrato (M) I order to make the vrtual resources whch do ot obta optmal resources get the optmal resources, M should clude ode mgrato ad lk mgrato 1) ode mgrato The ode mgrato may happe whe the locato of vrtual ode s ot satsfed or the lk dstace betwee substrate ode hosted vrtual ode ad substrate ode hosted adacet vrtual ode s ot the shortest lk Ths paper uses M : to deote that vrtual ode mgrates from to, that s: M (( ) ( )), F ( ) =, F ( ) = (6) ubect to: c( ) c( ), c( ) c( ) (6a) ds ( loc ( ), loc ( )) d ds ( loc ( ), loc ( )) d + λ, 3

4 d D (6b) M ( P P ) (8) old ew Or log ( P (, F ( ))) log ( P (, F ( ))) (6c) Costrat codto (6a) deotes CPU capacty of substrate ode, whether mgrato before or mgrato after, must meet the CPU capacty costrat of vrtual ode request Costrat codto (6b) deotes the locato of substrate ode after mgrato ca meet the locato costrat of vrtual ode request Costrat codto (6c) deotes there are badwdth resources whch ca be saved by ode mgrato s used to deote the set of vrtual odes adacet to vrtual ode λ s used to deote locato tolerato value of LA (ervce Lever Agreemet),whch s set 10 ths paper[9] log( P (, )) represets the sum of badwdth betwee ad used by vrtual lk, whch s defed secto of lk mgrato The obectve of ode mgrato s: m ( (, ( )) log P F (7) I Fgure 1, substrate ode C ad D also meet the locato costrat of vrtual ode A2 A2 s mappg o C because D do ot meet the CPU capacty costrat After etwork evromet s chaged, CPU capacty of ode D s creased A2 ca be mgrated from C to D, so as to save 10 uts of badwdth Because vrtual lk A2-B2 eed cosume 3*10 uts of badwdth before mgrato ad oly 2*10 after mgrato Aalogously, the mgrato B2 from F to ca save 10 uts badwdth 2) lk mgrato Ths paper uses M : P P to deote that vrtual lk e = (, ) mgrates from path cosumg badwdth more to path cosumg badwdth less, whch s defed as: ubect to: I whch, b( P ) b( e ), b( P ) b( e ), old ew p, p P ( F ( ), F ( )) old ew log( P ) log( P ) (8a) old ew log( p ) = log ( P ( F ( ), F ( ))) b ( l ) = l P p deotes the substrate path betwee vrtual ode ad P deotes all substrate paths betwee substrate odes whch hosted ad Costrat codto (8a) deotes vrtual lk badwdth cosumg mgrato after must less tha that of mgrato before For example, vrtual lk A1-C1 of 1 s mapped o substrate path A-C-D- o, log( P ) = log( P (, )) = A1C 1 A b( l ) + b( l ) + b( l ) = = 48 AC CD D The obectve of lk mgrato s m log ( p ) p P I Fgure 1, vrtual lk A1-C1 ca be mapped o substrate path A-C-D- or A- Because A- has ot adequate badwdth requested by A1-C1, A- s mapped o A-C-D- Whe A- has suffcet badwdth to meet the costrat of A1-C1, A- ca be mgrated to A- ad ca save 2*16 uts of badwdth 3) mgrato cost Mgrato ca cosume etwork resource ad affect performace of ad, so, the tmes of ode mgrato ad lk mgrato should less The mgrato cost s defed as : C mgrate = 1 Code + ω2 C path (9) ω (10) 4

