Off-Peak Energy Optimization for Links in Virtualized Network Environment

Transcription

1 Thi article ha ee accepted for pulicatio i a future iue of thi joural, ut ha ot ee fully edited. Cotet may chage prior to fial pulicatio. Citatio iformatio: DOI /TCC , IEEE Traactio o Cloud Computig JOURNAL OF IEEE TRANSACTIONS ON CLOUD COMPUTING 1 Off-Peak Eergy Optimizatio for Lik i Virtualized Network Eviromet Erahim Ghaziaeedi, Studet Memer, IEEE, Chagcheg Huag, Seior Memer, IEEE Atract Eergy coumptio i Iformatio ad Commuicatio Techology (ICT) i etimated to e 10% of the total eergy coumed i idutrial coutrie. Beide, the populatio of ICT cutomer i growig. I order to hadle the icreaig traffic demad, ervice provider eed to expad their etwork ifratructure. The recet propoed etwork virtualizatio techology help low dow the ifratructure expaio y allowig the coexitece of multiple virtual etwork over a igle phyical etwork. Although Virtualized Network Eviromet (VNE) low dow the ifratructure expaio ad therefore cotrol power coumptio, it i eetial to develop ew techique to decreae VNE eergy coumptio. I thi paper, we dicu multiple ovel eergy avig recofiguratio method that gloally/locally optimize VNE lik power coumptio, durig off-peak time. The propoed fie-graied local recofiguratio eale the provider to adjut level of the recofiguratio, ad accordigly cotrol poile traffic diruptio. A Iteger Liear Program (ILP) i formulated for each olutio accordig to two power model, ad coiderig the impact of traffic plitaility. Becaue the formulated ILP are ot calale to large etwork ize, a ovel heuritic algorithm i alo uggeted. The imulatio reult prove the propoed olutio are ale to ave otale amout of eergy i phyical lik durig off-peak time. Idex Term Virtualized Network Eviromet; Eergy Efficiecy; Eergy-Efficiet Virtualized Network Eviromet; Lik Recofiguratio I. INTRODUCTION Iformatio ad Commuicatio Techology (ICT) play a fudametal role i our everyday life. It i difficult to imagie a world without the ifratructure that coect people ad trafer their iformatio acro the gloe. Sigificat advatage of commuicatio etwork have timulated the demad for thi techology. It i predicted that the ize of the Iteret doule every 5.32 year [1]. The icreae i uer demad, availaility of roadad acce ad the ew ervice offered y ICT, have triggered the warig aout eergy coumptio of commuicatio techology [2]. I order to hadle the growig demad, Iteret Service Provider (ISP) eed to expad their phyical ifratructure, uch a addig extra erver, router, witche ad lik. Thi correpodigly icreae power coumptio which eceitate cotrollig ad decreaig etwork eergy uage. Recetly, virtualizatio ha ee propoed to hare reource i etwork eviromet [3]. A VNE upport the coexitece of multiple virtual etwork (VN) over a igle utrate etwork [4]. VNE emeddig proce map Erahim Ghaziaeedi, ad Chagcheg Huag are with the Departmet of Sytem ad Computer Egieerig, Carleto Uiverity, Ottawa, Caada. {eghaziaeedi; huag}@ce.carleto.ca Maucript Sumitted: Novemer 14, Revied: April 15, Accepted: May 15 requeted virtual ode ad lik oto utrate ode ad path, repectively. It allocate traffic capacitie to virtual lik i utrate path. A VNE ue the actual reource more efficietly y harig the utrate etwork capacity amog multiple virtual etwork. Sharig the phyical reource ad allowig coexitece of multiple virtual etwork o a igle utrate help low dow the ifratructure expaio, ad coequetly low dow the growig ICT eergy coumptio. Noethele, it i alo eetial to furthermore decreae a VNE eergy coumptio with additioal eergy avig techique, eve though VNE already decreae power coumptio y cocept. A eergy-aware VNE low dow the ifratructure expaio a well a etwork eergy coumptio. I fact, virtual etwork traffic load chage over time. Virtual etwork might e highly utilized durig a period of time (peak time, e.g. day hour), while they are uderutilized durig aother otale period of time (off-peak time, e.g. ight hour). Traffic variatio i virtual etwork correpodigly chage utrate etwork utilizatio. The report for North America ad 25 Europea etwork provider reveal % differece etwee peak ad miimum off-peak traffic rate over their utrate etwork [5]. However, today utrate etwork are proviioed to upport VN peak time traffic demad, with ome additioal over-proviioig accommodatig uexpected traffic rate [5]. The utrate etwork elemet are alway witched o, eglectig the traffic ehaviour. Network provider could determie the off-peak time period of the utrate etwork ad traffic demad of each VN i that period, through give iformatio y VN cutomer, or etwork traffic predictio techique, e.g. [6], [7], that etimate the future traffic y lookig at the curret traffic tate. Durig the off-peak period, it i poile to reduce VNE eergy coumptio y recofigurig mappig of the already emedded VN accordig to their decreaed traffic demad. I thi cotext, virtual etwork are accepted ad emedded oto the utrate etwork y a ormal (ot eergy-efficiet) VNE emeddig proce to accommodate the peak traffic ehaviour. The recofiguratio techique i ru durig ormal etwork operatio, upo etwork go from the peak period to the off-peak period, to ave eergy i the off-peak period. However, whe the traffic load chage from peak level to a off-peak level, ome traffic flow that lat i the oth time period might uffer from traffic diruptio impoed y applyig the recofiguratio [5]. Beide, recofigurig mappig of emedded VN may require additioal igallig traffic that i eceary for otifyig all the ivolved router [8]. Thi may itroduce igificat work load for the igallig cotroller epecially whe the recofiguratio trie to make chage to (c) 15 IEEE. Peroal ue i permitted, ut repulicatio/reditriutio require IEEE permiio. See for more iformatio.

2 Thi article ha ee accepted for pulicatio i a future iue of thi joural, ut ha ot ee fully edited. Cotet may chage prior to fial pulicatio. Citatio iformatio: DOI /TCC , IEEE Traactio o Cloud Computig JOURNAL OF IEEE TRANSACTIONS ON CLOUD COMPUTING 2 a large umer of ode at the ame time. Coequetly, it may ot e a good practice to recofigure mappig of every emedded virtual ode/lik. Due to impler techical implemetatio ad high potetial of eergy avig i etwork lik [9], thi paper i retricted to power avig olutio for lik i VNE. I thi paper, we dicu multiple ovel eergy avig olutio that optimize VNE lik power coumptio durig the off-peak time, accordig to two defied power model. We approach the prolem y recofigurig mappig of the already emedded virtual lik. Firt, we tudy a recofiguratio prolem that re-map every virtual lik accordig to it off-peak traffic demad, i order to to miimize VNE lik power coumptio durig the off-peak period. Thi i a coare-graied (the graularity i a virtual lik) ad gloal (it re-map every virtual lik) recofiguratio method. We tudy thi prolem a our echmark, ecaue it deliver the mot optimum level of eergy avig for thi prolem. However, a it i dicued, thi i ot a afe approach. We formulate thi method a a Mixed Iteger Liear Program (MILP). Secod, we propoe a ovel recofiguratio methodology. We defie a tre rate for a utrate lik. Accordigly, a olutio i propoed to miimize VNE lik power coumptio durig the off-peak time. Thi method may et a le treed utrate lik ito leep mode for the off-peak time. We re-map a allocated traffic capacity to a virtual lik i a le treed utrate lik if we et the utrate lik ito leep mode. Thi i a fie-graied (the graularity i a allocated traffic capacity to a virtual lik i a utrate lik) ad local (it doe ot re-map every allocated traffic capacity to virtual lik) recofiguratio trategy. Thi method eale the provider to chage level of the recofiguratio y adjutig the tre rate threhold, ad therefore cotrol the poile traffic iterruptio. Clearly, there i a trade-off etwee eergy avig level ad the poile traffic iterruptio. I order to tudy the impact of traffic plitaility o eergy avig capaility of our olutio, we formulate the latter method a a MILP for plittale traffic, ad a a Biary Iteger Liear Program (BILP) for o-plittale traffic. The formulated optimizatio olutio are N P-hard ad therefore they are ot calale to large etwork ize. Hece, a ovel heuritic algorithm i alo propoed. The imulatio reult cofirm the heuritic algorithm ca achieve cloely to the optimum poit et y the optimizatio program. While, it i calale to large etwork ize. Thi paper i orgaized a follow: The related work ad our cotriutio i thi paper, are dicued i Sectio II. Two phyical lik power model are defied i Sectio III. The optimizatio program are formulated i Sectio IV ad the uggeted heuritic i dicued i Sectio V. The performace of the ILP a well a the heuritic algorithm are evaluated i Sectio VI. The paper will coclude i Sectio VII. II. RELATED WORKS The literature i rich i term of etwork virtualizatio ad eergy avig olutio for commuicatio etwork. But, they have ee tudied eparately. There are few very recet work that cocered aout eergy coumptio i VNE. We review them i thi ectio. Four paper [10] [13] tried to ave eergy i VNE y makig it emeddig procedure eergy-aware. Thi ha ee doe y modifyig the lik weight aed o phyical lik power coumptio i [10], ad coolidatig VN to the mallet umer of utrate etwork elemet i [11] [13]. Modifyig the VNE emeddig algorithm i order to achieve a power-efficiet VNE uffer from a major difficulty. Whe VNE emeddig algorithm are modified to map the reource eergy-wie, everal extra cotrait will e added to the emeddig procedure. Accordigly, the emeddig algorithm ha a maller et of phyical ode ad lik cadidate to chooe from. Thi decreae the etwork admittace ratio for ew virtual etwork requet, which i ot cot efficiet for the provider. The mai ecoomic ojective of provider i to reject the miimum umer of virtual etwork requet. Thu, thee olutio are ot profitale for them i log term. Some other paper propoed heuritic that modify the already mapped VN. Jua Fleipe Botero i [14] offered a heuritic algorithm that recofigure mappig of accepted VN at each emeddig phae to ave eergy. Thi approach ha the ame prolem of eergy-efficiet emeddig method. Becaue recofigurig mappig of accepted VN at each emeddig phae for their life time, till might make capacity ottleeck that decreae etwork admittace rate for ew VN. Moreover, their heuritic aume each virtual lik i oly mapped oto a igle phyical lik. However, the virtual lik might e mapped oto phyical path. Fially, their recofiguratio prolem i ot formulated mathematically. A off-lie heuritic recofiguratio algorithm i propoed i our previou work [15]. The algorithm trie to maximize the umer of leep mode phyical lik durig the off-peak period of VNE. It reroute the off-peak traffic of already emedded virtual lik, to other already allocated traffic capacitie. It doe ot chage mappig of VN. Aumig fixed VN mappig prevet u to reroute a VN off-peak traffic to utrate lik that o traffic capacity i allocated i them to that particular VN. Thi decreae the level of eergy we could ave. Author i [16] uggeted a method to move emedded virtual machie (VM) oto erver, to other erver. Their olutio i ru over time periodically, to coolidate the VM. Neverthele, movig allocated VM ad ettig the erver ito leep mode i expeive, if it i ot impoile, due to two reao. Firt, ormally large amout of data i ditriuted over large umer of erver, ad it i ot profitale/poile for the provider to move data of a erver to aother oe. Secod, wakig up erver from leep mode (i the cae of uexpected demad, or goig ack to peak time), impoe hudred of milliecod delay to the tak that might violate Service Level Ojective (SLO) [17]. Beide, their olutio doe ot eale the provider to adjut level of the recofiguratio, ad cotrol the poile traffic diruptio. Sice we do ot recofigure mappig of allocated virtual ode i thi paper, the prolem might eem imilar to the claic routig prolem for multi-layer etwork deig. For example, Chuaheg Xi ad hi co-author i [18] propoed (c) 15 IEEE. Peroal ue i permitted, ut repulicatio/reditriutio require IEEE permiio. See for more iformatio.

