IEEE ICC 2014 - Next-Geneaton Netwokng Symposum 1 Jont Vtual Machne and Bandwdth Allocaton n Softwae Defned Netwok (SDN) and Cloud Computng Envonments Jonathan Chase, Rakpong Kaewpuang, Wen Yonggang, and Dust Nyato School of Compute Engneeng, Nanyang Technologcal Unvesty, Sngapoe. Abstact Cloud computng povdes uses wth geat flexblty when povsonng esouces, wth cloud povdes offeng a choce of esevaton and on-demand puchasng optons. Resevaton plans offe cheape pces, but must be chosen n advance, and theefoe must be appopate to uses equements. If demand s uncetan, the esevaton plan may not be suffcent and on-demand esouces have to be povsoned. Pevous wok focused on optmally placng vtual machnes wth cloud povdes to mnmze total cost. Howeve, many applcatons eque lage amounts of netwok bandwdth. Theefoe, consdeng only vtual machnes offes an ncomplete vew of the system. Explotng ecent developments n softwae defned netwokng (SDN), we popose a unfed appoach that ntegates vtual machne and netwok bandwdth povsonng. We solve a stochastc ntege pogammng poblem to obtan an optmal povsonng of both vtual machnes and netwok bandwdth, when demand s uncetan. Numecal esults clealy show that ou poposed soluton mnmzes uses costs and povdes supeo pefomance to altenatve methods. We beleve that ths ntegated appoach s the way fowad fo cloud computng to suppot netwok ntensve applcatons. Index Tems Cloud computng, softwae defned netwok, vtual machne, bandwdth allocaton I. INTRODUCTION Cloud computng pemts uses to access computng esouces fom cloud povdes ove the Intenet. Vtualzaton technology allows uses to access computng esouces by entng vtual machnes (VMs) that ae taloed to the equements. Cloud povdes offe pepad esevaton nstances at a educed usage pce, wth addtonal VMs obtanable on demand at a hghe pce. When demand s unknown n advance, thee s a hgh sk of ethe undepovsonng (when the use eseves too few esouces fo the needs) o ovepovsonng (use eseves too many esouces and pays fo esouces they do not need). A boke can be used to mnmze cost though effcent VM povsonng. Howeve, wth many cloud-based applcatons equng a lage amount of Intenet bandwdth, an appoach that focuses puely on VM placement s too smplstc, a unfed appoach that ncopoates bandwdth esevaton s needed. To acheve ths, we explot the contol offeed by a new and developng technology called softwae defned netwokng (SDN) [1]. SDN s an appoach to netwok vtualzaton that sepaates netwok contol fom the mechancs of outng. SDN uses a thee laye achtectue wth an applcaton laye whee uses can un contol pogams that ae mplemented tanspaently by the lowe level contol and nfastuctue layes. Ths applcaton laye allows the netwok contolle to offe a vtual netwok, wth vtual outes and lnks, that the contolle then mplements on the physcal netwok. Thus netwok contolles can offe esevaton and on-demand bandwdth. In ths pape, we popose a unfed optmal povsonng algothm that places VMs and netwok bandwdth to mnmze a uses costs. The algothm makes a decson to eseve VMs and netwok bandwdth fom cetan cloud povdes to mnmze costs, by tadng off the cost of ovepovsonng aganst the cost of on-demand esouces. We fomulate a stochastc ntege pogammng (SIP) poblem wth two-stage ecouse to obtan the optmal decson. We demonstate the soluton s effectveness though vaous numecal esults and show that uses costs can be mnmzed whle meetng use demand and cloud povde capacty lmts. II. RELATED WORK Cloud computng typcally offes thee man sevce