Dynamic Virtual Network Allocation for OpenFlow Based Cloud Resident Data Center

Transcription

1 56 IEICE TRANS. COMMUN., VOL.E96 B, NO. JANUARY 203 PAPER Speca Secton on Networ Vrtuazaton, and Fuson Patform of Computng and Networng Dynamc Vrtua Networ Aocaton for OpenFow Based Coud Resdent Data Center Tr TRINH a), Student Member,HroshESAKI b), Member, and Chaodt ASWAKUL c), Nonmember SUMMARY Dynamc vrtua networ aocaton s a promsng traffc contro mode for coud resdent data center whch offers vrtua data centers for customers from the provder s substrate coud. Unfortunatey, dynamc vrtua networ aocaton desgned n the past was amed to the Internet so t needs dstrbuted contro methods to scae wth such a arge networ. The prce for the scaabty of the competey dstrbuted contro method at both vrtua ayer and substrate ayer s the sow convergence of agorthm and the ess stabty of traffc. In ths paper, we argue that the dstrbuted contros n both vrtua and substrate networs are not necessary for the coud resdent data center envronment, because coud resdent data center uses centrazed controer as the way to gve networ contro features to customers. In fact, we can use the centrazed agorthm n each vrtua data center whch s not very arge networ and the dstrbuted agorthm s ony needed n substrate networ. Based on the specfc propertes of ths mode, we have used optmzaton theory to re-desgn the substrate agorthm for perodcay re-adustng vrtua n capacty. Resuts from theoretca anayss, smuatons, and experments show that our agorthm has faster convergence tme, smper cacuaton and can mae better use of the feedbac nformaton from vrtua networs than the prevous agorthm. ey words: networ vrtuazaton, OpenFow, data center, centrazed controer, traffc management. Introducton The coud resdent data center [], whch has been proposed to repace the Amazon vrtua prvate coud (Amazon VPC) [2], offers customers not ony a bunch of vrtua machnes but aso the networ servces to connect and contro traffcs among these vrtua machnes. The restrcted traffc contro features provded by the Amazon VPC (e.g. statcay add/remove routng entres, access contro st) are not enough for the varous requrements of customers. In fact, customers need the abty of freey choosng dynamc routng agorthms, securty systems and cachng systems to match wth ther operatng mode. A coud resdent data center offers those fexbtes by gvng each of vrtua data center customers a physca controer. Ths controer can then be used to enabe those customers to nsta proper networ contro features to contro ther vrtua networ porton rented from the nfrastructure coud. There are three man propertes of coud resdent data center to defne the traffc management mode. Frsty, a coud resdent data center s typcay based on the physca networ structure of ds- Manuscrpt receved May 8, 202. Manuscrpt revsed August 30, 202. The authors are wth Chuaongorn Unversty, Thaand. a) E-ma: tr.m@student.chua.ac.th b) E-ma: hrosh@wde.ad.p c) E-ma: chaodt.a@chua.ac.th DOI: 0.587/transcom.E96.B.56 trbuted data centers each wth a fat-tree topoogy. Ths aows the usage of cheaper swtches n the networ core ayer than wth a conventona topoogy requrng hgh-denstyport swtches for nterconnectons wthn each data center. Ths topoogy has many paths between each end-host par so the mut-path traffc engneerng s the most sutabe for the traffc management mode. Secondy, the traffc demands comng from vrtua networ customers are a pror unnown so statc traffc contros can ead to hgher chances of demand oss or capacty waste than dynamcay adaptve traffc contros can. Thrdy, the requrement for vrtua networ provson to each customer suggests that coud resdent data centers shoud support the networ vrtuazaton []. The mut-path oad baancng probem has been taced n [3] by desgnng a traffc scheduer to estmate the eephant or bg demands and usng heurstc agorthms to search for the optma mappng between these demands and physca paths. The dynamc congeston-contro probem presented n [4] uses a marng system to decrease the source sendng rate varaton for archvng the hgh throughput even wth a sma buffer sze. The combnaton of