DHA: Distributed Decisions on the Switch Migration Toward a Scalable SDN Control Plane

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1 DHA: Dstrbuted Decsos o the wtch Mgrato Toward a calable DN Cotrol Plae Guozhe Cheg, Hogchag Che, Zhmg Wag, huqao Che Natoal Dgtal wtchg ystem Egeerg & Techologcal R&D Ceter Zhegzhou, Cha [Emal: guozhecheg@hotmalcom, chc@dsccomc wagzm5@gmalcom, cheshuqao973@63com] Abstract Dstrbuted cotrol plae s a promsg approach to a scalable sotware-deed etworkg (DN) However, trac chages could cur load mbalace amog dvdual cotrollers Lve mgrato o swtches rom cotrollers that are overloaded to those that are uderutlzed may be a soluto to hadle peak swtch trac usg avalable cotrol resource uch mgrato has to be perormed wth a well-deed mechasm to ully utlze the avalable resource o cotrollers I ths paper, we study a scalable cotrol mechasm to decde whch swtch ad where t should be mgrated or a balaced cotrol plae, ad we dee t as swtch mgrato problem (MP) The ma cotrbutos o ths paper are as ollows Frst, we dee a DN model to descrbe the relato betwee the cotrollers ad swtches rom the vew o loads Based o ths model, we ormulate MP as a etwork utlty maxmzato (NUM) problem wth the obectve o servg more requests uder the avalable cotrol resource ecod, we desg a sytheszg dstrbuted algorthm or MP --- dstrbuted hoppg algorthm (DHA), by approxmatg our optmal obectve va Log-um-Exp ucto I such DHA, dvdual cotroller perorms algorthmc procedure depedetly Wth the soluto space, we prove that the optmal gap caused by approxmato s bouded by log, ad the DHA procedure s equal to a mplemetato o a tme-reversble markov cha process Fally, the results are corroborated by several umercal smulatos Keywords sotware-deed etworkg scalablty swtch mgratos markov cha I INTRODUCTION calablty s a key ssue or the DN cotrol plae Dstrbuted cotrol plae s a promsg approach to a scalable DN Each cotroller maages a part o swtches the etwork IBN IFIP but makes decsos based o a logcally cetralzed etwork vew However, the cotrol plae teds to ubalace ad ts perormace wll be degraded, sce the curret statc structure betwee cotrollers ad swtches caot adapt or the etwork trac chages At rst stage, DN deploys oly oe cetral cotroller that s resposble or all the swtches []-[3] Ths archtecture could readly acheve etwork state cosstecy ad avod commucatos amog deret cotrollers But the sgle resource-lmted cotroller coes the DN paradgm to a small-scale etwork, because a large etwork could experece the overloadg o the cotroller due to the requet ad resource-exhaustve evets such as OpeFlow (OF) PACKET- IN evets [4] For example, the low setup tme a overloaded cotroller ca rse sgcatly, ad ts perormace ca deterorate rapdly A ew recet attempts are subsequetly take to tackle ths problem va the dstrbuted schemes whch may all to two maor groups: those horzotally equalzg all cotrollers, e, lat archtecture [4, 5], ad those vertcally layerg rom root cotroller to lea oes, e, herarchcal archtecture [6] Both archtectures have comparatvely mproved the scalablty o DN cotrol plae, but the statc map betwee cotrollers ad swtches lead to load mbalace amog cotrollers For stace, real measuremet or etwork trac shows that -2 orders o magtude derece betwee the peak ad meda low arrval rates at a swtch [7] Curret statc coguratos could easly duce that some cotrollers are overcommtted ad become hot spots, but other cotrollers are uderutlzed ad tur to cold spots Workloads have to be oloaded rom the hot spots sce there s adequate resource to meet servce level agreemets (LAs) Oppostely, cold spots expect to serve more swtches or the hgh etwork utlty Wheever a swtch receves a low, t searches ts low table to d the etry matched As the match s aled, t requests the cotroller to calculate the low path ad stall approprate rules The tme requred to complete ths operato s kow as the low setup tme