models, Softwae-as-a-Sevce (SaaS), Platfom-as-a-Sevce (PaaS), and Infastuctue-as-a-Sevce (IaaS). IaaS sevces, such as Amazon EC2 [2], explot vtualzaton technology to offe esouces to uses n the fom of VMs. Allocaton methods may take a heustc appoach, such as n [3], whch also suppots mgaton. Altenatvely, [4] descbes an exact povsonng algothm that accommodates both VM demand and pce uncetanty. Intoducng the use of two-stage stochastc optmzaton [5] to computng esouce povsonng, these woks fnd optmal solutons to the NP-had VM allocaton poblem. Smlaly, [6] fomulates mxed ntege poblems, and compaes them, focusng on mnmzng executon tme. The lage amounts of bandwdth equed by moden cloud applcatons can be guaanteed though bandwdth esevaton. Fo example, [7] addesses the poblem of mappng use equests to data centes and outng the esponses but does not consde computaton. The OpenFlow [8] mplementaton of SDN allows the flexble allocaton of bandwdth though vtual netwoks, and theefoe the esevaton of bandwdth. Combnng ths powe wth methods used n Vtual Netwok Embeddng (VNE), bandwdth allocaton can be pefomed fo the cloud. Fo example, [9] fomulates the jont poblem of vtual node and lnk allocaton as an Intege Pogammng poblem, although wthout a stochastc element. Lke VM allocaton, ths poblem s NP-had, so s often solved wth heustcs nstead [10]. 978-1-4799-2003-7/14/$31.00 2014 IEEE 2969
IEEE ICC 2014 - Next-Geneaton Netwokng Symposum 2 SDN Contolle Bandwdth Povsonng VM Povsonng Demand Requests R1 R5 P1 Fg. 1. Tmelne showng the stages of decson-makng. Resevaton decsons last fo a longe peod of tme, wth second stage decsons made fo a shote duaton once demand s known. R2 R6 P2 R3 The above wok lays the foundaton fo a jont VM and bandwdth allocaton soluton. Howeve, as fa as we ae awae, thee ae cuently no woks that addess the poblem dectly. It s ou belef that the two must be consdeed togethe to acheve a globally optmal soluton to the cloud esouce povsonng poblem. Use R7 R4 R8 Te 1 Te 2 ISP Netwoks P3 P4 Cloud Povdes III. SYSTEM MODEL A. Cloud and Netwok Resouces The system model unde consdeaton fo jont VM and bandwdth allocaton s composed of cloud sevce povdes and ISPs. Thee s a cental contolle ecevng demand equests fo VM povsonng fom uses. The contolle then povsons the equed VMs fom cloud povdes and povsons vtualzed bandwdth fom ISPs. ISPs can mplement SDN (e.g. wth OpenFlow-enabled swtches), enablng the cental contolle to make bandwdth povsonng and outng decsons on vtualzed outes. A pactcal mplementaton may eque sepaate contolles to admnste netwoks and povdes, howeve, we ae nteested n the decson-makng pocess, whch we model wth a sngle contolle. The povsonng decson s made n two stages (Fg. 1). The fst stage s the esevaton phase, whee VMs and bandwdth ae eseved fo a long peod of tme, typcally a yea, n advance, befoe actual demand s known. The second stage happens at the tme of use, when the uses actual demand s ealzed (e.g., daly demand). The second stage s dvded nto two phases,.e., utlzaton and on-demand phases. In the utlzaton phase, the needed eseved esouces ae used, usually at a low pce. If the actual demand s hghe than the eseved esouces, the algothm entes the on-demand phase. In the on-demand phase, addtonal esouces can be povsoned at a hghe cost to satsfy any unsatsfed demand. Theefoe, t s mpotant fo the fst stage to be optmally detemned as t s sgnfcantly cheape than the second stage, but less flexble, due to the long duaton of esevaton. In the system