these two probems has been formuated and soved n the framewor of centrazed optmzaton agorthm [5]. However, a the aforementoned wors have deat wth the traffc management probems n ony one networ ayer. A coud resdent data center mode needs the co-operaton of traffcmanagement mechansms between vrtua ayer and substrate ayer to maxmze the tota utty and mae most uses of the physca resources. Davnc [6] has addressed ths traffc management probem n two ayers. At the vrtua ayer, an optmzaton probem has been formuated on the requrements of customers and soved dstrbutedy by a decomposton method. At the substrate ayer, a perodcay updated mechansm has been proposed to contro the capacty of vrtua ns accordng to the derved congeston prces. Unfortunatey, ths approach has been amed at such bg networs as the Internet so the dstrbuted agorthms have been used n both substrate ayer and vrtua ayer. Ths s not sutabe for the traffc management probem n the coud resdent data center wth vrtuazed networs each managed by a centrazed controer dedcated for each of the vrtua data center customers. Ths paper contans two orgna contrbutons. Frsty, n ths paper, the coud resdent data center testbed has been mpemented n the OpenFow patform. We have decded to use the OpenFow because of ts centrazed system structure whose controer can have a goba Copyrght c 203 The Insttute of Eectroncs, Informaton and Communcaton Engneers

2 TRINH et a.: DYNAMIC VIRTUAL NETWORK ALLOCATION FOR OPENFLOW BASED CLOUD RESIDENT DATA CENTER 57 vew on the overa networ. That centrazed controer can gve a better decson to manage the traffcs nsde the networ. Addtonay, the OpenFow s the open system aowng devces from dfferent vendors to n-operate smoothy va the OpenFow standard. Our testbed has been mpemented on Lnux-based computers nstaed wth OpenFow swtch [7] as the physca ayer, FowVsor [8] as the networ vrtuazaton ayer, and Networ Operatng System NOX [9] as the centrazed controer. A the system modues communcate va the OpenFow [7] protoco to emuate the dynamcs of a sma coud resdent data center testbed. Secondy, ths paper re-desgns the traffc contro mode n [6] for the OpenFow-based networ settng of coud resdent data center. Due to the centrazed contro structure of the OpenFow, we have decded to mpement the centrazed optmzaton agorthm on each vrtua networ nstead of dstrbuted agorthm. And we have mpemented the dstrbuted traffc contro agorthm n the substrate networ to perodcay contro the aocaton of vrtua n capacty for the new mode of coud resdent data center. The rest of ths paper s organzed as foows. Secton 2 descrbes the system mode. Secton 3 presents the dervaton of our vrtua n capacty updated agorthm for coud resdent data center. Secton 4 demonstrates how we mpement our agorthm n OpenFow based Testbed. Secton 5 shows the resuts and dscussons. The fna secton s Concuson and our future wors. 2. System Descrpton Fgure shows the OpenFow-based coud resdent data center system testbed constructed n ths research. The system s comprsed of four man eements,.e., vrtua networ controer, substrate node, end-host and host manager. The functon of vrtua networ controer s to contro how substrate nodes swtch the pacet fows to sutabe destnatons. The substrate nodes swtch the pacet fows n accordance wth the nstructons from the vrtua networ controer and perodcay cacuate as we as update to the controer about the new capacty requred for ther vrtua ns. An end-host s a vrtua machne on a vrtua networ. Each end-host gets traffc optma rates and mut-path spttng rato from ts host manager to adust ts outgong traffc rates. The host manager cacuates and contros the traffc rate of a end-hosts n ts vrtua networ n response to the demands requested from end-hosts and the vrtua networ state updated by the controer. 