5 I whch, C ode ad C path deote the tmes of ode mgrato ad lk mgrato Coeffcets ω1, ω2 are used to tradeoff the cost of ode mgrato ad lk mgrato order to compute coveece, the mgrato cost ca be deoted as badwdth cosumg Frequet mgrato wll greatly crease mgrato cost ad also caot guaratee mgrato success Therefore, mgrato tme s mportat problem for mgrato, whch wll be our ext work Ths paper set the mgrato tme as the tme of substrate etwork creases resources or the lfecycle of multple s s ed 4) mgrato reveue Mgrato reveue cludes two parts: (1) performace s ehaced through allocate vrtual ode locato more precse ad vrtual lk much short (2) ome lk badwdth resources ca be saved through ode mgrato ad lk mgrato Whe vrtual ode s mapped o substrate ode that ca meet locato request, ths paper sets reveue asδ adδ s equal to 10 uts of badwdth o, the mgrato reveue s defed as: Rmgrate 3 I whch, mgrato, mgrato = α Rode + α2 Rpath + α Tode δ 1 (11) Rode deotes the lk badwdth saved by ode Rpath Tode 5) mgrato obectve deotes the lk badwdth saved by lk deotes the tmes of ode mgrato The mgrato obectve s to mmze the mgrato cost ad maxmze the mgrato reveue, whch s defed as: max( R C ) (12) mgrate mgrate 4 ROURC ALLOCATIO ALGORITHM From secto 3 descrpto, we ca see that mappg s a P problem I ths paper, CMM cludes vrtual etwork mappg sub-algorthm (MsA) ad heurstc mgrato sub-algorthm (HMsA) MsA ca label vrtual odes ad vrtual lks whch do ot obta optmal resources HMsA ca realze saved resources maxmzato ad mgrato cost mmzato I ths secto, we descrpt the MsA HMsA wll be troduced secto 5 I MsA has two steps, whch are ode mappg ad lk mappg I the step of ode mappg, we preset greedy odes mappg algorthm (GMA) for each of vrtual ode ad substrate ode set whch ca satsfy the costrat of R s foud for each vrtual ode Durg the lk mappg step, lk mappg algorthm based o the k shortest paths s used to fd substrate path whch ca meet the badwdth costrat ad badwdth cost mmzg 41 Greedy odes Mappg Algorthm (GMA) Accordg to the locato ad CPU costrat of each vrtual ode, GMA fds substrate ode sets for them If there s ot substrate ode ca meet costrat of vrtual ode, the locato scope of vrtual ode ca be expaded λ accordg to the tolerato of LA, ad vrtual ode s marked as eed mgrato ode quato (13) s used to order the substrate odes substrate ode set AR( Where e ( ) b( e ) ) = c( ) e ( ) (13) deotes lk that pass the ode Algorthm 1 Greedy odes Mappg Algorthm (GMA) tep 1 Get out vrtual ode ; tep 2 Fd substrate odes whch has locato loc( ) them set ; tep 3 Delete the substrate odes costrat c( ); f ad put whch do ot meet s ot ull, GOTO tep 5; tep 4 If curret vrtual ode has marked, retur mappg fault, ad GOTO tep 7; else mark curret vrtual ode as eed mgrato ode, ad expad loc( ) to loc( )+ λ, ad GOTO tep 2; tep 5 Descedg order the substrate ode (13); usg quato tep 6 If vrtual ode set s ull, retur mappg success, ad GOTO tep 7; else GOTO tep 1; tep 7 Fsh; 5

6 42 Lk Mappg Algorthm based o K hortest Paths (LMAoK) Whe mappg each vrtual lk, the K shortest paths algorthm [10] s used to fd the optmal substrate path, whch ca meet the badwdth costrat ad cosume the badwdth mmzato The obectve of LMAoK s to fd the substrate path whch has the least k value Algorthm 2 Lk Mappg Algorthm based o K hortest Paths (LMAoK) tep 1 Get out vrtual lk tep 2 Fd vrtual odes vrtual lke ; e ; ad tep 3 Fd the shortest path set ode ad destato ode shortest paths algorthm; um tep 4 et, the shortest path ; tep 5 Delete paths of smaller tha b( e ) ; whch are the ed odes of,each oe of whch has source, usg k the equal to the umber of lks of path whch s whose avalable badwdth capacty s tep 