2 The recet verso o OpeFlow protocol [8] has realzed the problem caused by such statc coguratos Thereore, t proposes that each swtch could be cotrolled by three deret roles o cotrollers, master, equal ad slave Geerally, there s oly oe master cotroller or a swtch The master ca ot oly etch the swtches states but also wrte rules to ts swtches to struct the data plae The equal cotrollers are troduced to separate the loads rom the master They have the same authorty wth master The slaves oly read the states rom ts swtches Each swtch could have more tha oe equal ad slave cotrollers I the master s aled due to overload or some exceptos, the equal cotrollers, or eve slaves could be trasted to master as soo as possble However, the OF spec suggests o mechasm explctly dcatg the swtch mgrato or cotroller roles sht, because the wrters o ths spec thk that ths s the resposblty o the cotroller to choose a master amog themselves We beleve that such mgrato has to be perormed wth a well-deed mechasm to ully utlze the avalable resource o cotrollers I ths paper, we ocus o desgg a scalable cotrol mechasm va solvg MP problem To the best kowledge o the authors, ths s the rst work to specally solve the MP or a more balacg DN cotrol plae The ma cotrbutos ths paper are as ollows We rst gve a DN model to descrbe the relato betwee cotrollers ad swtches, ad the we dee MP problem as a NUM wth the obectve o servg more loads uder avalable cotrol resources Based o the Markov approxmato ramework [4], we approxmate our optmal obectve wth a Log-um-Exp ucto, ad desg a sytheszg dstrbuted algorthm, dstrbuted hoppg algorthms (DHA), to approach the optmal soluto o the MP We prove that the gap betwee the approxmated soluto ad the optmal oe s lmted ad the soluto search path o our DHA s a markov cha path wth a statoary probablty dstrbuto We mplemet a scalable cotrol mechasm based o our DHA algorthms, ad valdate ts perormace real IP topologes The remader o ths paper s orgazed as ollows The ext secto gves the related works The secto III dscusses the tuto ad detals o our model or DN I secto IV, we reduce our DN model to etwork utlty maxmzato problem ecto V presets the desg o dstrbuted hoppg algorthms ecto VI descrbes a mplemetato o scalable cotrol mechasm ecto VII valdates our DHA ecto VIII cocludes ths paper II RELATED WORK ON ELATIC CONTROL Curret statc map betwee cotrollers ad swtches prevets cotrollers rom exchagg the etwork loads accordg to the trac chages To address ths problem, ElastCo [9] s provded to dyamcally grow or shrk the amout o cotrollers set ad mgrate the swtches amog cotrollers alog wth the etwork trac mlarly, V Yazıcı [] proposed a coordato ramework or scalablty ad relablty o dstrbuted cotrol plae But the MP problem about how to select mgrated swtches ad ther target cotrollers s ot solved properly B Heller et al [] solve how to place the cotrollers based o propagato latecy But ths work oly ocused o where to place multple cotrollers statcally Guag Yao et al [2] cosder cotroller placemet problem rom the vew o the cotroller load To acheve more perormace ad scalablty large-scale WAN, Md Fazul Bar et al [3] provde a dyamc cotroller provsog ramework to adapt the umber o cotrollers ad ther geographcal locatos The ramework mmzes low setup tme ad commucato overhead by solvg a teger lear program But t has to perorm a reassgmet o the etre cotrol plae based o the collected trac statstcs Ths operato easly leads to etwork stablty because t curs massve state sychrozatos Furthermore, both ts greedy ad smulated aealg approaches are cetralzed algorthms whch do ot adequately utlze the resource o dstrbuted cotrollers To sum up, the exstg solutos to dyamc cotroller provsog problem (DCPP) are chagg the umber o cotrollers ad ther locato va reassgg the swtches or cotrollers Ths operato s lkely to cur etwork stablty due to a large umber o state sychrozatos amog cotrollers Ths artcle has two dereces compared wth the exstg works Frst, our pvot s to solve the MP problem so that we ca elmate the mbalace o the cotrol plae wth the avalable resource ecod, based o the archtecture o dstrbuted cotrollers, we desg a sytheszg dstrbuted algorthm that each cotroller rus ts ow algorthmc procedure depedetly III YTEM