3 Thi article ha ee accepted for pulicatio i a future iue of thi joural, ut ha ot ee fully edited. Cotet may chage prior to fial pulicatio. Citatio iformatio: DOI /TCC , IEEE Traactio o Cloud Computig JOURNAL OF IEEE TRANSACTIONS ON CLOUD COMPUTING 3 a mappig method to deig a tatic virtual topology for WDM optical etwork. They pre-compute poile route etwee ource ad detiatio of every requeted traffic demad, ad the their ILP chooe the et route accordig to their ojective. [9], [18], ad the other exitig approache for eergy-efficiet routig prolem, e.g. [19], [], are mappig method. They route every requeted traffic demad, etwee fixed ode. Thi i imilar to our coare-graied gloal recofiguratio method that re-map every virtual lik durig the off-peak time. However, a it i dicued i the previou ectio, it i ot afe to re-allocate every traffic demad durig the off-peak period. Thu, eergy-aware routig of every traffic demad i quite differet from locally recofigurig mappig of VN ad imultaeouly coiderig the poile traffic diruptio that might happe durig the recofiguratio. To the et of our kowledge there are few paper that tudied claic eergy-efficiet recofiguratio prolem ad coidered the poile traffic iterruptio. Author i [21] propoed a MILP that reroute off-peak traffic i order to miimize eergy coumptio durig the off-peak period. However, their approach, imilar to [15] ad [8], aume fixed VN mappig to decreae the poile traffic diruptio. But, a it i dicued, aumig fixed VN mappig reduce the level of eergy avig. Furthermore, they do ot provide a tool, o the provider could adjut level of the recofiguratio. Similarly, author i [5] uggeted a MILP to reroute off-peak traffic to ave eergy. Differet from previou paper [8], [15], [21], the method i [5] firt pre-compute tatic mappig for VN, accordig to their off-peak load. They do o coider eergy coumptio at thi tep. The, the MILP reroute the off-peak traffic of every virtual lik to the pre-computed path, to ave eergy. They do ot let the MILP to modify mappig of virtual lik, i order to reduce the poile traffic iterruptio ad decreae program complexity. However, pre-computig offpeak mappig ad the earchig i them to ave eergy do ot provide the mot optimum reult, ecaue it i poile to reroute traffic oly to the utrate lik i the pre-computed mappig. Beide, reroutig off-peak traffic of every virtual lik i ot a good practice, while the provider are ot ale to cotrol the poile traffic iterruptio. Our Cotriutio: a) Differet from previou reearch tudie [10] [14] our method doe ot decreae the etwork admittace ratio for ew virtual etwork. Thi i ecaue we recofigure mappig of the already accepted VN oly for the off-peak period, ad they could e recofigured ack to their peak mappig i the cae of uexpected ew demad. ) We do ot move VM, o our method doe ot have the difficultie of [16]. c) We defie a tre rate for a utrate lik. So, we propoe a fie-graied local recofiguratio approach that may et a le treed utrate lik ito leep mode for the off-peak time. Accordigly, we re-map a allocated traffic capacity to a virtual lik i a le treed utrate lik if we et the utrate lik ito leep mode. Our olutio make a deciio aout which allocated traffic capacitie of which virtual lik, are eceary to e re-mapped. Thi icreae the complexity of the prolem i compario to the claic routig prolem i [5], [8], [9], [18] [21]. However, it eale the provider to chage level of the recofiguratio y adjutig the tre rate threhold, ad therefore cotrol the poile iterruptio. We how the propoed fiegraied local recofiguratio i ale to reach the ame level of eergy avig a the coare-graied gloal recofiguratio (the echmark), y relaxig tre rate threhold. Thi i a ovel approach differet to ay exitig reearch tudie. d) A a coequece of thi ovel approach, our olutio i ot limited to a u-topology a the cae i [5], [8], [15], [21], ad o it ha larger degree of freedom to ave eergy. The imulatio reult prove the igificat improvemet i avig power y our method, i compario to the tate-of-the-art. e) We dicu how differetly we hould approach the prolem i the cae of o-plittale traffic i compario to plittale traffic, to have wide eough earch zoe for re-mappig. f) We alo preet a heuritic recofiguratio algorithm that could achieve cloely to the optimum reult, ut much fater tha the BILP. g) We evaluate the propoed olutio y exteive imulatio. To the et of our kowledge, there i ot uch a compreheive tudy i the literature that coider imultaeouly gloal/local, coare-graied/fie-graied VNE recofiguratio for plittale/o-plittale traffic, accordig to two power model. III. PHYSICAL LINK POWER MODEL We tudy two power model to defie the phyical lik power coumptio. The firt power model coider cotat amout of power coumptio (P m (l )) for a active phyical lik. P m (l ) i the maximum lik power coumptio of utrate lik l. l deote a utrate lik that coect ith utrate ode to jth utrate ode. Accordig to thi model, the actual traffic load o the lik doe ot affect the phyical lik power coumptio. We call thi model Fixed lik power model. Coequetly, the actual power coumptio p(l ) of a phyical lik l could e foud y Equatio 1, where α(l ) refer to l tate. α(l ) i 1 whe the lik i active, otherwie it i 0. p(l ) = α(l )P m (l ) (1) The ecod power model aume a ae amout of power P (l ) that keep the phyical lik l operatioal. However, differet from the previou model, the power coumptio varie liearly, etwee the ae power P (l ) (whe there i o traffic o the lik) ad the maximum power P m (l ) (whe the lik i fully utilized). We call thi model Semi Proportioal lik power model. Equatio 2 defie actual power coumptio of a phyical lik l accordig to thi power model. p(l ) = α(l )P (l ) ) + r(l C (l ) (P m (l ) P (l )) (2) Where, C (l ) tad for the adwidth capacity of utrate lik l, ad r(l ) i the traffic load o l. Note that P (l ), ad P m (l ) are ormally defied for differet rage of lik adwidth capacity, aed o the lik legth, ad type of the cale. Some umerical amout for P (l ) ad P m (l ) are give i [22] (c) 15 IEEE. Peroal ue i permitted, ut repulicatio/reditriutio require IEEE permiio. See for more iformatio.