shown n Fg. 2, an ISP manages a set of vtualzed outes, denoted by R = {1,...,R}, whee R s the total numbe of outes. Each oute has a bandwdth capacty, t. Resevaton, utlzaton, and on-demand bandwdth costs, though oute, ae gven by c (e), c, and c, espectvely. A set of cloud povdes s denoted by P = {1,...,P}, whee P s the total numbe of cloud povdes. Each cloud povde, p, has thee esouces,.e., pocessng powe, stoage, and ntenal netwok bandwdth, whose capactes ae gven by t (h) p, t (s) p, and t (n) p, espectvely. Hee ntenal bandwdth s Fg. 2. System model. Bandwdth esevaton s made fom ISP netwoks, VMs ae placed wth cloud povdes. Cental contolle makes povsonng choces based on use equements. bandwdth allocated fo a VM (e.g., fo a seve nsde a data cente), whle extenal bandwdth efes to the bandwdth of the outes of the ISP. V = {V 1,V 2,...,V last } denotes the set of VM classes. Each class has dstnct esouce equements, wth d (h), d (s), d (n), and d (b), denotng a VM fom class V s equements fo pocessng, stoage, ntenal bandwdth, and extenal bandwdth, espectvely. The costs of esevng, utlzng, and obtanng on-demand, a VM, fom class V, fom povde p, ae gven by c (e), c, and c, espectvely. All costs ae known n advance, but the VM demand (and theefoe the extenal bandwdth demand) s uncetan. B. Uncetanty of VM and Bandwdth Demand Wth uncetan demand, the numbe of VMs equed fom each class s unknown at the pont of esevaton. D = {d 1,d 2,...,d V } denotes the set of possble numbes of VMs that can be eseved fom class V. The set of all possble VM demand values can theefoe be gven by D = D = D 1 D 2 D V (1) whee and ae the Catesan poduct. Gven uncetan VM demand, the total bandwdth that needs to be obtaned s also unknown at the pont of esevaton. Snce each VM class,(1) can be used to gve the set of possble bandwdth equements fo class V. The set of possble bandwdth equements fo VM class V s defned as follows: has a fxed extenal bandwdth equement, d (b) B = D d (b). (2) Then the set of possble extenal bandwdth equements of all VM classes s expessed as follows: B = D d (b). (3) 2970
IEEE ICC 2014 - Next-Geneaton Netwokng Symposum 3 IV. PROBLEM FORMULATION A. Stochastc Optmzaton Poblem If VM demand wee known at the pont of esevaton, the poblem would be a smple detemnstc optmzaton, wth no on-demand phase. Snce demand s uncetan, we need to apply a two-stage stochastc optmzaton. The stochastc optmzaton poblem can be fomulated as follows: ( mn c (e) (e),y (e) (e) + c (e) Y (e) R p P ) (4) +E[L( (e),y (e),ω)]. The objectve functon n (4) mnmzes the total cost of esevaton added to the expected cost fom the second stage. The decson vaables (e) and Y (e) denote the amount of bandwdth eseved fom oute and the numbe of VMs of class eseved fom cloud povde p, espectvely. The expected second stage cost s epesented by E[L( (e),y (e),ω)], whee ω denotes a scenao of demand: ω Ω = D B. Fo a gven ω, the second stage cost functon s gven n (5), whee decson vaables (ω) and (ω) denote the amount of povsoned bandwdth fom oute n the utlzaton and on-demand phases gven demand scenao ω, espectvely. Decson vaables Y (ω) and Y (ω) denote the numbe of VMs fom class povsoned n the utlzaton and on-demand phases fom cloud povde p, espectvely. The full fomulaton, theefoe, s to mnmze (4), subject to the followng constants: p P Y (e),y X (e) (ω),y (ω) {0, 1,...