MODEL A The Motvatos The obectve o the swtch mgrato s to serve more etwork lows uder avalable resource ad maxmze the resource utlty the cotrol plae I practce, there are may cases that eed to chage the mappgs Frstly, sce a swtch request to a cotroller may peak at deret tmes, there s a opportuty to crease cotroller resource utlzato by movg more swtches to the same cotroller durg o-peak seasos The cotrollers wthout swtches could be shut dow or sleep or savg power ad commucato cost Ths ca hamper the cotrol plae sprawl, ad we call ths operato as swtches cosoldato ecodly, oce some swtches ecouters ther peak trac, they ca use up all avalable resources at the cotroller where

3 they are placed Oe bg problem we may ecouter s that cotrollers may become overloaded whle other cotrollers maybe uderutlzed order to mprove etwork perormace ad resource utlzato, a possble cogurato s movg some swtches rom heavy cotrollers to lght oes We call ths operato as load balace Thrdly, all actve cotrollers become overloaded, t s mpossble to elmate hotspots by swtch mgratos The operator wll deploy some ew cotrollers, ad swtches wll be mgrated to such ew cotrollers Wth lve swtch mgrato, the swtch trac beg served at the same tme may be eectvely creased by mgratg swtches wth addtoal resource eeded rom resourcedecet to resource-rch cotrollers However, such mgrato has to be perormed wth a well-desged mechasm to ully utlzed avalable resources Note that, the precedg three cases could be detected by a load estmato applcato o the cotroller Our algorthm could be used to solve them by desgg specc optmal obectves I the rst case, we should desg a cotrol power ucto as payo ucto, ad the mmze t such cotrollers I the secod case, we should desg a utlty ucto as payo ucto, ad the maxmze etwork lows requests uder avalable resource Essetally, the thrd oe s a specal case o secod oe For bre, we dscuss load balace case the resdual part o ths paper Our uture work wll explore the rst case whch could toward a gree etwork B DN Model Our pvot ths paper s the swtch mgrato problem towards more balaced cotrol plae o we assume that the DN cotrollers have bee optmally placed the dstrbuted topology As the lterature [2] stated, the load o a DN cotroller cossts o may actors, such as processg o PACKET_IN evets, matag the local doma vew, commucatg wth other cotrollers, as well as stallg low etres I deret scearo, the proportos o those actors der greatly But the processg o PACKET_IN evets s geerally regarded as the most promet part o the total load [5] Accordgly, the arrvg rate o PACKET_IN evets o a cotroller s couted to measure ts load Thereore, we gve our DN model as ollows We cosder a DN cosstg o N cotrollers c, c2,, c N, ad M swtches s s s,,, M 2 Let a be the cotrol load geerated by swtch s, ad d be the upper load lmts o swtch s Accordgly, the swtch s ca be deoted as s : a, d We use :, c A as the cotroller model A represets the capacty or the cotroller c, ad swtches maaged by cotroller c IV deotes the set o NETWORK UTILITY MAXIMIZATION PROBLEM IN DN Our prmary obectve s to d out how swtch mgrato polces should be employed so that the etwork utlty s maxmzed We assume that the more evets the cotroller hadles uder the avalable resource, the hgher the utltes wll be produced Based o the our DN model, we ormulate swtch mgrato problem as a cetralzed etwork utlzato maxmzato problem DN, MP : max c U () s t a A, c (2) s a d, s, c (3) c,, ad (4) (5) where U s etwork utlty produced by cotroller c I MP, the costrats (2) lmt that the total load caot exceed cotroller s capacty The costrats (3) lmt the upper boud o each swtch to avod that a small part o swtches exhausts cotroller resource The costrats (4) esure that deret cotrollers do ot overlap Ad the costrats (5) esure the sel-cota o set We beleve that oce a cotroller s powered o, the more resource t s possessed, the more utltes t wll produce all the resource cosumers are legal I addto, we assume that etwork utlty ucto s twce deretable, creasg ad strctly cocave Hece, we dee etwork utlty ucto or c wth log ucto, U loga (6) s The the obectve ucto ca be reormulated as, Where B max U max c c s t deotes the etwork utlty produced by swtch o the cotroller, e, B (7) B log a (8)