2. Traffc Contro n Each Vrtua Networ Intay, the vrtua networ controer creates tunnes to connect ts vrtua networ s end-hosts by addng the approprate swtchng entres to the OpenFow swtches. Each end-host montors ts aggregated traffc data at ts output port and sends the capacty request to ts host manager perodcay. On recevng the requests from a of ts end-hosts, the host manager w cacuate the optma rate for each tunne and repy these optma rate bac to the end-hosts. The endhosts can then adapt the traffc sendng rates to the tunnes accordngy. Wth ths mechansm, the appcatons on each end-host does not need to wat for the optma rate from host manager but they can send ther traffc out mmedatey each tme they want. 2.2 Traffc Contro n Substrate Networ The msson of traffc contro n a substrate networ s to adust the vrtua n capacty perodcay n order to maxmze the tota utty. In ths paper, the substrate networ uses congeston prce of each vrtua n to cacuate the sutabe bandwdth provded to vrtua ns. Here, a substrate node does not need to cacuate the congeston prce for vrtua ns one by one by tsef as prevousy mpemented n [6]. Instead, n ths paper, the substrate node coects the congeston prce for a vrtua ns from the host manager. The optmzaton sover n the host manager gves the souton of dua varabes, whch are congeston prces, whe sovng the centra optmzaton probem for end-host traffc sendngrate. Ths way of coectng congeston prce nformaton maes our agorthm outperform [6] because the substrate nodes do not need the computatona resources to cacuate the congeston prce for each vrtua n and they do not need to spend a ot of tme to wat for the agorthm of cacuatng congeston prce to converge. So, our agorthm can re-adust the vrtua n capacty faster and hence more frequenty than the approaches n [6]. Fg. System functona descrpton. 3. Proposed Optmzaton Framewor for Coud Resdent Data Center 3. Modeng and Notatons The substrate networ s modeed by a weghted, drected graph G(V s, E s ), where V s s the set of a substrate nodes and E s s the set of a drected substrate ns. In Fg. 2, there are three substrate nodes ndexed by {, 2, 3} and sx

3 58 IEICE TRANS. COMMUN., VOL.E96 B, NO. JANUARY 203 The n-path routng matrx for vrtua networ [] wth ts coumn representng each path n source-destnaton pars and ts row representng each substrate n ndex s denoted by H (),whereh () f demand of vrtua networ on path uses vrtua networ n and H () 0 otherwse. For exampe, n Fg. 2, there are two routng matrces H () for vrtua networ and H (2) for vrtua networ 2. Here, H () [0 ; 0 0; 0; 0 0; 0 ; 0 0] because demand of vrtua networ on path uses vrtua networ ns 3 and demand of vrtua networ on path 2 uses vrtua networ ns and 5. Smary, the second routng matrx H (2) [ 0; 0 0; 0 ; 0 0; 0 ; 0 0]. 3.2 Vrtua-Networ Centrazed Agorthm Fg. 2 System modeng exampe. drected substrate ns ndexed by {, 2, 3, 4, 5, 6} between substrate node pars { 2, 2, 3, 3, 2 3, 3 2}, respectvey. Smary, a vrtua networ s modeed as a graph G(V (), E () ), where K s an eement n the vrtua networ ndex set. Here, V () s the set of nodes n vrtua networ and E () s the set of vrtua ns n vrtua networ. For exampe, n Fg. 2, there are two vrtua networs, the yeow one and the red one, each wth the same topoogy as that of substrate networ. Let r () denote the demand of vrtua networ. The vrtua networ controers use ther own traffc engneerng agorthm to contro the traffc fowngthrough thernetwors. Andthe substrate networ contros the vrtua n capacty by usng vrtua n congeston prce nformaton. For the exampe mode n Fg. 2, there s one demand on each of the two vrtua networs, denoted as r () and r (2), respectvey. There are two paths { 3, 2 3} for demand r () and two paths { 2, 3 2} for demand r (2). Defne as the genera n ndex, where L denotes the substrate n n the substrate networ and L denotes the vrtua n n vrtua networ. Ln of substrate networ has the capacty of c.ln of vrtua networ has capacty. For vrtua networ, each demand can usuay be assgned aong more than one path at the same tme so et us defne z () as the max fow rate avaabe on path for demand of vrtua networ. Usuay, ths fow rate must be ess than or equa to the nstantanenous amount of capacty on path that s assgned to that demand to prevent any possbe traffc osses. The am of our optmzaton s to fnd the proper vaues of these capacty and fow rate aocaton parameters and z (). To defne the set of a possbe paths whose capacty and fow rate aocaton w