4 Thi article ha ee accepted for pulicatio i a future iue of thi joural, ut ha ot ee fully edited. Cotet may chage prior to fial pulicatio. Citatio iformatio: DOI /TCC , IEEE Traactio o Cloud Computig JOURNAL OF IEEE TRANSACTIONS ON CLOUD COMPUTING 4 Today etwork are deiged aed o Fixed lik power model, o it i a commo model that i widely ued [22]. Neverthele, it i ot efficiet that a active phyical lik coume a cotat amout of power, regardle of it traffic load. Therefore, phyical lik are expected to get modified, o their power coumptio will e more adaptive to their traffic load. The Semi Proportioal lik power model rig a traffic adaptive power model that phyical lik power coumptio i chagig accordig to it traffic load. Thee power model are validated y meauremet agait actual phyical lik i the previou tudie, e.g. [23], [24]. IV. INTEGER LINEAR PROGRAMS Toward decreaig total lik eergy coumptio i VNE durig the off-peak hour, the geeral prolem decriptio i the followig: Give: Phyical utrate etwork topology Allocated virtual etwork topologie For each utrate lik: It adwidth capacity, ad every allocated traffic capacity to a virtual lik, i the utrate lik Off-peak traffic demad of every virtual etwork (determied y VN cutomer or etwork traffic predictio techique) Fid: Modified off-peak lik mappig of VNE that lead to miimum utrate etwork lik power coumptio durig the off-peak time Cotrait: Supportig off-peak traffic demad The mot optimum reult for thi prolem could e achieved y the coare-graied gloal lik recofiguratio program. We call thi approach, off-peak lik eergy optimizatio y gloal lik recofiguratio. We coider the reult of thi method a the echmark. Neverthele, a it i dicued, thi method might caue ucotrolled traffic diputatio. Therefore, we propoe the fie-graied local lik recofiguratio program for the defied prolem. The latter approach i called offpeak lik eergy optimizatio y local lik recofiguratio. I thi regard, firt, we model VNE mathematically. The, accordig to oth Fixed ad Semi Proportioal lik power model, we defie ILP for oth of the approache. Sice the traffic type (plittale/o-plittale) ha a major impact o olutio methodology, we formulate off-peak lik eergy optimizatio y local lik recofiguratio prolem, for oth plittale ad o-plittale traffic. Emedded ik, virtual ode of, th Sutrate Node Fig. 1. j, Allocated traffic capacity for aother virtual lik, Secod allocated path for i Firt allocated path for,, th Sutrate Node Emedded ource virtual ode of, Example: A emedded virtual lik oto a utrate etwork Similar to the utrate etwork model, th virtual etwork, from et of all the ivolved virtual etwork Φ, i alo modelled a a directed graph G = (V, E ). V ad E tad for th virtual etwork vertice ad edge, repectively. L = E deote total umer of virtual lik i th virtual etwork. I VNE emeddig procedure, a requeted virtual etwork G i mapped oto the utrate etwork G : G G. Virtual ode are emedded oto the qualified utrate ode. A virtual lik could e mapped oto a igle utrate lik, or multiple utrate lik which make a utrate path. If traffic i plittale, requeted traffic capacity for a virtual lik could e allocated i multiple utrate path. However, if traffic i o-plittale each demaded traffic capacity i allocated oly i oe path. The allocated virtual lik of th VN are give a a et of ordered allocated virtual ode pair (a m, m ), m = 1, 2,..., L. l am,m repreet m th virtual lik, elogig to th VN, that coect the virtual ode mapped oto a m th utrate ode to the virtual ode mapped oto m th utrate ode. Off-peak traffic demad ŕ m of each virtual lik l am,m i alo give. I additio, l (m) repreet the allocated traffic capacity to lam,m i l. ŕ (m) deote the off-peak traffic demad of l (m), ad it i kow for every allocated traffic capacity i ay utrate lik. Durig the the off-peak period, the reerved traffic capacity for l (m) i equal to it off-peak traffic demad ŕ (m), ad ret of the phyical lik adwidth capacity could e hared. We might aggregate all the allocated traffic capacitie i a utrate lik. l deote the udled allocated traffic capacitie i a utrate lik l, ad ŕ i it aociated off-peak traffic demad. Beide, C (l ) of each utrate lik l i pecified. For example, Figure 1 demotrate a utrate etwork ad a mapped virtual lik l am,m oto the etwork. Sice traffic i plittale i thi example, two utrate path are allocated to the virtual lik. Figure 1 alo how l (m) ad l i l. A. Network Model The utrate etwork i modelled a a directed graph G = (V, E ) where V i the et of utrate vertice, ad E i the et of utrate edge. Vertice repreet ode ad edge deote lik i etwork eviromet. Sice the graph i directed, we have higher level of flexiility i term of reroutig traffic flow. B. Program aed o Fixed Lik Power Model Accordig to Fixed lik power model, a active phyical lik coume a cotat amout of eergy, regardle of it traffic load. I thi paper, we aume all the phyical lik i the utrate etwork are i the ame rage of adwidth capacity. Therefore, active utrate lik coume the ame amout of power. Accordigly, the power avig olutio ha to put maximum umer of phyical lik ito leep mode, i (c) 15 IEEE. Peroal ue i permitted, ut repulicatio/reditriutio require IEEE permiio. See for more iformatio.

5 Thi article ha ee accepted for pulicatio i a future iue of thi joural, ut ha ot ee fully edited. Cotet may chage prior to fial pulicatio. Citatio iformatio: DOI /TCC , IEEE Traactio o Cloud Computig JOURNAL OF IEEE TRANSACTIONS ON CLOUD COMPUTING 5 order to miimize the etwork lik power coumptio. We aume the ideal cae, i which a phyical lik i leep mode coume o power. The followig optimizatio program i thi ectio are deiged accordig to thi methodology. 1) Off-peak Lik Eergy Optimizatio y Gloal Lik Recofiguratio (OL-GL-F): I thi ectio, we ited to remap every virtual lik for the off-peak time, to miimize umer of active utrate lik durig that period. We remap every virtual lik accordig to it kow off-peak traffic demad. Thi i a coare-graied olutio, a the graularity i a virtual lik. Beide, it i a gloal optimizatio, ecaue we re-map every virtual lik. The traffic i aumed to e plittale i thi prolem, to give larger degree of freedom for re-mappig. Thi program i expected to deliver the mot optimum eergy avig level for our prolem. But, it might caue ucotrollale traffic iterruptio. We tudy thi program a the echmark. Whe thi prolem i formulated accordig to the Fixed lik power model, it i called OL-GL- F. Thi prolem could e formulated a a multi-commodity flow prolem. I the cotext of thi prolem, a virtual lik i a commodity. We have L commoditie for th virtual etwork. OL-GL-F i writte a a MILP a follow: Optimizatio Variale: α(l l f ) i a auxiliary iary variale. α(l i active. Otherwie, α(l ) i 0. (m) i a real-valued variale. f i l (m) i the reallocated traffic capacity to l am,m. ) i 1 whe Ojective Fuctio: The ojective fuctio i Equatio 3 miimize umer of active utrate lik for the off-peak time. Miimize () E α(l ) (3) Cotrait: The firt cotrait i Equatio 4 i flow coervatio cotrait that maitai the flow alace o the ode ad re-allocate off-peak traffic demad of every virtual lik. {j () E } f (m) {j (j,i) E } f j,i (m) ŕ m if i = a m = ŕ m if i = m 0 otherwie i V, { G Φ}, m = 1, 2,..., L (4) The ecod cotrait i Equatio 5 eure the total reallocated traffic capacitie r(l ) i each utrate lik l i le tha it phyical adwidth capacity. where: r(l ) C (l ), (i, j) E (5) r(l ) = L { G Φ} m=1 f (m) (6) A cotrait i Equatio 7 i added to make the program liear. Note that B i a large iteger umer. It mut e large eough to e greater tha the larget amout of r(l ). r(l ) could e 0 or greater tha 0. Firt, aume r(l ) = 0, o accordig, to the ojective fuctio ad cotrait i Equatio 7, α(l will e 0. Secod, aume r(l ) > 0. I thi cae, α(l mut e 1 to covice the cotrait. ) ) r(l ) Bα(l ), (i, j) E (7) I additio, the variale mut hold the followig oud: f (m) 0, (i, j) E, { G Φ}, m = 1, 2,..., L (8) α(l ) {0, 1}, (i, j) E (9) The formulated MILP for OL-GL-F i a type of VNE emeddig prolem. MILP i N P-hard i geeral, ecaue ILP i N P-hard. Beide, VNE emeddig proce i N P- hard [4]. I coequece, the defied MILP for off-peak lik eergy optimizatio y gloal lik recofiguratio prolem i N P-hard, ad therefore the optimizatio olutio i ot calale to the large etwork ize. 2) Off-peak Lik Eergy Optimizatio y Local Lik Recofiguratio: The previou recofiguratio approach might caue ucotrolled traffic iterruptio, a dicued. Therefore, we propoe a ecod methodology. Firt, we defie a tre rate for a utrate lik. The, we develop olutio that may et a le treed utrate lik ito leep mode for the off-peak time. We re-map a allocated traffic capacity to a virtual lik i a le treed utrate lik if we et the utrate lik ito leep mode. Differet from the previou approach, thi i a fie-graied olutio a the graularity i a allocated traffic capacity to a virtual lik, i a utrate lik. Beide, thi i a local optimizatio, ecaue it doe ot re-map every allocated traffic capacity i ay phyical lik. Thi method eale the provider to chage level of the recofiguratio y adjutig the tre rate threhold, ad therefore cotrol the poile traffic iterruptio. The tre rate (l ) of a utrate lik l deote the iteity of ivolved VN ad the total off-peak traffic demad, if at leat oe of it emedded virtual lik pae through l. Aume η(l ) a the umer of VN ivolved i utrate lik l, Equatio 10 defie (l ). L (l ) = η(l ) { G Φ} m=1 ŕ (m) Φ C (l (10) ) i the lik. A VN i ivolved i a utrate lik l (l ) coider two parameter. The firt parameter ( η(l ) Φ ) i the fractio of the umer of ivolved VN i the utrate lik, over total umer of active VN. Thi parameter deote iteity of the ivolved VN i l. Thi i a importat factor. If a utrate lik i highly itee i regard to the ivolved VN, traffic of large umer of ivolved VN pae through the lik. Therefore, leepig uch a utrate lik might affect ormal operatio i large umer of VN. The ecod parameter (all the term except the firt parameter) cocer aout the off-peak traffic demad y fidig the fractio of total off-peak traffic pae the utrate lik, over adwidth capacity of the lik. Thi i eetial, ice leepig a utrate lik with high traffic utilizatio (c) 15 IEEE. Peroal ue i permitted, ut repulicatio/reditriutio require IEEE permiio. See for more iformatio.