} (6), (ω),x (ω) 0 (7) (ω)+ (ω) t, R (8) d (h) d (s) d (n) Y (ω)+y (ω)) t(h) p,p P (9) (ω)+y (ω)) t(s) p,p P (10) (ω)+y (ω)) t(n) p,p P (11) (ω) (e), R (12) (e) (ω) Y,p P,V V (13) (ω)+y (ω)) v (ω), v V. (14) (6) pevents negatve o patal povsonng of a VM. Smlaly, (7) ensues non-negatve bandwdth povsonng, but pemts non-ntege amounts. (8)-(11) ensue that the povsoned esouces do not exceed capacty, wth t gvng the capacty of oute, and t p (n) gvng the capacty of cloud povde p fo each of the thee esouces,.e., pocessng powe, stoage, and ntenal bandwdth, espectvely. (12) and (13) ensues that the povsonng n utlzaton phase does not exceed the eseved amount. (14) ensues the VM demand ealzed n the second stage, denoted by v (ω) fo VM class, s satsfed., and t (h) p, t (s) p Bandwdth demand must also be met, as well as ensung that flow s conseved acoss the whole netwok. We consde the netwok of outes as a gaph, G =(R, E), whee each oute n R s a vetex, and each lnk n E s an edge, wth flow pesevaton defned n tems of edges. Howeve, as bandwdth s allocated at the oute, we defne a set of constants to contol flow based on outes as follows: R(p) k R out() R pov (ω)+ (ω) k R use R(p m) R out( m) (ω)+x k (ω)+x d (b) (ω) (ω) p P (ω)+y (ω)),p P (15) (ω)+ (ω), R d (b) (ω)+ (ω) R pov (ω)+ (ω) d (b) p p m (16) (ω)+y (ω)) (17) (ω)+ (ω) (18) (ω)+y (ω)), p m P adj (19) (ω)+ (ω) m (ω)+x (ω), m R adj. (20) The man dea of the above constants s to balance the nput bandwdth wth output bandwdth at the outes. The nequaltes ensue that the bandwdth supply s at least suffcent to meet demand thoughout the netwok, elyng on the mnmzaton to emove excess bandwdth povsonng. Total actual povsoned bandwdth s gven by the utlzaton and on-demand values fo a gven ealzaton. (15) ensues that the bandwdth equements of each ndvdual cloud povde ae met, whee R(p) s a set of outes dectly connected to cloud povde p. (16) ensues that the bandwdth allocated to each oute, R, s suppled suffcently by the outes, k R out (), that connect to t wth the outwad lnks. (17) ensues that the total bandwdth equements of all cloud povdes ae met by the outes that dectly 2971
IEEE ICC 2014 - Next-Geneaton Netwokng Symposum 4 L( (e),y (e),ω)= mn (ω), (ω),y (ω),y c (ω) (ω)+c (ω)+c Y (ω)+c Y (ω) (5) connect to them. The set of all outes that lnk dectly to cloud povdes s gven by R pov. (18) s to ensue that the total bandwdth supply s povded to the use, whee R use s the set of all outes wth connectons dectly to the use. In (19) the set P adj s the set of dsjont pas, p m,of povdes whee the povdes n the pa ae connected dectly to at least one oute n common. R(p m ) denotes the set of outes that connect dectly to ethe of the povdes n the pa, p m. In (20), the set m R adj, s the set of dsjont pas of outes, m, whee the outes n the pa both eceve nput fom at least one oute n common, but ae not dectly connected to each othe. R out ( m ) denotes the set of all outes that connect dectly to the outes n pa m wth the outwad lnks. Whee outes have two o moe outwad lnks, thee s a dange that the same bandwdth allocaton wll be assumed to supply multle outes o cloud povdes; (19) and (20) pevent ths. Although the flow s symmetcal, we consde the lnks that come fom the use to be nwad, and the lnks that go towads the cloud povdes to be the outwad lnks. B. Detemnstc Equvalent Fomulaton The stochastc fomulaton above can be tansfomed nto a detemnstc equvalent fomulaton by ntoducng fou vaables as equvalents to the decson vaables n (4). These new vaables ae (b, d), (b, d), Y (b, d), and Y (b, d). When VM and bandwdth demand s ealzed, we have the obseved values d