4 Uder the costrats o MP, the more load a cotroller serves, the more etwork utltes t wll produce V DITRIBUTED HOPPING ALGORITHM Theoretcally, the problem MP ca be reormulated as - teger lear program, whch s a typcally combatoral etwork optmzato problem, ad very dcult to solve Although we ca approach the optmal soluto through lagraga relaxato wth quadratc equalty costrats ad solve ts dual problem, or decouplg t to several kapsack problems, t curs tme cosumg [6] Actually, may mportat etwork desg problem ca be ormulated as a combatoral etwork optmzato problem, ad a surge o studes have bee provded to solve t ad have made a sgcat progress, but may o them are desged to cetralzed mplemetatos [7] or tme-cosumg as the etwork sze becomes larger [8][9] I our scearo, we eed a approach that ca be cocurretly processed a dstrbuted maer, because each DN cotroller maages ts local swtches ad teracts wth ts eghbors Moreover, etwork rug the dstrbuted algorthms are more robust to the etwork dyamcs (eg, swtch mgrato ad cotroller sleep) I ths artcle, we reer to a markov approxmato ramework usg the log-sum-exp ucto to approxmate the optmal value o our MP Based o ths, we provde a dstrbuted hoppg algorthm a sytheszg orm I the subsequet secto, we rst descrbe the log-sum-exp approxmato o MP The we llustrate the detaled desg o DHA A Log-um-Exp Approxmato Let deote the -algebra o, ad s cossted o all the subsets o (cludg empty set ad ), we dee a etwork cogurato as a etwork partto Deto Network Cogurato,,,, N s a cogurato o etwork, ad,, c, where deotes the swtch set cotrolled by c uder the cogurato Let be the set o all easble The MP problem ca be rewrtte as ollows, MP : max B c s (9), c ad () s t a A s a d, s ad () where B deotes B calculated by equato (8) uder cogurato a represets cotrol load geerated by swtch s uder cogurato The problem maxmzes etwork utlty by choosg a optmal cogurato However, sce the easble cogurato set s expoetally large, t s stll a NP-hard combatoral etwork optmzato problem Let p be the percetage o tme that cogurato s use o cogurato space A equvalet ormulato o the problem MP s as ollows, MP EQ : max p B p c s (2) Besdes all the costrats o the problem MP, the equato p s satsed or the problem MP EQ To solve ths problem, we use the log-sum-exp ucto to approxmate the optmal value o MP EQ as ollows, max log exp s B B c c s (3) where s a postve costat As the Theorem lterature [4] stated, we solve the approxmated verso o the problem MP EQ, o by a etropy term p log p o the obectve o MP EQ ca be rewrtte approxmated orm, MP MA : max p B p log p p c s (4) Ths addtoal etropy term opes a ew desg space or explorato ce the obectve ucto o problem MP MA s twce deretable, creasg ad strctly cocave or all p, ad all the costrats are lear, Karush-Kuh-Tucker (KKT) codtos are ecessary ad sucet or a exstg optmal soluto We ca coclude that, Theorem The optmal soluto o the problem * s p B, lke that, * p B exp c exp s c s B B, UM MA

5 The optmalty gap betwee MP ad MP MA s bouded by log, where represets the sze o The symbol B B, B2, B BMN The proo ca reer to our techcal report about ths paper [2] B Dstrbuted Hoppg Algorthm Desg Based o Markov Cha As stated Lemma o the lterature [4], there exsts at least oe cotuous-tme tme-reversble ergodc markov cha * p A The state space has to wth statoary dstrbuto satsy two codtos Frst, wth the property o ergodcty, ay two states ths state space ca commucate wth each other through at least oe path ecod, the markov cha must obey p B q B p B q B detaled balace equato, e,,, where q B, We dee eghbor set deotes the trasto rate rom the strategy to o c as the cotrollers whose swtch drectly lks to at least oe o swtch trasto rate q B, The wll be ot zero, both coguratos,,,,,, 2 N ad,,,,,, 2 N satsy, C: c \{ c, c },, 2 2, where represets the elemet 2 2 umber o set That meas oly oe swtch s mgrated rom oe swtch set to aother C2: c 2 amog