6 If s ull, retur lk mappg falure, GOTO tep 11; tep 7 Allocate path whch has the smallest k value to vrtual lk; tep 8 If um, tep 9 If um, mgrato lk; = k, GOTO tep 10; < k, mark curret vrtual lk e as eed tep 10 Get out the ext vrtual lk, f all vrtual lks have bee tep 11 Fsh; mapped success, retur lk mappg success; 5 HURITIC MIGRATIO UB-ALGORITHM (HMA) I secto 4, we ca see that there are some vrtual odes ad vrtual lks whch are ot allocated optmal resources I ths secto, HMsA s used to mgrato these vrtual resources to get optmal resources Mgrato ca affect ad performace ad cosume the eergy of ad I order to solve ths P problem, we frst gve three mgrato prcples, ad the HMsA s proposed 51 Mgrato Prcples (A) mgrato tme: tme that substrate etwork resources are creased ad decreased; tme that multple s lfecycle s ed (B) mgrato scope: mgrato odes ad mgrato lks whch have the remader tme trema to lfecycle ed s more tha the remader tme threshold TH t ; mgrato lks whch have the mgrato badwdth bw used s more tha TH bw After cofrmg the mgrato resources, mgrato odes ad mgrato lks are ordered decreasg whch are descrbed as follows: (a) ortg method of mgrato odes uses the quato (14), bwsaved s used to preset saved badwdth after ode mgrato or lk mgrato; (b) ortg method of mgrato lks uses the quato (15) The coeffcets α1, α 2, α3, α 4, α 5 are used to tradeoff amog dfferet varable α1 t + α2 ds ( loc ( ) loc ( F ( ))) + α3 bw (14) rema saved α4 t + α5 bw (15) rema saved (C) mgratg odes frst ad mgratg lks secod: ode mgrato ca volve the lk chage, so old lks related to mgrato ode eed to be mgrated ad obta optmal substrate paths 52 Heurstc Mgrato sub-algorthm (HMsA) Because mgrato s a P problem, HMsA s proposed accordg to mgrato prcples metoed above Mgrato cludes ode mgrato ad lk mgrato two steps Durg the lk mgrato, lk mgrato sortg algorthm based o preorder relatoshp (LMAoPR) s preseted, whch ca solve the ssues that there are coflct ad depedece relatoshp amog mgrato lks (such as Table 1) 6

7 Algorthm 3 Heurstc Mgrato sub-algorthm (HMsA) tep 1 If the mgrato tme arrve usg mgrato prcple (A); tep 2 Determe the mgrato resources scope usg mgrato prcple (B), get mgrato ode set M ad mgrato 35+0 lk set M ; tep 3 ode mgrato: (a) ort odes M usg quato (14); (b) Delete odes whch ca ot be met CPU capacty costrat to mgrato; (c) Mgrate odes order ad updatg the substrate path accordg ew locato of mgrato odes; tep 4 Lk mgrato: tep 5 Fsh; (a) ort lks M usg quato (15); (b) Delete lks whch ca ot be met badwdth capacty costrat to mgrato; (c) ort lks of (d) Mgrate lks order; M usg LMAoPR; Algorthm 4 Lk Mgrato ortg Algorthm based o Preorder Relatoshp (LMAoPR) tep 1 olve substrate lk resources eeded for each vrtual lk to mgrato; tep 2 olve substrate lk resources released for each vrtual lk after mgrato; tep 3 Fd preorder set for each vrtual lk; tep 4 Merge all preorder sets to obta the order of mgrato lks; tep 5 Retur the order of mgrato lks; ow we gve the detal descrpto to LMAoPR From Fgure 2, we ca see that there are 4 vrtual lks wat to be mgrated whch are show Table 1 But, these mgratos are faled all because of the scarce of lks resources Assume that P creases the badwdth 10 to substrate lk 1-3, ad creases the badwdth 10 to substrate lk 2-3 ow