Dand b B. Ths pemts the efomulaton of the objectve functon defned n (4) as shown n (21). In ths case, the pobabltes of VM and bandwdth demand ae denoted by p(d) and p(b), beng ealzed n the second stage. The ealzaton nstance (b, d) eplaces the scenao ω that was used n the stochastc fomulaton. To ensue that the uncetan demand s accounted fo, the detemnstc fomulaton consdes each possble nstance of demand and chooses utlzaton and on-demand values fo each one, wth the total cost weghted by the pobablty of each ealzaton. We can also substtute n the new decson vaables and obtan new constants. Space does not pemt lstng each constant n full, but we gve an example fo llustaton. (b, d)+ (b, d) t, R,b B,d D (22) (22) s the detemnstc equvalent of (6). ω has been eplaced by the ealzaton of VM and bandwdth demand,.e., (b, d), and the equaton s evaluated fo each demand ealzaton, gven by b B and d D. The detemnstc equvalents of the emanng constants, (9)-(20), can be obtaned smlaly. The detemnstc equvalent fomulaton s a mxed ntege lnea pogammng poblem. Theefoe, a standad solve (e.g., CPLEX) can fnd an optmal soluton. V. PERFORMANCE EVALUATION A. Paamete Settng Ou fomulaton focuses on cost mnmzaton, wth a elatvely small envonment used fo pefomance evaluaton to demonstate optmalty. Resouce allocaton and ntege pogammng poblems ae NP-had, causng scalablty poblems n a cloud envonment wth a lage numbe of outes and VMs. The queston of computatonal effcency s an mpotant one to addess, pehaps though a dstbuted method, o a heustc elaxaton of the ntege constants. Investgaton of computatonal pefomance s left fo futue wok. 1) VMs and Cloud Povdes: We consde a epesentatve cloud computng envonment wth a sngle cloud use, fou cloud povdes, thee VM classes, and eght outes, aanged n two tes, as depcted n Fg. 2. Smla to [4], the demand equed fo each VM class anges fom 1 to 50,.e., D = {1, 2,...,50}. Fo smplcty, the sets of possble demands ae dentcal fo the thee VM classes as follows: D = {d 1,d 2,d 3 d 1 D 1,d 2 D 2,d 3 D 3,d 1 = d 2 = d 3 }. (23) The esouce equements fo each VM class ae dawn fom a synthess of easonable bandwdth equements, and the computng and stoage equements of the small, medum and lage standad nstances avalable fom Amazon EC2 [2]. Requements ae gven n daly quanttes, wth computng powe measued n CPU-hous, and stoage and bandwdth measued n GBs. Computng equements fo V 1, V 2, and V 3 ae 24, 24, and 48 CPU-hous, espectvely. Stoage equements fo classes V 1, V 2, and V 3 ae 160, 410, and 840, espectvely. Bandwdth equements fo V 1, V 2, and V 3 ae 3GB, 3GB, and 9GB pe day, espectvely. Compehensve pcng of esouces ae gven n Table I, whee the aconyms R, U, and O stand fo esevaton, utlzaton, and ondemand, espectvely. We hee explan the atonale fo these paamete settngs. As n [4], P 1 s consdeed as a pvate cloud mantaned by the use s ogansaton. The pvate cloud conssts of 10 seves, wth esevaton costs equal to the enegy costs of unnng the seves, gven by $357 pe seve pe yea. We take ths as the esevaton cost fo 24 CPUhous n the cloud. P 2 s pcng s the same as Amazon EC2, whlst P 3 s based on Wndows Azue s pcng schemes [11]. Wndows Azue does not have sepaate esevaton and utlzaton pcng, so we povde easonable values fo each. P 4 also follows [4] by only offeng an On-Demand plan, albet at cheape ates than the othe cloud povdes. The capacty of povdes P 2 to P 4 s taken to be unlmted, as they ae lage scale commecal cloud povdes. The computng capacty of P 1 s 240 CPU-hous, whch s the avalable computaton n a day fom 10 seves. The Stoage capacty s gven as 5000GB, based on the easonable assumpton that each seve has a 500GB had dsk dve. Intenal bandwdth fo the cloud 2972