eghbors, e, the swtch mgrato oly happes We dee the set as satses to the above two codtos wth We ca see that the ump rom to s scale-lmted so that oly two correspodgly eghborg cotrollers chage ther utlzato ratos ad take the remder, deotes the varable varable Accordgly, let domas uder both cogurato ad It wll appear betwee both sdes o detaled balace equato, we thus gore t The trasto rate q, B our scearo s ormulated as the revsed verso o OPT the lterature [4], e, q, B exp B c, s (5) Where the ucto a c b a, b c else q B, ca be calculated a symmetrc way I we lmt that the swtch oly mgrated to ts eghbors, we ca see that the trasto rate ca be calculated a local way I DN, there s a logcally cetralzed global vew where all cotrollers share the ormato Thereore, each cotroller ca collect resh value ad q B, B, to calculate q B, Let q B q B, the etwork wll soour the state, or a perod that reduces to the expoetal dstrbuto wth parameter q ca deduce that, B Based o the theorem, we q B B c, s exp (6) The cogurato s composed o the local parttos o all dvdual cotrollers The trasto rom cogurato to s take place by a swtch mgrato rom oe cotroller to ts eghbor I each cotroller couts dow a clock ad wats or trasto utl clock termates, we ca desg that the trastos are preset at two eghbor cotrollers The, the Markov Cha ca be calculated a dstrbuted maer We brely descrbe the dstrbuted hoppg algorthm (DHA) as ollows The ollowg procedure rus o each cotroller depedetly, ad we ocus o a partcular cotroller c tage : Itally, gve a DN topology wth dstrbuted cotrollers, ay cotroller c s allocated a swtch doma uder the cogurato tage 2: Cotroller c radomly selects a swtch s rom ts doma wth the sze o ad a cotroller c rom ts eghbor set The c wll cout dow a radom umber The radom umber s geerated by the expoetal dstrbuto wth mea u whch represets as ollows, u exp Bˆ (7) c, s tage 3: I the cout s expred ad o exstg swtch mgrato actvty ts eghbors s sesed, the cotroller c wll broadcast the comg mgrato actvty betwee c ad c to ts eghbors The the cotroller c wll mgrate the selected swtch to the cotroller c Ater mgrato, the cotroller c wll update all utlzato ratos Bˆ o the swtches

6 , to the etwork global vew, ad broadcast t to ts eghbors tage 4: Coversely, there s such a actvty betwee ts eghbors, the cotroller c resets the tmer The algorthm returs to tage 2 The pseudocode o DHA s show Algorthm whch rus o each dvdual cotroller depedetly We ocus o a partcular cotroller c Algorthm Dstrbuted Hoppg Algorthm : Italzato: 2: Ital cogurato, cotroller c wth swtch set 3: Let c s eghbor set be 4: Let k, tag = 5: Ed 6: Procedure electo( c ) 7: Radomly select a swtch s rom 8: Radomly select a cotroller c rom 9: Acqures total utlzato ratos o, : Geerates a tmer wth T ' ', rad exp u : Beg coutg dow T 2: whle the tmer T does ot expre do 3: sese the exstece o swtch mgrato actvty the 4: tag = 5: break 6: ed 7: ed whle 8: I tag == the 9: Termates curret coutdow tmer ad voke ecto( c ) 2: Tag = 2: else 22: Cotroller c mgrate swtch s to cotroller c 23: Aouces to ts eghbors 24: ed We the have the cocluso as ollows Theorem 2 The process o dstrbuted hoppg algorthm s the mplemetato o tme-reversble Markov Cha wth * statoary dstrbuto p B, The proo ca reer to our techcal report about ths paper [2] VI IMPLEMENTATION A I ths secto, we mplemet a cotrol mechasm prototype atop Beaco cotroller [26] based o DHA algorthm, called, cludg a load estmato module, a DHA decso module ad a dstrbuted data store module Load Estmato A load estmato module rus as a cotrol applcato It tracks the cotroller loads, ad predcts the average message arrve rate rom each swtch We set two thresholds, upper lmt ad lower lmt, to dcate whether startup our DHA modules I the loads are less tha lower lmt or bgger tha upper lmt or oe mute, load estmato trggers DHA module to swtch mgrato DHA Decso Each cotroller rus a DHA stace to decde the swtch mgrato There are two operatg models or DHA, the balace oe ad the gree oe Frst, a cotroller s a hot spot, e, ts loads are bgger tha the upper lmt or oe mute, DHA wll