A,B,C,D ca be mgrated Fg2 lk mgrato Table 1 Lk mgrato aalyss sequece umber A B C D vrtual lk substrate path optmal obectve lk resources eeded ; ;6-3 lk resources Released 1-2; ;5-1; ; ;8-1;1-3 coflct C A depedece A,B A,B; C,D C,D preorder set B,D A B,D C We use lk mgrato Fgure 2 as a example Lk A ad lk B are depedece o each other because resources released by lk A ca be used by lk B, ad vce versa There s a coflct betwee Lk A ad lk C because substrate lk 1-3 s eeded by lk A ad lk C smultaeously Preorder set of vrtual lk cossts of vrtual lks whch ca release substrate lk resources ad these substrate lk resources released are eeded by curret vrtual lk I table 1, vrtual lk A eeds substrate lk resource of 1-2,2-3 whch ca be released by vrtual B ad vrtual D o, preorder set of vrtual lk A cossts of vrtual lk B ad D ow we expla the methods of mergg all preorder sets to obta the order of mgrato lks Frst gettg out the preorder set sp whch has the most umber of elemets, ad the mergg the other preorder sets to s I table 1,for example, preorder sets clude{b,d,a},{a,b},{b,d,c}, p {C,D} {B,D,A}has the most umber of elemets ad s 7

8 frot of others, so B,D are put to preorder set, that s sp = { B, D} Whe mergg {A,B}, because vrtual lk A s frot of vrtual lk B, so, we put lk A to s ad frot of B, that s s = { A, B, D} Lastly, we ca get s p = { A, B, C, D} 53 Tme Complexty Aalyss p Assumg there are vrtual lks whch wat to be mgrated, HMsA eeds two steps to mgrate lks Frst, each vrtual lk s aalyss such as table 1, whch cosumes tme ο ( ) ecod, vrtual lks are sorted, whch eeds Therefore, the total tme s ο 3 ( ) p 2 ο ( ) However, f usg greedy mgrato algorthm (GMA) whch mgrates vrtual lks cotuously utl all vrtual lks mgrato falure, whch eeds tme ο (!) If usg radom mgrato algorthm (RMA) whch mgrates vrtual lks usg radom order ad each vrtual lk s mgrated oly oce o, RMA eeds tme ο ( ) 6 IMULATIO I ths secto, we frst descrbe expermet evromet, ad the preset some results There are ot exstg researches whch are related wth problem solved ths paper We compare mappg algorthm CMMA ad CMMA-o-HMsA, where CMMA-o-HMsA deotes that HMsA s ot executed, ad s used to smulate exstg vrtual etwork mappg algorthms 61 mulato vromet mlar to [4,5], ths paper uses GT-ITM[11] to create vrtual etwork ad substrate etwork The umber of substrate odes chages from 50 to 200 ach par of substrate odes are coected wth probablty pr= 02 The CPU capacty of substrate odes ad badwdth capacty of substrate lks dstrbute the rage (10,100) The umber of vrtual odes of R s uform dstrbute (2,10) Probablty that each par of vrtual odes s coected s 02 The CPU capacty of vrtual odes ad badwdth capacty of vrtual lks dstrbute the rage (2,10) rtual odes (or substrate odes) are coected by vrtual odes (or substrate odes) selected radomly, f whch s coected by oe of vrtual lk (or substrate lk) 62 mulato Results (1) Comparso of aved Badwdth I order to valdate the result of mgrato, Rs arrve cotuously utl the RA fals The mgrato algorthm HMsA s used to mgrato vrtual odes ad vrtual lks Fgure 3 shows the saved badwdth resources through usg CMMA We ca see that CMMA saves more badwdth resources tha CMMA-o-HMsA I addto, saved badwdth resources crease gradually whe substrate etwork sze becomes bgger Ths stuato dcates that there are more vrtual odes ad vrtual lks whch ca ot be allocated optmal resources badwdth CMMA CMMA-o-HMsA saved badwdth substrate odes sze Fg3 comparso of saved badwdth (2) Comparso of Lk Mgrato Algorthms Lk mgrato algorthms clude LMAoPR, GMA ad RMA, whch have bee descrbed secto 53 Fgure 4 represets mgrato reveue of three algorthms, amely saved badwdth capacty mgrato reveue GMA LMAoPR RMA substrate odes sze Fg4 comparso of lk mgrato algorthms 8