IEEE ICC 2014 - Next-Geneaton Netwokng Symposum 5 mn R c (e) (e) + p P c (e) Y (e) + R b B d D p(b)p(d)(c p P b B d D (b, d)+c p(b)p(d)(c (b, d))+ Y (b, d)+c Y (b, d)). (21) TABLE I VM COSTS FOR EACH CLOUD PROVIDER AND PROVISIONING PHASE. PRICES ARE GIVEN FOR A DAY S USAGE. Povde VM and Phase V 1 V 2 V 3 R U O R U O R U O P 1 0.978 NA NA 0.978 NA NA 1.956 NA NA P 2 0.189 1.656 2.184 0.378 3.312 4.368 0.756 6.600 8.736 P 3 0.150 1.680 2.160 0.330 3.360 4.320 0.725 6.960 8.640 P 4 NA NA 1.920 NA NA 3.840 NA NA 7.68 TABLE II COST PER GB PER DAY OF BANDWIDTH PROVISIONING THROUGH ISP ROUTERS 500 400 Routes Povsonng Phase R U O R 1,R 5 0.10 0.03 0.50 R 2, R 6 0.16 0.02 0.20 R 3, R 4, R 7, R 8 0.17 0.01 0.30 Total Cost ($) 300 200 100 Total cost 1st stage cost 2nd stage cost povdes s taken to be unlmted, as oute bandwdth lmts wll be stcte. 2) ISP Routes: Ou envonment has eght outes, wth the outes dvded nto thee sets of pcng, gven n Table II. Snce bandwdth esevaton and on demand pcng schemes ae not yet commonly avalable fom ISPs, we synthesze easonable values. The bandwdth pcng s based on the Sngtel 1 busness fbe boadband schemes [12]. Bandwdth pcng s gven pe GB pe day, wth the esevaton pcng fo each scheme adapted fom the monthly Gbps pces of the thee dffeent subsctons avalable fom Sngtel. Utlzaton pcng s a low cost acoss all outes and s chosen to be sutably popotonate to the esevaton pces. On-demand pces ae detemned as easonable values usng Sngtel s pe- GB excess usage fees fo moble boadband [13]. 3) Demand Uncetanty: We model the VM demand uncetanty as a Nomal dstbuton, wth μ = 76.5 and σ =36, wth bandwdth demand calculated as the sum of the bandwdth equements fo each equed VM. Fo smplcty, bandwdth demand s teated as a detemnstc functon of VM demand, so p(d) and p(b) ae equal, meanng that t s suffcent to evaluate only acoss one demand set. B. Numecal studes The detemnstc equvalent poblem above s encoded usng GAMS (Geneal Algebac Modelng System) [14]. 1) Impact of esevaton: We conduct two studes of the effects of esevaton n the system. In Fg. 3, we vay the numbe of eseved VMs and show the effect on total cost ncued to the use, both oveall, and n fst and second stages. 1 Sngtel s one of the lagest netwok opeatos n Sngapoe. 0 0 50 100 150 Numbe of eseved vtual machnes (VMs) Fg. 3. Cost of use when the numbe of eseved VMs s vaed. As expected, as the numbe of eseved VMs nceases, the fst stage cost nceases, and the second stage cost deceases. Ths esults n a dop of total pce untl the optmum pont s eached, when the benefts fom esevaton ae exceeded by the exta cost of esevng edundant VMs. We smlaly vay the amount of eseved bandwdth, but omt the gaph due to space constants. As expected, the bandwdth esevaton esult follows a smla patten to the VM esevaton esult. 