work the balace model to oload part o loads or equlbrum ecod, a cotroller s cold spot, e, ts loads are less tha lower lmt, DHA wll work the gree model to oload all loads ad shut dow ths cotroller Dstrbuted data store A dstrbuted data store provdes a logcally cetral vew or cotroller cluster It stores all swtches ormato, cludg data rom load estmato module B Cotroller-to-Cotroller Iterace We eed to exted eastboud ad westboud terace so that cotrollers could commucate wth each other durg DHA process As show Fg, suppose cotroller c wth eghbors, each rus a DHA thread Whe the coutdow tmer c expres, ad there are o exstg mgrato actvtes ts eghbors, t wll emt mgratg request message to ts selected destato c d Ths message cludes the mgratg swtch ID The cd wll reply a ACK message to c The cotroller c broadcast otcato message to ts eghbors to suggest that there s a mgrato actvty betwee c ad c d Fally, the swtch mgrato could be started We reer the reader to [9] or detals o messages eeded durg swtch mgrato Fg The message teractos amog cotrollers

7 Ater oe tme o swtch mgrato, cotroller c ad c d update ther utlzato ratos the cetral data store, ad broadcast updates to ther eghbors respectvely VII THE NUMERICAL EVALUATION A mulato etup I ths secto, we evaluate the perormace o our prototype uder the expermetal evromet show Fg 2 Cosder perormace terereces betwee Met ad cotrollers, we deploy Met [2], Beaco cotroller ad our o deret physcal maches Each physcal mache rus Ubutu 24 LT wth JDK 7 Istead o the artcal topologes, we use two real etwork topologes Chaet [22] (38 odes ad 59 lks) ad Ceret [23] (36 odes ad 53 lks) rom zoo topology Chaet s a real IP topology rom Cha Telecom, oe o three largest IPs Cha Ceret s the largest educato ad research etwork Cha I addto, we stall Beaco cotroller a dvdual mache to smulate sgle cetralzed cotroller Other ve physcal maches ru staces All physcal maches have exactly the same cogurato wth 34GHz Itel Core 7 processor, 4GB o DDR3 RAM ad a Gbps NIC They are coected by a H3C 55 swtch We use per [24] to geerate TCP lows betwee hosts To smulate realstc trac, all lows are geerated as trac characterzato descrbed by [25] such as low sze dstrbuto ad arrvg rate Fg 2 the expermetal topology We ocus o veryg whether our dstrbuted hoppg algorthm ca mprove the perormace ad scalablty o dstrbuted cotrol plae We compared our (4 cotrollers) wth the scearos o sgle cotroller (), statc dstrbuted cotrollers () (4 cotrollers), ad Dyamc Cotroller Provsog Problem wth Greedy Kapsack ad mulated Aealg ( ad DCP-A) I or DCP-A, we tally deploy our cotrollers, ad we wll add a ew oe whe oe o ts cotrollers overload peccally, we rst compare average low setup tme alog wth trac lows The, we evaluate the mgrato cost caused by DHA Thrd, we compare the average utlzato ratos o cotrollers Fally, we evaluate utlty gap o DHA I our expermet, we dee utlty gap as the derece betwee system utlty acheved by DHA ad the optmal utlty obtaed by exhaustvely searchg algorthm whch search the easble cogurato space B Parameters Measuremet Beore our evaluato, we have to get the values o some parameters DHA, that s, cotroller capacty ad the upper lmts o swtch We use the topology that two physcal maches are coected wth a swtch Oe mache rus a Beaco stace, aother rus Cbech [27], a program or testg OpeFlow cotrollers Each mache has oe NIC wth Gbps Cbech works throughput mode wth the commad, cbech -c p m -l -s 6 -M -t We d that the average throughput o Beaco s about 5 klo requests per secod wth 4 threads I our expermet, sce the swtch badwdth s lmted by the loopback terace o Met, t s dcult to overload the dstrbuted cotrollers o we have to restrct the cotroller capacty at a low level so that the cotroller s over-subscrbed less tha the actors o :5 (I dataceter etwork up-lks rom ToRs are typcally :5 to :2 oversubscrbed [28]) The capacty o each cotroller our expermet s lmted to 3 klo requests per secod Ad the upper lmt o swtch s smply calculated by equato (8), where k represets the umber o swtches uder the cotroller, ad a represets average loads geerated by swtch s d throughput k r a (8) At the rght had o the equato, the rst tem, called basc tem, s calculated based o the cotroller throughput, cotrol scale ad over-subscrpto rato The secod tem, called dvdual tem, s a radom umber ot beyod a C Numercal Results Our obectve s to crease etwork utltes, so that they ca hadle as may OF evet requests as possble wth ther avalable resources We set 5 durg smulatos Flow cout (k) Flow cout (k) Tme (hour) Tme (hour) (a) Chaet (b) Ceret Fg 3 Flow cout 8