6 Thi article ha ee accepted for pulicatio i a future iue of thi joural, ut ha ot ee fully edited. Cotet may chage prior to fial pulicatio. Citatio iformatio: DOI /TCC , IEEE Traactio o Cloud Computig JOURNAL OF IEEE TRANSACTIONS ON CLOUD COMPUTING 6 might caue large traffic iterruptio. Higher lik tre rate mea larger umer of VN i ivolved, or the lik i more utilized for the off-peak time. I thi regard, we do ot remap the allocated traffic capacitie i utrate lik with ) T, i order to cotrol traffic diruptio due to the recofiguratio. T i tre rate threhold, ad it i a real umer etwee 0 ad 1. Provider could adjut T. Decreaig T degrade amout of power the program could ave, ut alo reduce the traffic iterruptio due to the recofiguratio. Thi i ecaue maller umer of phyical lik are coidered for power avig. The impact of ettig differet value of T o eergy avig aility of the olutio i dicued i Sectio VI. The traffic might e plittale or o-plittale. I plittale cae, the traffic demad of each virtual lik could e carried y oe or multiple path i the utrate etwork. However, if the traffic i o-plittale each virtual lik traffic demad may e required to follow the ame path through the etwork, rather tha e divided amog multiple path. It i expected to ave higher amout of eergy whe traffic i plittale, ecaue we are more flexile i term of fidig alterative path durig the recofiguratio. Thi i a major retrictio that ha a importat impact i the olutio methodology. I thi regard, we formulate the off-peak lik eergy optimizatio y local lik recofiguratio program, for oth plittale ad o-plittale traffic. a) Splittale Traffic (OL-LL-F): Becaue the traffic i aumed to e plittale, it i the ame to aggregate all the allocated traffic capacitie i a phyical lik ad the reallocate the udled traffic capacity oto multiple path, or re-allocate every igle allocated traffic capacity i the lik oto multiple path. I order to implify the program we reallocate the udled traffic capacitie accordig to their offpeak traffic demad. I thi prolem, we re-map the udled allocated traffic capacity i a le treed utrate lik if we et the utrate lik ito leep mode. The off-peak lik eergy optimizatio y local lik recofiguratio prolem for plittale traffic, that i defied accordig to Fixed lik power model, i called OL-LL-F. The defied recofiguratio prolem could e formulated a a multi-commodity flow prolem. I the cotext of thi (l prolem, the udled allocated traffic capacity l i a utate lik l with (l ) < T, i a commodity. Each commodity i aociated with a kow off-peak traffic demad ŕ l OL-LL-F i formulated a a MILP a follow: Optimizatio Variale:. α(l ) i a auxiliary iary variale. α(l ) i 1 whe the utrate lik l i active, otherwie α(l ) i 0. f x,y (l ) i a real-valued variale. It i the re-allocated traffic capacity to l i l x,y. l x,y i a utrate lik coect xth utrate ode to yth utrate ode. Similarly, f (l x,y ) i a real-valued variale. β(l ) i a iary variale. It how l tatu, after recofiguratio. It i 0 i the cae l i removed, after recofiguratio. Otherwie, β(l ) i 1. Ojective Fuctio: The ame ojective a Equatio 3. Cotrait: The cotrait i Equatio 5, 7, ad the followig: The cotrait i Equatio 11 i flow coervatio cotrait that re-allocate off-peak traffic demad of a removed commodity. The program doe ot re-allocate off-peak traffic demad of every udled allocated traffic capacity. It re-allocate the off-peak traffic demad of a commodity if the commodity i removed. If the program decide to remove a udled allocated traffic capacity l, l tatu chage, ad o 1 β(l ) i equal to 1. Therefore, the cotrait i Equatio 11 require re-allocatig oe or multiple alterative path from ith utrate ode to jth utate ode, which upport it off-peak traffic demad ŕ. Neverthele, if l i ot removed durig the recofiguratio proce, 1 β(l ) i equal to 0, ad therefore l i ot re-mapped. f x,y (l ) f y,x (l ) {y (x,y) E } {y (y,x) E } (1 β(l )ŕ if x = i = (β(l ) 1)ŕ if x = j 0 otherwie x V, (i, j) E (11) I thi prolem, differet from OL-GL-F, there might e two type of allocated traffic capacity i a utrate lik, durig the off-peak time. The firt type i a u-recofigured udled allocated traffic capacity. Thi mea l wa allocated ad it i ot removed i the recofiguratio proce, therefore β(l ) = 1. I thi cae, β(l )ŕ i equal to ŕ that i it reerved amout of traffic capacity for the off-peak period. If the program re-allocate l, β(l ) = 0. So, it origial allocated traffic capacity i o loger reerved. The ecod type i the re-allocated udled traffic capacity of other lik (like l x,y ), i utrate lik l. f (l x,y ) i the re-allocated traffic capacity to l x,y i l, for the off-peak period. Equatio 12 calculate the total allocated traffic capacitie r(l ) i l, for thi prolem. r(l ) = β(l )ŕ + f (l x,y ) (12) (x,y) E Moreover, the cotrait i Equatio 13 avoid re-mappig a udled allocated traffic capacity i utrate lik with (l ) T, i order to decreae the traffic iterruptio. Thi cotrait eale provider to cotrol level of the recofiguratio, ad therefore cotrol the poile iterruptio. β(l ) = 1, (i, j) {(i, j) (i, j) E, (l ) T } (13) Furthermore, the variale mut hold the oud i Equatio 9, ad the followig: f x,y (l ) 0, (x, y) E, (i, j) E (14) β(l ) {0, 1}, (i, j) E (15) ) No-Splittale Traffic (OL-LL-F): Sice traffic i o-plittale, it i ot poile to re-allocate a allocated traffic capacity to a virtual lik i a utrate lik, oto multiple utrate path. Coequetly, aggregatig all the allocated traffic capacitie i a utrate lik ad the reallocatig the udled traffic capacity, i ot a efficiet, (c) 15 IEEE. Peroal ue i permitted, ut repulicatio/reditriutio require IEEE permiio. See for more iformatio.

7 Thi article ha ee accepted for pulicatio i a future iue of thi joural, ut ha ot ee fully edited. Cotet may chage prior to fial pulicatio. Citatio iformatio: DOI /TCC , IEEE Traactio o Cloud Computig JOURNAL OF IEEE TRANSACTIONS ON CLOUD COMPUTING 7 approach. Thi i ecaue there would e a maller umer of alterative path that could upport the udled off-peak traffic demad. I thi prolem, we re-map a allocated traffic capacity to a virtual lik i a le treed utrate lik if we et the utrate lik ito leep mode. We alo might re-map a allocated traffic capacity to a virtual lik i a le treed utrate lik if re-mappig the traffic capacity provide eough adwidth capacity i the utrate lik for re-mappig of aother traffic capacity, which lead to miimum total lik power coumptio. The off-peak lik eergy optimizatio y local lik recofiguratio prolem for o-plittale traffic, that i formulated accordig to the Fixed lik power model, i called OL-LL-F. Thi prolem could e formulated a a BILP i category of multi-commodity flow prolem. Differet from plittale form, a allocated traffic capacity l l am,m i a utrate lik l with (l OL-LL-F i formulated a a BILP a follow: Optimizatio Variale: α(l (m) to a virtual lik ) < T, i a commodity. ) i 1 whe the phyical lik l ) i 0. z ( x,y l (m)) i a iary variale. If the re-allocated path for commodity l (m) pae through l x,y, z ( x,y l (m) ) = 1. Otherwie, z ( x,y l (m) ) = 0. ) i a auxiliary iary variale. α(l i active, otherwie Similarly, z (l x,y (m)) i a iary variale. β(l (m)) i a iary variale. It how l (m) tatu, after recofiguratio. It i 0 i the cae l (m) i removed, after recofiguratio. Otherwie, l (m) i 1. Ojective Fuctio: The ame ojective a Equatio 3. Cotrait: The cotrait i Equatio 5, 7, ad the followig: If the program decide to remove a allocated traffic capacity l (m), β(l (m)) will e equal to 0. Therefore, Equatio 16 eed to route a igle uit of data from ith utrate ode to jth utrate ode. Becaue variale z ( x,y l (m) ) i iary, the uit of data could ot e plitted. Beide, the cotrait i Equatio 17 limit the program routig, o maximum umer of icomig ad outgoig flow of every commodity, i ay ode, i two flow. Thi maitai a igle loople path. Thu, the drive route will e ued a a replaced path for l (m). If a allocated traffic capacity (m)) = 1), it will ot e re- l (m) i ot removed (β(l allocated. {y (x,y) E } z x,y ( l (m) ) {y (y,x) E } z y,x ( l (m) ) 1 β(l (m)) if x = i = β(l (m)) 1 if x = j 0 otherwie x V, { G Φ}, m = 1, 2,..., L, (i, j) E (16) {y (x,y) E } z x,y ( l (m) ) + {y (y,x) E } z y,x ( l (m) ) 2, x V, { G Φ}, m = 1, 2,..., L, (i, j) E (17), The total allocated traffic capacitie r(l ) i a phyical lik l durig off-peak period, i the ummatio of total urecofigured allocated traffic capacitie (β(l (m) = 1)) i l a well a the re-allocated traffic capacitie of other lik (like l x,y ) i l. r(l ) i calculated i Equatio 18. z (l x,y (m)) ŕx,y (m) i the re-allocated traffic capacity to (m) i l l x,y. r(l ) = L { G Φ} m=1 + (x,y) E { G Φ} m=1 { β(l (m))ŕ (m) } L { z (l x,y (m)) ŕx,y (m) } (18) The cotrait i Equatio 19 prevet the program to remap a allocated traffic capacity i a phyical lik l with (l ) T. β(l (m)) = 1, (i, j) {(i, j) (i, j) E, (l ) T }, { G Φ}, m = 1, 2,..., L (19) I additio, the variale mut hold the oud i Equatio 9, ad the followig: z x,y ( l (m)) {0, 1}, (x, y) E, { G Φ}, m = 1, 2,..., L, (i, j) E () β(l (m)) {0, 1}, (i, j) E, { G Φ}, m = 1, 2,..., L (21) The formulated iteger liear program for off-peak lik eergy optimizatio y local lik recofiguratio prolem, either for plittale traffic (OL-LL-F), or o-plittale traffic (OL-LL-F), could e reduced to the prolem dicued i [25] that i a imple two-commodity iteger flow prolem. It i prove at [25] that thi imple two-commodity iteger flow prolem i N P-hard. Hece, the formulated program are N P-hard. C. Program aed o Semi Proportioal Lik Power Model The previou ectio developed power avig program for VNE lik, coformig to Fixed lik power model. A it i dicued i Sectio III, Semi Proportioal lik power model defie a traffic adaptive power model for a phyical lik. Baed o thi lik power model, large portio of coumed eergy y ay phyical lik i for keepig the lik operatioal. Noethele, differet from Fixed lik power model, traffic load o the lik alo chage it power coumptio. Hece, every phyical lik i the utrate etwork doe ot coume the ame amout of eergy. I thi regard, it i poile reduce lik power coumptio y either ettig the lik ito leep mode, or y reroutig it traffic load to other phyical lik with higher adwidth capacity. However, we could ave larger amout of eergy y leepig the lik, i compario to reroutig it traffic load (c) 15 IEEE. Peroal ue i permitted, ut repulicatio/reditriutio require IEEE permiio. See for more iformatio.