be found by our proposed optmzaton, we use the m-shortest path frst agorthm [0] to fnd m east cost paths from each source to each destnaton n the substrate networ as we as n the vrtua networs. Then we restrct our optmzaton search space wthn those obtanabe paths ony. For each fxed wth fxed vaues of maxmze: subect to: : U ( ) () z (), H () z () z () 0, L varabes: z () () As n [6], the obectve functon of the vrtua networ centrazed probem () can be any concave utty functon whch vares wth the capacty aocaton parameters. The frst constrant mpes for each vrtua networ that the nstantateous capacty requrement or tota fow rate from a demands on ther paths sharng a gven vrtua n cannot exceed the capacty assgned for that vrtua n by the substrate networ. The second constrant states that the capacty aocatons must be non-negatve. 3.3 Substrate-Networ Dstrbuted Agorthm Our startng pont s the same as [6] but wth the settng of coud resdent data center n mnd, we have derved a dfferent vrtua n capacty updated agorthm to match wthn our OpenFow based networ testbed. Our centrazed substrate networ optmzaton s stated by: maxmze: w () U ( ) () z (), subect to: H () z () L, varabes: c L, z () 0,, z (), (2) Here, w () s the weght for each vrtua networ. Byusng the centrazed sover for each vrtua networ, we can derve the new vrtua n capacty updated agorthm whch s expectedy convergng faster and better n processng bursty

4 TRINH et a.: DYNAMIC VIRTUAL NETWORK ALLOCATION FOR OPENFLOW BASED CLOUD RESIDENT DATA CENTER 59 traffcs than that of [6]. The probem n (2) s the convex probem because the obectve functon of ths probem s the postve-weghted sum of concave obectve functons () and the constrants are affne wth z (),. The probem has couped varabes z (), so we decoupe t by the prma decomposton method [2]. We fx the the varabe to mae the probem ony vares wth z () and the new probem can be d- vded nto many centrazed probems of (). The optmzaton sover CVXOPT [5] whch mpements the so caed prma-dua nteror pont method [3] s used to sove each probem of () centray n the controer of each vrtua networ. The resuts of optmzaton sover for each sub-probem are optma fow rates z () and n congeston prce λ (). Now, after sovng the sub-probem, we need to fnd the new vrtua n capacty that we have fxed n the prevous step. The updated agorthm s derved from the master probem as foows: maxmze: w () U ( ) () z (), c L 0, varabes: (3) The above master optmzaton probem s aso the convex probem because t has the same concave obectve functon as (2) and the affne constrants. As suggested n [3] for the convex optmzaton probem, because t s easy to proect on the non-negatve orthant constrant 0, we smpfy the way to sove the probem (3) by consderng the constrant 0 as mpct constrant and sove the probem wth expct constrant frst then proect the resuts on the mpct constrant doman. The probem wth expct constrant has couped constrant c so we use the dua decomposton [2] to decoupe t. We fnd the Lagrange functon of (3) as foow: L ( ),μ w () U ( () z () w () U ( () z (),, ) μ ) c μ + μ c (4) Note that μ s the dua varabe for the master probem whch s dfferent from λ (), the dua varabe of subprobems. We use the subgradent proecton method to fnd the supremum of probem (4) whch has mpct constrant of non-negatve orthant and the varabe of. The update functon for s (t + T s ) y() (t) + α L ( ) +,μ (5) where T s s the tme perod for updatng vrtua n capacty n the substrate networ and the updated tme argument has been appended n the parenthess foowng the varabe. [] + denotes the proecton on to non-negatve orthant doman. Le [3], we have the parta dervatve of obectve functon at the optmaty as the n congeston prce so K U () ( z (), ) λ () (6) Usng (6) we have parta dervatve of Lagrange functon as L ( ),μ w () λ () μ (7) To fnd μ,wedefnep () as the optma vaue of () and p as the optma vaue of (3). We have p w () p () p c μ () p () w c K w () λ () K c (8) where K s the set of vrtua networs hosted on substrate n. In practca networs, a servce provder prefers to aocate a ther capacty fary to ncrease the quaty of servces. In our system, by constranng on c K,we aocate fary a of our resdua capacty to vrtua networ customers: (9) c κ K y (κ) Hence, we have from (8), (9) that K μ w () λ () K (0) And the fna vrtua n capacty update functon can be obtaned by combnng (5),(7),(0) : (t + T s ) (t)+α w() λ () K w () λ () K (t) (t) + () As a summary, n (), we can fnd the vaue of at tme t + T s from the prevousy updated vaue of at tme t. In the recurson, α s a constant stepsze that can be chosen through experments to mprove the agorthm convergence. The vaue of n congeston prce λ () n vrtua networ can be obtaned by centrazed optmzaton sover. Ths