8 We ru each smulato or 6 hours Fg 3 shows the low couts o Ceret ad Chaet respectvely mulatos are repeated or three tmes At each tme, we record low setup tme, the umber o packets exchaged betwee cotrollers, ad cotroller utlzatos or deret scearos We show the average results o three repeated smulatos Flow setup tme I the smulato, we use average low setup tme to measure the eect o our, because t relects cotroller load chages caused by swtch mgrato We compare the average low setup tme o (4 cotroller staces),, (4 cotroller staces), ad DCP-M (4~5 cotroller staces) two deret topologes Fg 4 shows ther tme curves We ca see that s a costat, sce sgle cotroller s overloaded durg the smulato However, the low setup tme or other our scearos luctuates alog wth low cout, yet has deret rages That s, has the largest luctuato, takes secod place, ad ad DCP have less luctuato Avg low setup tme(ms) Emprcal CDF DCP-M Avg low setup tme(ms) Tme (hour) Tme (hour) (a) Chaet (b) Ceret Fg 4 Average low setup tme Emprcal CDF DCP-M 2 DCP-M Flow setup tme(ms) Flow setup tme(ms) (a) Chaet (b) Ceret Fg 5 Emprcal CDFs There are several reasos to expla the above results Frst, sgle cotroller has the lowest scalablty due to ts resourcelmted archtecture ecod, compared wth, although has a dstrbuted cotrol plae, ts statc archtecture s lkely to duce some heavy cotrollers that suer rom log low setup tme Thrd, ad DCP-M could elmate overloaded cotroller va addg a ew cotroller, ad DHA- CON acheves such scalablty va swtch mgrato That s, ad DCP-M must ru reassgmet betwee cotrollers ad swtches whle our oly mgrate several swtches rom oe overloaded cotroller to lght oe DCP-M The emprcal CDFs Fg 5 detely preset that dyamc cotrol plae (e, ad DCP) are less vulerable to low cout tha Overhead We compare the overhead or ve scearos Fg 6 presets the commucatg overhead ad average low setup tme wth Chaet ad Ceret topologes has the lowest commucatg overhead because there are o cotrollerto-cotroller messages Compared wth, has hgher overhead, because cotrollers eed to state sychrozato or global etwork vew geerates more packets tha, sce t eeds to mgrate swtches except state sychrozato DCNTL But the cost or mgrato swtches s small, o more tha 2% o ad DCP-M have hghest commucatg overhead Ther cost s twce tmes that o, ad 5 tmes that o, because DCP that reassgs the mappgs betwee cotrollers ad swtches wll cur more swtch mgratos tha As metoed earler, average low setup tme or s lowest tha other scearos, about 2 s The average low setup tme or ad DCP-M are close to our DHA- CON, about 25 s or Chaet ad Ceret respectvely But the average low setup tme or ad are more tha 65 s ad 35 s or both topologes AvgFlow setup tme (s) % Utlzato AvgFlow setup tme Overhead DCP-M 6 Overhead (packets) Avg Flow setup tme (s) (a) Chaet (b) Ceret Fg 6 ummary o Overhead ad Average Flow etup Tme DCP-M % Utlzato Tme (hour) Tme (hour) (a) Chaet (b) Ceret Fg 7 Average cotroller utlzato Average utlzato rato To valdate the scalablty o DHA- CON, we cout the average utlzato rato or deret scearos As show Fg 7, has % utlzato due to ts lmted resource Each cotroller has more tha 9% utlzato ce balaces the loads amog cotrollers so that more requests ca be served Cotroller has less tha 8% utlzato average because the load mbalace amog deret cotrollers DCP AvgFlow setup tme Overhead DCP-M DCP-M Overhead (packets)