8 Thi article ha ee accepted for pulicatio i a future iue of thi joural, ut ha ot ee fully edited. Cotet may chage prior to fial pulicatio. Citatio iformatio: DOI /TCC , IEEE Traactio o Cloud Computig JOURNAL OF IEEE TRANSACTIONS ON CLOUD COMPUTING 8 The ojective fuctio i previou program are required to e modified, o they optimize the eergy aed o Semi Proportioal lik power model. I thi regard, the ojective fuctio i Equatio 3 eed to e replaced y Equatio 22. { Miimize () E α(l )P (l ) + r(l ) C (l ) ( P m (l ) P (l ) ) } (22) By modifyig the ojective fuctio ad keepig the ame cotrait ad oud, the program recofigure mappig of allocated VN, accordig to Semi Proportioal lik power model defied i Equatio 2. Note that the off-peak lik eergy optimizatio y gloal lik recofiguratio prolem, which i formulated accordig to Semi Proportioal lik power model, i called OL-GL- SP. Beide, the off-peak lik eergy optimizatio y local lik recofiguratio prolem that i defied accordig to Semi Proportioal lik power model i called OL-LL-SP i the cae of plittale traffic, ad OL-LL-SP i the cae of oplittale traffic. V. HEURISTIC ALGORITHM The dicued BILP for OL-LL-F i Sectio IV-B2 i N P-hard, ad therefore the optimizatio olutio i ot calale to large etwork ize, due to it log executig time. I thi ectio, we propoe a calale heuritic algorithm for OL-LL-F. Peudo code of the propoed heuritic algorithm i how i Algorithm 1. The algorithm check the poiility of ettig VNE phyical lik ito leep mode durig the off-peak time. Thi proce mut e doe preciely i order to guaratee that etwork upport off-peak traffic demad of all the ivolved VN. I thi regard, the algorithm firt calculate ome metric ad the ort the phyical lik i order to check the lik removal poiility. Afterward, it trie to fid a alterative path for off-peak traffic of every allocated traffic capacity to a virtual lik i the removed phyical lik. Thi proce i doe i multiple phae. Durig the off-peak period, the availale adwidth capacity i l i repreeted y C (l ). C (l ) i equal to it phyical capacity utracted y total reerved off-peak traffic capacitie for virtual lik i l. Equatio 23 defie C (l ). Beide, G T i off-peak utrate topology. At firt, G T i the ame a utrate etwork topology. C (l ) = C (l ) L { G Φ} m=1 ŕ (m) (23) Becaue the utrate lik with higher tre rate are more eetial i regard to traffic demad ad the poile iterruptio, the algorithm tart ettig utrate lik ito leep mode from the lik that ha the lowet tre rate. It ort the utrate lik with (l ) < T i acedig order aed o. The lit i repreeted y S L. I the ext phae, the algorithm remove the phyical lik that are capale to e et ito leep mode, from G T, ad Algorithm 1 Heuritic Algorithm for OL-LL-F 1: for all (i, j) uch that (i, j) E do 2: if (l ) < T the 3: place the lik i S L i acedig order aed o 4: ed if 5: ed for 6: for all (i, j) uch that l i the top uchecked lik i S L do 7: 8: remove (i, j) from G T for all uch that G Φ do 9: for all m uch that m = 1, 2,..., L do 10: if there i a alterative path from ode i to ode j (y Dijktra) i G T the 11: for all (x, y) uch that l x,y i o the alterative path do 12: C (l x,y ) = C (l x,y ) ŕ (m) 13: if C (l x,y ) < 0 the 14: C (l x,y ) = C (l x,y ) + ŕ (m) 15: place (i, j) ack to G T 16: udo all the previou capacity ad traffic modificatio repective to l 17: reak ad go for ext utrate lik i S L 18: ele 19: ŕ x,y (m) = ŕ x,y (m) + ŕ (m) : ed if 21: ed for 22: ele 23: place (i, j) ack to G T 24: udo all the previou capacity ad traffic modificatio repective to l 25: reak ad go for ext utrate lik i S L 26: ed if 27: ed for 28: ed for 29: ed for : retur G T at the ed it retur G T a the eergy-efficiet off-peak utrate topology. Thi phae alo eure the rearraged etwork accommodate the off-peak traffic demad. I thi regard, there mut e a igle replaced path for each removed traffic capacity that upport it off-peak traffic demad. The algorithm trie to fid uch a alterative path for every allocated traffic capacity to a virtual lik i every phyical lik with (l ) < T. The algorithm ue Dijktra algorithm a the preferred routig algorithm to fid the hortet alterative path, while every active phyical lik cot i aumed a 1. It i eeded to check eligiility of every utrate lik o the path i regard to the availale off-peak adwidth capacity. Three coditio might happe while the algorithm earche for uch a replaced path: There i uch a alterative path i G T. So, the algorithm update the repective C, ad allocate the repective traffic capacity i all the utrate lik over the path. There i a alterative path i G T, ut oe or ome of the utrate lik over the path do ot upport the off-peak traffic demad. Therefore, the algorithm place the repective phyical lik ack to G T, cacel all the previou capacity ad traffic modificatio, ad aort checkig proce for ret of the allocated traffic capacitie i thi phyical lik. There i o alterative path i G T. Hece, the algorithm place ack the repective phyical lik to G T, cacel all the previou capacity ad traffic modificatio, ad aort checkig proce for ret of the allocated traffic capacitie i thi phyical lik. After checkig proce for all of the removed phyical (c) 15 IEEE. Peroal ue i permitted, ut repulicatio/reditriutio require IEEE permiio. See for more iformatio.