5 60 IEICE TRANS. COMMUN., VOL.E96 B, NO. JANUARY 203 equaton aso has a reasonabe nterpretaton because f the weghted rate of utty ncrease per unt of capacty beng added for a gven vrtua n,.e.thetermw () λ (),s greater than the rate of utty ncrease as averaged over a the vrtua n capacty upgrade, then that vrtua n of the vrtua networ shoud be aocated more capacty. On the contrary, f the weghted rate of utty ncrease per unt of capacty beng added for a gven vrtua n s ower than the rate of utty ncrease as averaged over a the vrtua n capacty upgrade, then that vrtua n shoud be assgned ess capacty. 3.4 Convergence and Optmaty Theorem: The updated Eq. () converges to optma pont of (2) f: The probem () s convex optmzaton. The vrtua n bandwdth aocaton s updated after the convegence of () The stepsze α n () s sma enough or dmnshng (dmnshng stepsze usuay converge faster constant stepsze). Proof: From the above nterpretaton of () about the prncpa for ncreasng and decreasng bandwdth of each vrtua n, the aggregated utty on each physca n and hence, the tota utty overa substrate networ: w () U () (z (), ) w be ncreased after each vrtua n capacty updated perod T s. Because we aways eep c, L(,μ ) ncreases monotoncay after every perod of updatng vrtua n capacty. But, L(,μ ) s concave functon so t s ony abe to ncrease unt the maxmum pont whch aso be the statonary pont when moves to the mted pont ỹ (). At the mted pont we have: w () λ () K w () λ () K ỹ () ỹ () (2) 4. Impementaton 4. Genera Testbed Descrpton We have but a testbed to mpement and evauate our optmzaton agorthm wth a rac of seven computers named PC-5 and TA, TB, respectvey. Each computer s equpped wth Core 2 quad 2.40 GHz and 4 GBytes of RAM. Ubuntu OS.04 wth the core of has been nstaed on each physca computer. 4.2 Logca Mode The ogca mode of our networ s presented n Fg. 3. In ths mode, three substrate nodes have been created by nstang OpenFow swtch software v0.8.9r2 on computers PC-3 to mae them wor as PC-based swtches. FowVsor has been used to create a vrtuazaton ayer on those substrate nodes. The vrtua networ controer has been nstantated by a Python scrpt runnng on top of the networ operatng system NOX. We have wrtten a Python scrpt to add the swtchng entres to OpenFow swtches and contro them to forward pacets accordng to VLAN IDs. To mpement end-hosts to spt the traffc through paths and mt the rate of outgong traffcs, we have wrtten a Python scrpt usng Scapy [4] to create two nds of pacets wth VLAN ID 2 and VLAN ID 3. And the end-hosts send the pacets to output ports accordng to the contro nformaton from the centra host manager. Ths host manager has been mpemented on PC5 by a Python scrpt whch communcates wth a end-hosts and the controer n the correspondng vrtua networ. Ths scrpt perodcay taes traffc demands from end-hosts and vrtua n capacty vaue updates from substrate nodes as ts nputs and use CVX- OPT [5] to cacuate the optma rates for a end-hosts It means that at the mted pont ỹ (), the weghted rate of utty ncrease per unt of capacty beng added for a gven vrtua n s equa to the rate of utty ncrease as averaged over a the vrtua n capacty upgrade and does not change anymore. At the ỹ () : L(ỹ (),μ ) 0, ; c,andμ ( c ) 0. The KKT condtons [3] are satsfed for the convex probem of (3), then the mted pont of () s the optma pont of (3). Because Eq. () s converged before the vrtua n bandwdth update tme, at ỹ () and they are the optma pont y () z () probem of (2).,weasohavez () and z () for the Fg. 3 Logca mode.