9 LMAoPR obtas the maxmal mgrato reveue, GMA secodly ad RMA obtas the least mgrato reveue o, LMAoPR uses less tme ad gets more mgrato reveue tha GMA GMA gets more reveue tha RMA, but GMA cosumes more tme tha RMA To llustrate these stuatos, GMA ad RMA do ot solve the ssues of lk mgrato depedece ad lk mgrato coflct I addto, three lk mgrato algorthms all obta more mgrato reveue alog wth substrate etwork sze becomes bgger, whch are the result that more ad more vrtual odes ad vrtual lks are ot assged optmal resources the bg substrate etwork 7 COCLUIO AD FUTUR WORK To save substrate resources maxmzato ad mgrato cost mmzg, ths paper puts forward a ew resource allocato algorthm whch ca realze mappg cost mmzato, called CMMA CMMA s very good soluto to the problem that vrtual odes ad vrtual lks do ot obta optmal resources, caused by some substrate etwork resources scarce Although algorthm CMMA ca save more resources tha others algorthms, mgrato tme s eeded to research further I addto, autoomc computg resource maagemet s a research hotspot I ext work, we wll try to use o-cooperatve games to realze resource depedet optmzato mgrato ACKOWLDGMT Ths work was partly supported by 973 proect of Cha (2007CB310703), Fuds for Creatve Research Groups of Cha ( ) ad atoal atural cece Foudato [5] M M K Chowdhury, M R Rahma, ad R Boutaba, rtual etwork embeddg wth coordated ode ad lk mappg, Proc of I IFOCOM, 2009 [6] Marqueza, CC, Gravlle, LZ,uz, G, Bruer, M, Dstrbuted autoomc resource maagemet for etwork vrtualzato I etwork Operatos ad Allocato ymposum (OM) [7] Zhpg Ca, Fag Lu, og Xao, rtual etwork mbeddg For volvg etworks, Proceedgs of the I Telecommucatos Coferece (GLOBCOM), 2010 [8] Zhu Y, Amm ar M Algorthms for assgg substrate etwork resources to vrtual etwork compoets Proceedgs of the I IFOCOM Barceloa, Cataluya, pa, [9] AT&T Maaged Iteret ervce (MI), [10] D ppste, Fdg the k shortest paths I Proc I ymposum o Foudatos of Computer cece, 1994 [11] W Zegura, K L Calvert, ad Bhattacharee, How to model a teretwork I Proc I IFOCOM, 1996 Frst Author: ZHAG hu-l, bor 1981, PhD caddate Hs research terests clude ext geerato etwork ad etwork maagemet ecod Author: QIU Xue-sog, bor 1973, professor, PhD supervsor Hs research terests clude ext geerato etwork ad etwork maagemet of Cha ( , ) RFRC [1] J Turer, D Taylor, Dversfyg the Iteret, Proceedgs of the I Telecommucatos Coferece (GLOBCOM 05), 2005,vol 2 [2] Feamster, L Gao, ad J Rexford, How to lease the Iteret your spare tme, IGCOMM Computer Commucato Revew, 2007, vol 37, o 1, pp [3] MChowdhury, RBoutaba, etwork rtualzato:the Past,The Preset,ad The Future, I Commucatos Magaze,July,2009 [4] M Yu, Y Y, J Rexford, M Chag, Rethkg vrtual etwork embeddg: ubstrate support for path splttg ad mgrato ACM IGCOMM CCR 2008,38(2),