9 Thi article ha ee accepted for pulicatio i a future iue of thi joural, ut ha ot ee fully edited. Cotet may chage prior to fial pulicatio. Citatio iformatio: DOI /TCC , IEEE Traactio o Cloud Computig JOURNAL OF IEEE TRANSACTIONS ON CLOUD COMPUTING 9 lik, G T i retured a the eergy-efficiet off-peak utrate topology. It i expected the uggeted heuritic for OL-LL-F i much impler ad fater tha the BILP. The larget loop, tart i lie 6 ad ed i lie 29, determie the complexity of the propoed heuritic. Thi loop ru for every phyical lik, o it complexity i O( E ). The firt u-loop tart i lie 8 ru for every VN, ad therefore it complexity i O( Φ ). The ecod u-loop tart i lie 9 ru for every virtual lik i the repective virtual etwork. Coiderig the wort cae, the complexity of thi u-loop i O( Ev m ), where Ev m i the et of edge of the ivolved virtual etwork with the larget umer of virtual lik. The heuritic call Dijktra algorithm i lie 10. The complexity of Dijktra algorithm i the wort cae i O ( E + V logv )). The third u-loop tartig i lie 11 check the capaility of every utrate lik o the foud path. So, it complexity i O( E ). I the wort cae ceario, the heuritic might eed to check all the phyical lik agai, i order to udo the capacity ad traffic modificatio for each re-allocated traffic capacity. So, complexity of the udoig fuctio i O( E Φ Ev m ). Hece, the complexity of the propoed heuritic i O ( E 3 Φ 2 Ev m 2 ( E + V log V ) ). Coequetly, the propoed heuritic algorithm i much impler ad it could e olved i a polyomial time. VI. EVALUATION The propoed eergy avig olutio are uppoed to reduce total lik power coumptio i VNE durig off-peak hour. However, they eed to guaratee the off-peak traffic requiremet. I order to evaluate their effectivee, everal radom VNE etup have ee evaluated. Recetly, Waxma algorithm [26] i widely ued y the reearcher to geerate radom virtual/utrate topologie for VNE [13], [14], [27] [29]. Therefore, i thi paper, utrate ad virtual etwork topologie are geerated y Waxma algorithm. Waxma geerate radom etwork topologie aed o two parameter, λ ad µ. A λ grow the proaility of havig a edge etwee ay ode i the topology i icreaed. A µ grow there i a larger ratio of log edge to hort edge. I thi paper, we chooe the Waxma parameter, for oth utrate ad virtual etwork topologie, a λ = µ = 0.5, i the area ize of After creatig radom utrate ad virtual etwork topologie, the utrate lik capacity ad virtual lik peak demad are geerated radomly with a uiform ditriutio. The adwidth capacity of each phyical lik i a radom amout etwee 100Mp ad 0Mp, ut each virtual lik adwidth demad i geerated radomly etwee Mp ad 80Mp. Both radomly geerated utrate ad virtual etwork are ymmetric, o if there i a lik from ith ode to jth ode with a pecific amout of adwidth capacity, there i alo a lik from jth ode to ith ode with the ame amout of adwidth capacity. I the ext tep, the created virtual ode are mapped to the utrate ode radomly with the uiform ditriutio. Afterward, every geerated virtual lik peak adwidth demad i allocated o a utrate path through a tate-of-art heuritic algorithm. y coordiate Virtual Node Virtual Lik x coordiate Fig. 2 (a) A Radom VN y coordiate Sutrate Node Allocated Virtual Node 10 Sutrate Lik Allocated Virtual Lik x coordiate () A Radom Sutrate Network For example, Figure 2a how a radomly geerated virtual etwork. Beide, Figure 2 demotrate a radomly geerated utrate etwork that iclude allocated ode ad lik of the geerated virtual etwork i Figure 2a. A it i dicued, the formulated ILP are N P-hard, o they are ot calale to large etwork ize. Therefore, we ae capaility of the defied ILP o mall radom imulatio etup, imilar to the other related work i [13] [15], [22]. The ILP are olved y MOSEK olver []. Noethele, theoretical complexity aalyi reveal the propoed heuritic algorithm i much impler, ad therefore it i calale to large etwork ize. Hece, performace of the uggeted heuritic i examied o large radom imulatio etup. Every mall radom imulatio etup cotai 10 radomly geerated VNE. Each VNE i a mall radom imulatio etup ha 2 radom virtual etwork that are allocated o a igle radom utrate etwork, while every utrate ad virtual etwork ha 10 ode. The average umer of phyical lik i the mall radom imulatio etup i. Furthermore, every large radom imulatio etup iclude 10 radomly geerated VNE. All the VNE i a large radom imulatio etup have at leat 2 radom virtual etwork that are mapped o a igle radom utrate etwork, while the utrate etwork ha phyical ode ad each virtual etwork ha virtual ode. The average umer of phyical lik i the large radom imulatio etup i 590. We aume T = 0.6, ule otherwie tated. The average reult icludig cofidece iterval with the cofidece level of 90% are calculated for each etup. Firt, we olved the formulated MILP for OL-GL-F, ad OL-LL-F o a mall radom imulatio etup, while traffic i aumed to e plittale. Both have ee olved for differet amout of off-peak traffic ratio. Off-peak traffic ratio i the fractio of etwork off-peak traffic rate y it peak traffic rate. The average umer of phyical lik i leep mode durig the off-peak period ha ee proed ad how i Figure 3a. The reult illutrate oth of OL-GL-F ad OL- LL-F are ale to et otale umer of phyical lik ito leep mode durig thi time. Beide, the umer of phyical lik i leep mode i decreaig y icreaig the off-peak traffic ratio. Thi i ecaue icreaig off-peak traffic ratio icreae the amout of traffic program eed to re-allocate, o they are more limited i term of fidig alterative path. OL-GL-F i expected to deliver the mot optimum level of eergy avig. However, differet from OL-GL-F, OL-LL- F eale the provider to adjut level of the recofiguratio ad cotrol the poile traffic diruptio. Thi i poile (c) 15 IEEE. Peroal ue i permitted, ut repulicatio/reditriutio require IEEE permiio. See for more iformatio.

10 Thi article ha ee accepted for pulicatio i a future iue of thi joural, ut ha ot ee fully edited. Cotet may chage prior to fial pulicatio. Citatio iformatio: DOI /TCC , IEEE Traactio o Cloud Computig JOURNAL OF IEEE TRANSACTIONS ON CLOUD COMPUTING 10 Phyical Lik i Sleep Mode (%) Total Lik Power Coumptio (Watt) OL-GL-F OL-LL-F (a) OL-LL-SP Semi Proportioal-Before Recofiguratio OL-LL-F Fixed-Before Recofiguratio 10 (d) Total Lik Power Coumptio (Watt) Total Saved Power i Phyical Lik (%) OL-GL-SP Semi Proportioal-Before Recofiguratio OL-GL-F Fixed-Before Recofiguratio () (e) OL-LL-SP OL-LL-F OL-LL-SP OL-LL-F Total Lik Power Coumptio (Watt) Phyical Lik i Sleep Model (%) OL-LL-SP Semi Proportioal-Before Recofiguratio OL-LL-F Fixed-Before Recofiguratio (c) Heuritic for OL-LL-F BILP for OL-LL-F 0 Fig. 3. (a) Off-peak lik eergy optimizatio y gloal lik recofiguratio v. local lik recofiguratio (plittale traffic). () Total lik power coumptio of off-peak lik eergy optimizatio y gloal lik recofiguratio. (c) Total lik power coumptio of off-peak lik eergy optimizatio y local lik recofiguratio for plittale traffic. (d) Total lik power coumptio of off-peak lik eergy optimizatio y local lik recofiguratio for o-plittale traffic. (e) Total aved power with off-peak lik eergy optimizatio y local lik recofiguratio for plittale ad o-plittale traffic. (f) BILP v. heuritic for off-peak lik eergy optimizatio y local lik recofiguratio (o-plittale traffic). through the cotrait i Equatio 13 that prevet the local lik recofiguratio olutio to modify the allocated traffic capacitie i phyical lik with tre rate larger tha a threhold, et y the provider. Although thi approach could help decreaig the poile traffic diruptio, it eed to provide the poiility of achievig the maximum eergy avig level for the provider. Sice the ize of geerated VNE are mall i the mall imulatio etup, the tre rate for mot of the phyical lik i le tha choe tre rate threhold of 0.6. Therefore, Figure 3a cofirm whe the cotrait i Equatio 13 i relaxed, OL-LL-F could achieve the ame eergy avig level a OL-GL-F. I additio, we meaured total lik power coumptio for oth off-peak lik eergy optimizatio y gloal lik recofiguratio ad local lik recofiguratio olutio o a mall radom imulatio etup. Thi meauremet ha ee doe accordig to oth Fixed ad Semi Proportioal lik power model. The total lik power coumptio ha ee meaured for off-peak ratio rage of 0.1 to 0.9, efore ad after applyig the propoed eergy avig olutio. Accordig to [22] ad ecaue the radom phyical lik capacitie are geerated uiformly i the rage of 100-0Mp, P i 0.9Watt ad P m i 1.0Watt for ay phyical lik. The meauremet reult for off-peak lik eergy optimizatio y gloal lik recofiguratio, ad off-peak lik eergy optimizatio y local lik recofiguratio for plittale ad o-plittale traffic, are how i Figure 3, 3c, ad 3d, repectively. The reult i Figure 3, 3c, ad 3d, demotrate all of the formulated program are ale to reduce VNE lik power coumptio, effectively. Coiderig the reult of whe Fixed lik power model i ued, the total lik power coumptio for ay off-peak traffic rate i cotat, while o eergy avig olutio i employed. Neverthele, the power coumptio i chagig with the traffic rate eve efore applyig ay eergy avig olutio, whe Semi Proportioal lik power model i ued. By applyig ay of the propoed eergy avig techique (gloal/local lik recofiguratio), the total lik power coumptio aed o oth lik power model will e decreaed. Note that icreaig the off-peak ratio raie the total lik power coumptio, a the larger umer of lik will e left activated. I the ame imulatio etup, we calculated the percetage of power aved i phyical lik, y the formulated program for off-peak lik eergy optimizatio y local lik recofiguratio prolem. Thi i teted i the cae of plittale ad o-plittale traffic, for oth Fixed ad Semi Proportioal lik power model. The reult are how i Figure 3e. The outcome of program how the rate of power we could ave i phyical lik i decreaig whe the off-peak ratio i icreaig, ecaue the program are more limited i term of fidig alterative path. Beide, Figure 3e illutrate it i proale to ave higher amout of eergy whe traffic i plittale, i compario to whe traffic i o-plittale. Thi i ecaue the program are more flexile i term of fidig alterative path whe they could plit the traffic to multiple path. Moreover, Figure 3e cofirm we could reach higher rate of eergy avig whe the ojective fuctio i formulated accordig to the Fixed lik power model, i compario to whe the ojective fuctio i formulated aed o Semi Proportioal lik power model. Thi i maily due to two reao. Firt, ice the power coumptio i varyig aed o traffic load i Semi Proportioal lik power model (f) (c) 15 IEEE. Peroal ue i permitted, ut repulicatio/reditriutio require IEEE permiio. See for more iformatio.