9 GK ad DCP-M have lowest utlzato average Although DCP could serve the same total loads wth, but t eeds more cotrollers tha (oe more tha DHA- CON our smulato) Utlty gap Theorem provdes a utlty loss boud or our DHA algorthm I the worst case, the Log-sum-exp approxmato ca lead to utlty loss o log, where s the umber o easble etwork coguratos I our smulatos, we have, log or Chaet 5 log log or Ceret 5 We obta the optmal etwork cogurato by exhaustvely searchg the easble etwork coguratos Whe 5, the average actual utlty loss s 23 ad 22 or Chaet ad Ceret We see that the perormace loss boud s guarateed, ad the observed utlty loss s qute smaller tha the boud VIII CONCLUION I ths paper, we make the rst attempt to explore MP problem or more scalable cotrol plae uder the avalable resource We rst model ths problem as a NUM problem rom the vew o etwork loads Ad the, we desg a sytheszg dstrbuted algorthm to solve t Fally, we mplemet a prototype ad valdate t two real topologes O cause, the cotrol load ad localty are ot the oly mportat actors whe choosg target cotrollers Reslece s also a mportat aspect We wll study them the uture Reereces [] N McKeow, T Aderso, H Balakrsha, G Parulkar, et al, Opelow: eablg ovato campus etworks, IGCOMM CCR, 28, pp-6 [2] N Gude, T Kopoe, J Pettt, B Pa, M Casado, N Mckeow, ad heker, NOX: Towards a Operatg ystem or Networks, IGCOMM CCR, 28 [3] Davd Erckso, "The Beaco OpeFlow Cotroller," I Proc st Workshop o Hot Topcs otware Deed Networkg (HotDN 23), pages 3-8, Hog Kog, 23 ACM Press [4] A Tootoocha ad Y Gaal, HyperFlow: A Dstrbuted Cotrol Plae or OpeFlow, INM/WREN, 2 [5] Teemu Kopoe, Mart Casado, Natasha Gude, et al, Ox: a dstrbuted cotrol platorm or large-scale producto etworks, I Proc ODI 2, pages , Berkeley, 2 UENIX Assocato [6] ohel Hassas Yegaeh ad Yashar Gaal Kadoo: a ramework or ecet ad scalable oloadg o cotrol applcatos I Proc HotDN 22, pages 9-24, New York, 22 ACM Press [7] T Beso, A Akella, ad D Maltz, Network trac characterstcs o data ceters the wld, IMC, 2 [8] OpeFlowhttps://wwwopeetworkgorg/mages/stores/dowloads/sd -resources/o-speccatos/opelow/opelow-spec-v4pd [9] A Dxt, F Hao, Mukheree, T Lakshma, R Kompella, "Towards a Elastc Dstrbuted DN Cotroller," I Proc st Workshop o Hot Topcs otware Deed Networkg (HotDN 23), pages 7-2, Hog Kog, 23 ACM Press [] V Yazıcı, M Oğuz uay, Al Ö Erca Cotrollg a otware- Deed Network va Dstrbuted Cotrollers I NEM submt 22 arxv:4765(22) [] B Heller, Rob herwood, ad Nck McKeow The cotroller placemet problem I Proc st Workshop o Hot Topcs otware Deed Networkg (HotDN 22), pages 7-2, New York, 22 ACM Press [2] Guag Yao, Ju B, Yulag L, ad Luy Guo O the Capactated Cotroller Placemet Problem otware Deed Networks IEEE COMMUNICATION LETTER, 24 [3] Md Fazul Bar, Arup Rato Roy, hhabur Rahma Chowdhury, Q Zhag, Mohamed Fate Zha, Reaz Ahmed, ad Raou Boutaba Dyamc Cotroller Provsog otware Deed Networks I CNM, pp [4] M Che, Lew, Z hao, ad C Ka, Markov Approxmato or Combatoral Network Optmzato, Proceedgs o IEEE INFOCOM 2, a Dego, CA, U, March, 2 [5] A Tootoocha, Gorbuov, ad Y Gaal, et al, O cotroller perormace sotware-deed etworks, Proc o HotICE, 22 [6] Y Feg, B L, ad B L, Bargag towards maxmzed resource utlzato vdeo streamg dataceters, Proc o INFOCOM, 22 [7] P Laarhove ad E Aarts, mulated aealg: theory ad applcatos prger, 987 [8] Raagopala ad D hah, Dstrbuted algorthm ad reversble etwork, Proceedgs o CI, 28 [9] J Lu, Y Y, A Proutere, M Chag, ad H Poor, Towards Utlty optmal Radom Access Wthout Message Passg, pecal ssue Wley Joural o Wreless Commucatos ad Moble Computg, Dec, 29 [2] B Latz, B Heller, ad N McKeow A etwork a laptop: rapd prototypg or sotware-deed etworks I Proceedgs o HotNets 2, pages 9: 9:6 [2] -TR-, [22] [23] [24] [25] Gebert, R Pres, D chlosser, ad K Heck Iteret access trac measuremet ad aalyss, I Trac Motorg ad Aalyss, volume 789 o LNC, pages [26] Davd Erckso, "The Beaco OpeFlow Cotroller," I Proc st Workshop o Hot Topcs otware Deed Networkg (HotDN 23), pages 3-8, Hog Kog, 23 ACM Press [27] ROB HERWOOD AND KOK-KIONG YAP Cbech: a OpeFlow Cotroller Bechmarker [28] Albert Greeberg, James R Hamlto, Navedu Ja, et al, VL2: A calable ad Flexble Data Ceter Network, Proc o IGCOMM 9, Pages 5-62, Barceloa pa Aug 29, ACM Press