2) Meetng Demand: To obseve ou soluton s effectveness n handlng vayng demands, we examne the costs unde dffeent demand ealzatons. We consde the total cost, the VM cost, and the bandwdth cost, and compae ou stochastc pogammng (SP) soluton s esults to a detemnstc veson (that knows the demand n advance), and an on-demand soluton, that has no esevaton opton. Fg. 4 shows the total costs of each soluton. As expected, the detemnstc soluton pefomed best, but ou soluton acheved pefomance that was close to the detemnstc soluton. The on-demand-only opton s sgnfcantly nfeo n all thee cases, although when the numbe of equed VMs s vey small t offes a lowe cost, because thee s no ovepovsonng cost. 3) Compason wth altenatve methods: In Fg. 5, we vay the mean of the pobablty dstbuton and compae ou stochastc pogammng (SP) soluton to two othe methods - one that employs no esevaton phase, and an Expected Value Fomulaton (EVF) that uses the mean as ts VM esevaton value. We also set the standad devaton of the demand dstbuton to 120 to bng out the dffeences n 2973
IEEE ICC 2014 - Next-Geneaton Netwokng Symposum 6 Total cost ($) 1200 1000 800 600 400 200 Stochastc pogammng Detemnstc On demand only Total cost ($) 120 100 80 60 40 Povde P1 Povde P2 Povde P3 Povde P4 0 0 50 100 150 Numbe of equed vtual machnes (VMs) Fg. 4. Oveall costs, when the demand s known. 20 0 0.1 0.15 0.2 0.25 Cost of esevaton and on demand phase fom outes R7 & R8 ($) Fg. 6. Effect of oute pce vaaton on vtual machne (VM) placement 700 Total cost ($) 650 600 550 500 450 400 Expected value functon (EVF) Stochastc pogammng On demand only 350 30 40 50 60 70 80 90 100 110 120 Mean of vtual machne (VM) demand Fg. 5. Compang total cost of stochastc pogammng soluton wth altenatves pefomance between the methods. EVF pefoms well, as the optmal esevaton decson s close to the mean when usng nomally dstbuted demand. We antcate that f un aganst eal demand data, EVF would pefom sgnfcantly wose. As expected, on-demand-only s consdeably moe expensve. 4) Effect of vayng oute pces: To see the mpact of oute pcng on VM placement, we ase the pces fo outes R7 and R8. We set the esevaton and on-demand costs to be equal, as the dffeence n pce between VMs and bandwdth wll absob the exta cost of on-demand povsonng. In ths way, we can see that nceasng the pce of bandwdth povsonng foces mgaton of VMs fom P 3 and P 4 to altenatve cloud povdes. P 1 emans constant as t offes only esevaton. P 3 changes fst, wth VMs movng to P 2, whlst P 4 ntally stays nealy constant. Snce P 4 s ondemand only and offes the cheapest on-demand pces, t stll makes sense to use t. Howeve, once thee ae no moe VMs to emove fom P 3, the nceasng bandwdth costs affect P 4 as well, and the load s mgated to P 3, whee some of the taffc can be outed though the cheape R6. We show ths n Fg. 6 and obseve that even wth elatvely low pe-gb bandwdth pces, VM mgaton can be foced. VI. CONCLUSION We poposed an optmal algothm fo povsonng VMs and netwok bandwdth n a cloud computng envonment, enabled by softwae defned netwokng. We have accounted fo uncetan demand by fomulatng and solvng a two-stage stochastc optmzaton poblem to optmally eseve VMs and bandwdth to mnmze cost. We have evaluated ou soluton s pefomance n the descbed envonment. We have obseved that the soluton s optmal and outpefoms altenatve methods, achevng esults close to those acheved when demand s pefectly known. Futue dectons fo eseach nclude consdeng ISP netwoks that cay othe taffc and ntoduce a andom delay facto, consdeaton of non-detemnstc pevtual machne bandwdth demand, numecal studes based on eal usage data, and desgn of a dstbuted soluton fo lage-scale applcatons to mpove scalablty. REFERENCES [1] Softwae-defned netwokng: The new nom fo netwoks, Whte Pape, Apl 2012. [Onlne]. Avalable: https://www.opennetwokng.og/mages/stoes/downloads/ sdn-esouces/whte-papes/wp-sdn-newnom.pdf [2] (2013, Aug.) 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