11 Thi article ha ee accepted for pulicatio i a future iue of thi joural, ut ha ot ee fully edited. Cotet may chage prior to fial pulicatio. Citatio iformatio: DOI /TCC , IEEE Traactio o Cloud Computig JOURNAL OF IEEE TRANSACTIONS ON CLOUD COMPUTING 11 rather tha eig a cotat amout aed o Fixed lik power model, a phyical lik power coumptio i the cae of Semi Proportioal lik power model i le tha whe Fixed lik power model i employed. Coequetly, the amout of aved eergy with Semi Proportioal lik power model might e le tha the amout of aved eergy with Fixed lik power model, if the program et the ame phyical lik ito leep mode. I additio, if the eergy avig program et a phyical lik ito leep mode, it eed to fid a alterative path to upport the off-peak traffic of the removed lik. I the cae of Semi Proportioal lik power model, the rerouted traffic icreae the power coumptio over the alterative path. However, i the cae of Fixed lik power model, ice traffic load doe ot affect lik power coumptio, the rerouted traffic doe ot icreae the power coumptio over the alterative path. Furthermore, we olved the formulated BILP for OL-LL- F ad compared it aility i term of leepig phyical lik to the propoed heuritic for the ame prolem. The average reult are meaured for differet off-peak traffic ratio o a mall radom imulatio etup, ad how i Figure 3f. The BILP reult et the optimum poit, while the heuritic algorithm till reveal reaoale reult. However, the heuritic algorithm i much impler ad fater i term of required ru time. Note that i Figure 3f, the differece etwee BILP ad heuritic reult i maller whe off-peak traffic ratio i high, ecaue there are le eergy avig opportuitie whe off-peak traffic rate are high. Whe offpeak ratio i low, it i more proale to fid alterative path for off-peak traffic demad, ad a the BILP i more effective tha the heuritic, the BILP ave higher level of eergy i compario to the heuritic. Neverthele, whe off-peak ratio i high, there will e le alterative optio to reallocate the traffic, o the BILP ad the heuritic work more cloely. It i alo importat to evaluate effectivee of the propoed heuritic algorithm for OL-LL-F. We ae the aility of the heuritic aed o differet factor o the defied large radom imulatio etup. The heuritic i formulated aed o Fixed lik power model. I thi regard, the total lik power coumptio i meaured for differet off-peak ratio, efore ad after applyig the propoed heuritic o a large radom imulatio etup. The average reult are how i Figure 4a. The power coumptio i cotat efore applyig the heuritic. By applyig the heuritic, the total VNE lik power coumptio will e reduced. Note that icreaig the off-peak ratio raie the total lik power coumptio, a the larger umer of lik are left active. Beide, it i eetial to check aility of the heuritic for differet umer of ivolved virtual etwork, a icreaig the umer of virtual etwork add everal cotrait i term of leepig a igle phyical lik. The aility of the propoed heuritic o ettig phyical lik ito leep mode durig the off-peak hour, i teted over two large radom imulatio etup. I the firt large radom etup, each VNE cotai two virtual etwork, ut i the ecod large radom etup, every VNE iclude three virtual etwork. The effectivee of the algorithm i evaluated for the rage of off-peak traffic ratio. The average reult for oth etup are how i Figure 4. Figure 4 how it i proale to et otale umer of phyical lik durig the off-peak period, y implemetig the uggeted heuritic algorithm. For the firt etup, whe the off-peak traffic ratio i 0.1, the propoed heuritic et 89.12% of the phyical lik ito leep mode. Thi happe while the recofiguratio heuritic till accommodate offpeak traffic demad of ivolved VN. I additio, Figure 4 cofirm mappig a extra virtual etwork oto the utrate etwork degrade the aility of heuritic i term of avig power. Thi i ecaue the algorithm aee the allocated traffic capacitie to every virtual lik i each utrate lik i order to fid a replaced path. By addig ew virtual etwork, ew virtual lik are mapped oto phyical lik, ad therefore there are more cotrait for the algorithm. Coequetly, maller umer of phyical lik i capale to e et ito leep mode over off-peak hour. Moreover, decreaig off-peak ratio decreae the differece etwee outcome of the firt ad ecod imulatio etup. Whe off-peak traffic rate i low, the program are more flexile i term of fidig alterative path. Hece, the eergy avig aility of the program i le affected y addig extra virtual etwork whe off-peak ratio i low, i compario to whe we have high off-peak traffic rate. Moreover, it i explaied i Sectio V that the propoed heuritic, imilar to the formulated BILP for OL-LL-F, doe ot re-allocate the allocated traffic capacitie i phyical lik ) T, i order to decreae ervice diruptio due to recofiguratio. Figure 4c tudie the effect of chagig tre rate threhold T o capaility of the heuritic for ettig phyical lik ito leep mode, over a large radom imulatio etup. Figure 4c how decreaig T, decreae umer of phyical lik the heuritic et ito leep mode, ecaue maller umer of utrate lik are coidered for power avig. Although ettig maller T decreae amout of power the olutio could ave, it reduce the traffic iterruptio, due to recofiguratio. Coequetly, the provider could cotrol poile traffic iterruptio y adjutig T. Note that ecaue of the pecific choe amout of phyical ad virtual lik adwidth capacity i our defied large radom imulatio etup, the tre rate of mot of the phyical lik i the coidered imulatio etup i le tha 0.3. Coequetly, the heuritic outcome i almot cotat for T of greater tha 0.3. Additioally, a metioed i Sectio II, the uggeted heuritic for OL-LL-SP i expected to e more effective compared to our previou work [15] ad other imilar tudie i [8], [21]. We compared the outcome of the propoed heuritic i thi paper to our previou algorithm i [15], over a large radom imulatio etup. A the reult i clear i Figure 4d, thi lik recofiguratio algorithm i ale to et higher umer of phyical lik ito leep mode over off-peak hour, with the ame cotrait. Thi i ecaue the method i [8], [15], [21] doe ot modify the allocatio of mapped virtual etwork, while they oly reroute the traffic to the already allocated traffic capacitie to virtual lik. Noethele, i thi paper, we recofigure mappig of virtual lik to reach higher eergy avig rate. Furthermore, re-allocatig the traffic capacitie i the other with (l (c) 15 IEEE. Peroal ue i permitted, ut repulicatio/reditriutio require IEEE permiio. See for more iformatio.

12 Thi article ha ee accepted for pulicatio i a future iue of thi joural, ut ha ot ee fully edited. Cotet may chage prior to fial pulicatio. Citatio iformatio: DOI /TCC , IEEE Traactio o Cloud Computig JOURNAL OF IEEE TRANSACTIONS ON CLOUD COMPUTING 12 Total Lik Power Coumptio (Watt) Phyical Lik i Sleep Mode (%) After Recofiguratio Before Recofiguratio (a) 0 (d) Our Previou Algorithm Recofiguratio Heuritic Phyical Lik i Sleep Mode (%) Mea Utilizatio Each ceario ha 2 VN Each ceario ha 3 VN () Peak Time Off-Peak Time efore Recofiguratio Off-Peak Time after Recofiguratio (e) Phyical Lik i Sleep Mode (%) Total Lik Power Coumptio (Watt) Stre Rate Threhold 80 (c) Before Recofiguratio After Recofiguratio Fig. 4. (a) Total lik power coumptio of off-peak lik eergy optimizatio y local lik recofiguratio heuritic. () Lik recofiguratio heuritic for differet umer of ivolved VN. (c) Effect of chagig tre rate threhold o heuritic outcome (d) Lik recofiguratio heuritic v. our previou algorithm. (e) Mea lik utilizatio over differet cofiguratio. (f) Total lik power coumptio efore ad after applyig the heuritic o the GÉANT imulatio etup. utate lik caue chage to the lik utilizatio. Accordigly, it i eeded to make ure the icreaed utilizatio i cotrolled ad doe ot caue cogetio. Lik utilizatio for three differet cofiguratio i teted o a large radom imulatio etup, ad the average reult are how i Figure 4e. The firt cofiguratio i for peak time whe allocated adwidth i ale to hadle Wort-Cae ceario. The ecod cofiguratio i for the off-peak period while o eergy avig algorithm i implemeted. Over thi period the lik are le utilized while the ame adwidth capacity i allocated ad coume the ame power a the peak time. After applyig our uggeted heuritic, the average lik utilizatio i icreaed, ut it i till le tha the maximum utilizatio. It i alo eceary to validate the effectivee of our propoed approach agait a real topology. I thi regard, we teted the propoed heuritic o a ew radom imulatio etup that cotai 10 radomly geerated VNE. Each VNE i thi ew radom imulatio etup, ha 2 radom virtual etwork that are mapped oto the GÉANT etwork topology [31], while every virtual etwork ha 10 ode. GÉANT ha 22 ode ad 36 idirectioal lik. We coidered GÉANT etwork a the utrate etwork, ecaue it i a real uiveral topology. Figure 4f how the reult for thi etup. The reult cofirm the heuritic i ale to effectively reduce the etwork lik power coumptio. All the formulated ILP i thi paper are N P-hard, while complexity of the propoed heuritic algorithm i O ( E 3 Φ 2 E m v 2 ( E + V log V ) ). So, it i expected the propoed heuritic eed le ru time i compario to the formulated iteger liear program. We verified ru time for each method (whe the ojective i defied aed o Fixed lik power model) o a igle mall radom VNE that ha a utrate etwork ad 2 virtual etwork, while each ha 10 ode. The ru time i meaured for each formulated optimizatio program a well a the heuritic, whe off-peak ratio i 0.5. The ru time of the MILP for OL-GL-F ad OL- LL-F are ecod ad 3,2.4 ecod, repectively. Beide, the ru time of the BILP for OL-LL-F i,322.0 ecod. However, the ru time of the heuritic for OL-LL- F i oly 0.09 ecod, which i o mall i compario to the required ru time for the formulated BILP of the ame prolem. The ru time for local lik recofiguratio BILP for o-plittale traffic i higher tha the MILP of the ame prolem for plittale traffic. Thi i ecaue the BILP eed to fid a alterative path for every allocated traffic capacity i utrate lik, while the MILP ha to fid a alterative path for every udled traffic capacity. Therefore, the BILP for o-plittale traffic ha more cotrait tha the MILP for plittale traffic. I additio, the ru time of local lik recofiguratio MILP for plittale traffic i larger tha the ru time for gloal lik recofiguratio MILP, ice the local lik recofiguratio i more complex ad ha larger umer of cotrait tha the gloal lik recofiguratio. The imulatio reult prove the uggeted eergy avig olutio are ale to reduce VNE lik power coumptio, durig the off-peak period, effectively. Beide, the propoed heuritic i a imple ad fat algorithm that work cloely to the optimum poit. Note that every imulatio etup i quite large to cover a utatial umer of radom topologie i order to verify the effectivee of the propoed olutio. Beide, the calculated cofidece iterval cofirm the reult are precie eough to reveal igificace of uggeted eergy (f) (c) 15 IEEE. Peroal ue i permitted, ut repulicatio/reditriutio require IEEE permiio. See for more iformatio.