6 TRINH et a.: DYNAMIC VIRTUAL NETWORK ALLOCATION FOR OPENFLOW BASED CLOUD RESIDENT DATA CENTER 6 and congeston prce vaues for a vrtua ns n the vrtua networ. There are three networs used to connect a eements of system as depcted n Fg. 3. Controer networ ( x) s used for controers on PC4 to send contro sgnas to swtches PC-3. Host contro networ ( x) s used by the host manager to get nformaton from end-hosts and controers as we as to send contro sgnas to end-hosts. The man networ s used for end-hosts n a vrtua networ to send traffcs to each other. Swtches are connected to the frst controer (named ENG) va tcp port:7000 and the second controer (named SCI) va tcp port: Vrtua-Networ Centrazed Agorthm Impementaton We have mpemented the throughput-senstve centrazed agorthm on each host manager usng Python CVXOPT [5] wth the obectve functon of maxmzng the overa networ throughput, meanwhe eeps the n capacty uncongested as foows: max : w () og where the utzaton u () z () q L exp ( ) u () (3) of vrtua n can be cacuated from u () H() z () and q serves as a weghtng coeffcent for reguatng the utzaton of vrtua ns. Ths obectve functon s dfferent from [6] n that we add weght w () to each demand for controng the networ resources provded to each demand. Ths weght s cacuated by w () r(), r () where r () s the demand of vrtua networ. End-hosts TA, TB perodcay send the requested demand to the host manager whch cacuates the optma fow rate for each endhost to send ts traffc through each path. Upon recevng ths optma sendng rate, end-hosts then adust ther outbound fow rate. We use Scapy [4] to create the pacets wth the wanted VLAN IDs to spt traffc todfferent paths. For exampe, f end-host TA receves the optma rate of (00, 40), t nows that t shoud send the traffc wththerateof00 pacets/s on VLAN 2 and 40 pacets/s onvlan3. The end-host uses Scapy to create and send 00 pacets wth VLAN-ID 2 as we as 40 pacets wth VLAN-ID 3to swtch PC. Then, at swtch PC, the pacets wth VLAN- ID 2 are forwarded through the upper path wth two hops and the pacets wth VLAN-ID 3 are forwarded through the ower path wth one hop. OpenFow swtches. Each OpenFow swtch on recevng the congeston prce cacuates the new capacty of ts vrtua ns by usng the equaton that we have derved n (). The new vrtua n capacty nformaton s then updated to the host manager, whch n turn uses ths nformaton n ts capacty constrants to cacuate the optma fow rate for end-hosts n the next optmzaton step. 4.5 Smuator Snce our physca testbed s restrcted to 7 PCs wth 3 swtchng nodes, we have mpemented our agorthm n MATLAB envronment for two nodes topoogy and Abene topoogy [6] to test and compare our agorthm wth the prevous approach n arger topoogy. We not ony use throughput-senstve utty functon for both vrtua networs as n testbed mpementaton but aso add the deaysenstve utty functon whch tres to mnmze the tota deay of networ as foows: mn: z () H () (p + f (u () )) (4) In our testbed mpementaton, wth two throughputsenstve utty functons, congeston prce aone s enough to refect the demand for more bandwdth of each vrtua n. But n our smuaton, the throughput-senstve utty functon and deay-senstve utty functon are so dfferent n the form, we have added to congeston prce λ to U () better refect the demand for bandwdth than the congeston prce aone. 5. Evauaton 5. Smuaton Resuts Fgure 4 compares the tme to convergence between our proposed agorthm and Davnc agorthm [6] n two nodes topoogy. The upper graph of Fg. 4 shows that wth the same settng of q 0.5,w,w2 0 5 α.2 and r () 0 Mbps, our proposed agorthm needs neary the same number of outer teratons, whch are the number of teratons to sove the master probem (3) dstrbutedy, as n 4.4 Substrate-Networ Dstrbuted Agorthm Impementaton We have mpemented our substrate agorthm on each OpenFow swtch. After each tme a host manager competes cacuatng the optma rate for a end-hosts, the host manager sends the newy updated congeston prce to the Fg. 4 Comparng wth Davnc n two nodes topoogy.