13 Thi article ha ee accepted for pulicatio i a future iue of thi joural, ut ha ot ee fully edited. Cotet may chage prior to fial pulicatio. Citatio iformatio: DOI /TCC , IEEE Traactio o Cloud Computig JOURNAL OF IEEE TRANSACTIONS ON CLOUD COMPUTING 13 avig method. VII. CONCLUSION ICT eergy coumptio i growig fat, accordig to the latet pulihed report. ISP are eeded to expad their ifratructure i order to hadle the higher traffic load. VNE techology help to low dow the ifratructure expaio. Noethele, it i alo eetial to have eergy avig techique that decreae VNE eergy coumptio. I thi paper, we dicued multiple ovel eergy avig olutio that gloally/locally optimize VNE lik power coumptio, durig off-peak time. The propoed fie-graied local recofiguratio eale the provider to adjut level of the recofiguratio, ad accordigly cotrol the poile traffic diruptio. A Iteger Liear Program (ILP) i formulated for each prolem. Sice the ILP are N P-hard, a ovel heuritic algorithm i alo propoed. Simulatio reult how the eergy avig olutio are oticealy effective ad the heuritic achieve cloely to the optimum poit. Becaue phyical ode are alo eetial power coumer i VNE, it i eceary to develop eergy avig techique that miimize oth ode ad lik power coumptio i VNE, i the future work,. REFERENCES [1] G.-Q. Zhag, G.-Q. Zhag, Q.-F. Yag, S.-Q. Cheg, ad T. Zhou, Evolutio of the iteret ad it core, New Joural of Phyic, IOP Pulihig, vol. 10, o. 12, p. 1227, 08. [2] R. Bolla, F. Davoli, R. Bruchi, K. Chritee, F. Cucchietti, ad S. Sigh, The potetial impact of gree techologie i ext-geeratio wirelie etwork: I there room for eergy avig optimizatio? Commuicatio Magazie, IEEE, vol. 49, o. 8, pp , 11. [3] J. S. Turer ad D. E. Taylor, Diverifyig the iteret, i Gloal Telecommuicatio Coferece (GLOBECOM), IEEE, vol. 2, 05, pp. 6 pp. 7. [4] N. Chowdhury ad R. Boutaa, A urvey of etwork virtualizatio, Computer Network, Elevier, vol. 54, o. 5, pp , 10. [5] G. Rizzelli, A. Morea, M. Toratore, ad O. Rival, Eergy efficiet traffic-aware deig of o-off multi-layer tralucet optical etwork, Computer Network, Elevier, vol. 56, o. 10, pp , 12. [6] H. Feg ad Y. Shu, Study o etwork traffic predictio techique, i Iteratioal Coferece o Wirele Commuicatio, Networkig ad Moile Computig, IEEE, 05, pp [7] A. S. Sa-Qi, A predictaility aalyi of etwork traffic, Computer Network, Elevier, vol. 39, o. 4, pp , 02. [8] F. Idzikowki, S. Orlowki, C. Raack, H. Woeer, ad A. Woliz, Dyamic routig at differet layer i ip-over-wdm etwork-maximizig eergy avig, Optical Switchig ad Networkig, Elevier, vol. 8, o. 3, pp , 11. [9] L. Chiaraviglio, M. Mellia, ad F. Neri, Reducig power coumptio i ackoe etwork, i Iteratioal Coferece o Commuicatio (ICC), IEEE, 09, pp [10] A. Ficher, M. T. Beck, ad H. D. Meer, A approach to eergy-efficiet virtual etwork emeddig, i Iteratioal Sympoium o Itegrated Network Maagemet (IM), IFIP/IEEE, 13, pp [11] S. Su, Z. Zhag, X. Cheg, Y. Wag, Y. Luo, ad J. Wag, Eergyaware virtual etwork emeddig through coolidatio, i Computer Commuicatio Workhop (INFOCOM WKSHPS), IEEE, 12, pp [12] B. Wag, X. Chag, J. Liu, ad J. K. Muppala, Reducig power coumptio i emeddig virtual ifratructure, i Gloecom Workhop (GC Wkhp), IEEE, 12, pp [13] J. F. Botero, X. Heelach, M. Duelli, D. Schloer, A. Ficher, ad H. D. Meer, Eergy efficiet virtual etwork emeddig, Commuicatio Letter, IEEE, vol. 16, o. 5, pp , 12. [14] J. F. Botero ad X. Heelach, Greeer etworkig i a etwork virtualizatio eviromet, Computer Network, Elevier, vol. 57, o. 9, pp , 13. [15] E. Ghaziaeedi, N. Wag, ad R. Tafazolli, Lik leepig optimizatio for gree virtual etwork ifratructure, i Gloecom Workhop (GC Wkhp), IEEE, 12, pp [16] M. F. Zhai, Q. Zhag, G. Simo, ad R. Boutaa, Vdc plaer: Dyamic migratio-aware virtual data ceter emeddig for cloud, i Iteratioal Sympoium o Itegrated Network Maagemet (IM), IFIP/IEEE, 13, pp [17] D. Lo, L. Cheg, R. Govidaraju, L. A. Barroo, ad C. Kozyraki, Toward eergy proportioality for large-cale latecy-critical workload, i Proceedig of the 41t aual iteratioal ympoium o Computer architecuture, IEEE Pre, 14, pp [18] C. Xi, B. Wag, X. Cao, ad J. Li, Logical topology deig for dyamic traffic groomig i wdm optical etwork, Joural of Lightwave Techology, IEEE, vol. 24, o. 6, p. 2267, 06. [19] G. She ad R. Tucker, Eergy-miimized deig for ip over wdm etwork, Joural of Optical Commuicatio ad Networkig, IEEE/OSA, vol. 1, o. 1, pp , 09. [] L. Chiaraviglio, M. Mellia, ad F. Neri, Miimizig ip etwork eergy cot: formulatio ad olutio, Traactio o Networkig (TON), IEEE/ACM, vol., o. 2, pp , 12. [21] Y. Zhag, M. Toratore, P. Chowdhury, ad B. Mukherjee, Eergy optimizatio i ip-over-wdm etwork, Optical Switchig ad Networkig, Elevier, vol. 8, o. 3, pp , 11. [22] A. P. Biazio, C. Chaudet, F. Larroca, D. Roi, ad J. Rougier, Eergy-aware routig: a reality check, i GLOBECOM Workhop (GC Wkhp), IEEE, 10, pp [23] P. Mahadeva, P. Sharma, S. Baerjee, ad P. Ragaatha, A power echmarkig framework for etwork device, er. NETWORKING, Spriger, 09, pp [24] C. Guarate, K. Chritee, ad B. Nordma, Maagig eergy coumptio cot i dektop pc ad la witche with proxyig, plit tcp coectio, ad calig of lik peed, Iteratioal Joural of Network Maagemet, Wiley Olie Lirary, vol. 15, o. 5, pp , 05. [25] S. Eve, A. Itai, ad A. Shamir, O the complexity of time tale ad multi-commodity flow prolem, i 16th Aual Sympoium o Foudatio of Computer Sciece, IEEE, 1975, pp [26] B. M. Waxma, Routig of multipoit coectio, Selected Area i Commuicatio, IEEE, vol. 6, o. 9, pp , [27] A. Ficher, J. F. B. Vega, M. Duelli, D. Schloer, X. H. Serra, ad H. D. Meer, Alevi-a framework to develop, compare, ad aalyze virtual etwork emeddig algorithm, Ope-Acce-Joural Electroic Commuicatio of the EASST, 11. [28] J. Zhu ad T. Wolf, Vmech: a echmark for virtual etwork mappig algorithm, i 21t Iteratioal Coferece o Computer Commuicatio ad Network (ICCCN), IEEE, 12, pp [29] M. T. Beck, A. Ficher, H. de Meer, J. F. Botero, ad X. Heelach, A ditriuted, parallel, ad geeric virtual etwork emeddig framework, i Iteratioal Coferece o Commuicatio (ICC), IEEE, 13, pp [] E. D. Adere ad K. D. Adere, The MOSEK iterior poit optimizer for liear programmig: a implemetatio of the homogeeou algorithm, er. High performace optimizatio. Spriger, 00, pp [31] Geat; the pa europea data etwork project. Erahim Ghaziaeedi received hi M.Sc. degree i Moile ad Satellite Commuicatio from the Uiverity of Surrey, Eglad, i 11. He i curretly puruig the Ph.D. degree i Electrical ad Computer Egieerig at the Departmet of Sytem ad Computer Egieerig, Carleto Uiverity, Caada. Hi mai reearch iteret are i commuicatio etwork, etwork virtualizatio, ad etwork optimizatio. Chagcheg Huag received hi Ph.D. degree i Electrical Egieerig from Carleto Uiverity, Caada, i Sice July 00, he ha ee with the Departmet of Sytem ad Computer Egieerig at Carleto Uiverity, where he i curretly a profeor. Hi reearch iteret are tochatic cotrol i computer etwork, reource optimizatio i wirele etwork, reliaility mechaim for optical etwork, etwork protocol deig ad implemetatio iue (c) 15 IEEE. Peroal ue i permitted, ut repulicatio/reditriutio require IEEE permiio. See for more iformatio.