7 62 IEICE TRANS. COMMUN., VOL.E96 B, NO. JANUARY 203 Fg. 5 Stepsze α vs. convergence n Abene topoogy. Fg. 7 Tme to converge vs. T s. Fg. 6 Traffc on ENG and SCI networ. [6]. But, as showed n the ower graph, our agorthm needs much shorter tme to converge than the one n [6]. The reason for ths phenomenon s that for each outer teraton we need maxmum 0.2 seconds to sove optmzaton probems on two vrtua networs centray but [6] needs 2 seconds to sove them dstrbutedy. The more tme needed for [6] to sove probem at each teraton mae t converge sower than our proposed agorthm. Fgure 5 presents the number of teratons to convergence of our agorthm n the Abene topoogy. From the fgure, the agorthm converges very sow when stepsze α s so sma and dverses when stepsze α s arge. The reason s that when α s arge, the searchng pont w ump through optma pont after each teraton. Aso from the fgure, the graph wth demand r () 200 Mbps on deay senstve networ converges faster than the graph wth demand r () 0 Mbps. The reason of ths phenomenon s that the nta capacty for a vrtua ns of a vrtua networs are set to be 500 Mbps whch s the haf of each substrate n capacty. The nta vrtua n capacty vector s the nta pont for our optmzaton agorthm. Ths nta pont s nearer to the souton of demand 200 Mbps than the souton of demand 0 Mbps. So, the agorthm wth nput demand of 200 Mbps converges faster than the agorthm wth nput demand of 0 Mbps. 5.2 Testbed Evauaton Resuts Fgure 6 depcts the dynamcs of actua traffc on ENG vrtua networ (upper graph) and SCI vrtua networ (ower graph). Ths resut s based on the demands whch are changed randomy every 40 optmzaton teratons and α whch s 0.05 at the begnnng and beng added by 0.05 each tme the demand changes. The substrate n capacty s set to 5 Mbps. From the fgure, the convergence rate ncreases after each tme demand changes. But there are some perods such as 20, 200, 320, the convergence rate decreases even wth hgher α. Ths phenomenon s caused by the arge changng n demand. Our agorthm uses the optma ponts from prevous optmzaton perod to be the nta pont for the next optmzaton perod. If the nta pont s so far from the demand, our agorthm needs more teratons to converge. Fgure 7 depcts the vrtua n updated perod T s and the tme to convergence n 2 demand patterns whch are: ncrease wth Mbps step and 2 Mbps step. From the fgure, f the vrtua n update perod s smaer than the maxmum tme to sove the optmzaton probem n each vrtua networ added wth the communcaton tme between end hosts wth HostManager of that vrtua networ whch s equa 0.7 n our case, our agorthm w need very ong tme to converge. If T s 0.7 second, the vrtua networ optmzaton probem s guaranteed to be soved competey before the updated tme of our proposed agorthm () and our agorthm s converged. When our proposed agorthm converge, the tme to convergence s qute near wth the teraton perod (T s ). The reason s that the number of teratons needed to sove the master probem s neary constant. The near ncrease of tme to converge s ony caused by the ncrease n the updated tme perod T s. Fgure 8 shows how vrtua capacty of each vrtua networ adapts when there s a n-down event from teraton At teraton 36, when the physca n VLAN 3 s down, the capacty whch was aocated to both vrtua networs ENG (y () 2 )andsci(y(2) 2 ) from physca n VLAN 3 s vanshed. The capacty aocated to vrtua networ ENG (y () )andsci(y(2) ) from physca n VLAN 2 s adusted n around 20 teratons by our updated Eq. () to converge to the new optma pont that the aocated vrtua n capacty are proportona to the demands from both vrtua networs. When the physca n of VLAN 3 s up agan at teraton 48, our updated agorthm mmedatey aocates the equa bandwdth 3.5 Mbps to each vrtua n hosted on the physca n VLAN 3. Ths nta aocaton

8 TRINH et a.: DYNAMIC VIRTUAL NETWORK ALLOCATION FOR OPENFLOW BASED CLOUD RESIDENT DATA CENTER 63 Fg. 8 Ln recovery. phenomenon caused by far aocaton of Eq. (9). After the nta aocaton, our agorthm graduay adusts the aocated capacty to the new optma pont whch aocates tota 3 Mbps of traffc for the vrtua networ ENG and 7 Mbps of traffc for the vrtua networ SCI. 6. Concuson In ths paper, we have derved an agorthm to dynamcay aocate the capacty to vrtua networ ns for maxmzng the aggregated utty. Wth the coud resdent data center settng n mnd, we have used the centrazed agorthm to mpement n each vrtua networ to be sutabe wth Open- Fow centrazed controer. At the substrate networ, we have derved a new updated agorthm to mae use of congeston prce whch s cacuated from the centrazed controers. We have mpemented our agorthm n MATLAB as we as testbed envronment and the resuts show that our agorthm converge to the optmaty faster than the prevous approach so t can use physca resource more effectvey. To mae any optmzaton agorthm wor n the rea word, we need to tune many parameters of our agorthm. The convergence tme of our agorthm s based heavy on the convergence tme of each centrazed agorthm on each vrtua networ. In the future, we ntend to mprove the convergence rate of vrtua networ agorthm by precacuatng the optmzaton probem n vrtua networs wth a the nput demands and mae a mappng tabe between traffc demands and prma/dua soutons. When there s a demand come to the networ, the host manager ony needs to fnd the optma resuts from the mappng tabe. Future resuts w be reported accordngy. References [] E. Keer, D. Drutsoy, J. Szefer, and J. Rexford, Coud resdent data center, [2] Amazon vrtua prvate coud (amazon vpc), com/vpc/, 20. [3] M. A-Fares, S. Radharshnan, B. Raghavan, N. Huang, and A. Vahdat, Hedera: Dynamc fow schedung for data center networs, Proc. 7th USENIX Conference on Networed Systems Desgn and Impementaton, p.9, 200. [4] M. Azadeh, A. Greenberg, D. Matz, J. Padhye, P. Pate, B. Prabhaar, S. Sengupta, and M. Srdharan, Data center tcp (dctcp), ACM SIGCOMM Computer Communcaton Revew, pp.63 74, 200. [5] K. Ousterhout and J. Rexford, Reef: A reactvate, effcent, and fexbe system for nternet traffc management, 20. [6] J. He, R. Zhang-Shen, Y. L, C.Y. Lee, J. Rexford, and M. Chang, Davnc: Dynamcay adaptve vrtua networs for a customzed nternet, Proc ACM CoNEXT Conference, CoNEXT 08, pp.5: 5:2, New Yor, NY, USA, [7] N. McKeown, T. Anderson, H. Baarshnan, G. Paruar, L. Peterson, J. Rexford, S. Shener, and J. Turner, Openfow: Enabng nnovaton n campus networs, ACM SIGCOMM Computer Communcaton Revew, vo.38, no.2, pp.69 74, [8] R. Sherwood, G. Gbb, K. Yap, G. Appenzeer, M. Casado, N. McKeown, and G. Paruar, Fowvsor: A networ vrtuazaton ayer, OpenFow Swtch Consortum, Tech. Rep [9] N. Gude, T. Koponen, J. Pettt, B. Pfaff, M. Casado, N. McKeown, and S. Shener, Nox: Towards an operatng system for networs, ACM SIGCOMM Computer Communcaton Revew, vo.38, no.3, pp.05 0, [0] D. Eppsten, Fndng the shortest paths, SIAM J. Comput., vo.28, no.2, pp , 998. [] M. Póro and D. Medh, Routng, fow, and capacty desgn n communcaton and computer networs, Esever/Morgan Kaufmann, [2] D. Paomar and M. Chang, A tutora on decomposton methods for networ utty maxmzaton, IEEE J. Se. Areas Commun., vo.24, no.8, pp , [3] S. Boyd and L. Vandenberghe, Convex optmzaton, Cambrdge Unv Pr, [4] Scapy. [5] Cvxopt: Python software for convex optmzaton. uca.edu/cvxopt/ndex.htm Tr Trnh receved Bacheor as we as Master degree from Hano Unversty of Scence and Technoogy, Vetnam n 2004 and 2006 respectvey. He s now a Ph.D. student n the Department of Eectrca Engneerng, Chuaongorn Unversty snce In 20, he was an exchanged researcher n Esa s ab, The Unversty of Toyo. Hs research nterest s Networ Vrtuazaton, Coud Resdent Data Center, OpenFow, Traffc Engneerng, Networ Optmzaton. Hrosh Esa receved the Ph.D. degree from the Unversty of Toyo, Toyo, Japan, n 998. In 987, he oned the Research and Deveopment Center, Toshba Corporaton. From 990 to 99, he was wth the Apped Research Laboratory, Be-Core Inc., NJ, as a Resdenta Researcher. From 994 to 996, he was wth the Center for Teecommuncaton Research, Coumba Unversty, New Yor. Snce 998, he has served as a Professor at the Unversty of Toyo, and as a board member of WIDE Proect. Currenty, he s the Executve Drector of IPv6 promoton counc, Vce Presdent of JPNIC, IPv6 Forum Feow, Drector of Green Unversty of Toyo Proect, and Drector of WIDE Proect.

9 64 IEICE TRANS. COMMUN., VOL.E96 B, NO. JANUARY 203 Chaodt Aswau receved the B.Eng. degree wth st cass honour n Eectrca Engneerng from Chuaongorn Unversty, Thaand, n 994. From 995 to 2000, he receved the Ananda Mahdo Foundaton schoarshp to study for Ph.D. at the Impera Coege of Scence, Technoogy and Medcne, Unversty of London, U.K. After gettng Ph.D. n communcatons networng, he returned to Thaand and s currenty an assstant professor at the Department of Eectrca Engneerng, Chuaongorn Unversty. In , he has aso served as the manager of the Next Generaton Networ Testng/Tra Use Proect n Phuet of the Natona Teecommuncatons Commsson of Thaand. He s the cofounder of the unversty s Networ Research Group wth focuses on researchng n the quaty of servce and reabty ssues of both communcaton and transportaton networ systems.