Research of Flow Allocation Optimization in Hybrid Software Defined Networks Based on Bi-level Programming

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1 Reserch of Flow Alloction Optimiztion in Hybrid Softwre Defined Netwo Bsed on Bi-level Progrmming Abstrct Lulu Zho, Mingchun Zheng b School of Shndong Norml Univeity, Shndong , Chin fryrlnc@163.com, b zhmc163@163.com As trnsition from Trditionl Netwo to Softwre Defined Netwo, Hybrid Softwre Defined Netwo (SDN) shows significnt reserch vlue. Hybrid SDN successfully fces the chllenges tht SDN comes with, such s robustness nd sclbility. In this pper, we describe the networ rchitecture of flow-bsed hybrid softwre defined netwo. We show how to distribute different flows in flow-bsed hybrid SDN to relize optimiztion of the entire networ, using models of bi-level progrmming nd stochstic user equilibrium. Keywords softwre defined netwo, bi-level progrmming, hybrid SDN. 1. Introduction Softwre Defined Netwo(SDN) [1] promises to ese design, opertion nd mngement of communiction netwo by seprting routing nd forwrding function in trditionl route. However, SDN comes with its own set of chllenges, including sclbility nd robustness. Those chllenges me full SDN deployment difficult in the short-term nd possibly inconvenient in the longer-term. Therefore, lots of schol come up with conceptions of hybrid SDN. Besides the role s trnsition from trditionl netwo to SDN, Hybrid SDN hs its own superiority. On the one hnd, Hybrid SDN bsorbs dvntges of SDN [2], such s flexibility by decoupling control plne from dt plne, stbility by centrlized controller nd complete view of the underlying networ. On the other hnd, Hybrid SDN retins dvntges of trditionl netwo, such s sclbility nd robustness [3]. Hybrid SDN rchitecture cn be clssified into node-bsed hybrid SDN nd flow-bsed hybrid SDN. Flows in different networ system follow their own forwrding protocols; s result, flows in SDN system nd trditionl netwo (hereinfter referred to s TN) system possess different chrcteristics. SDN flows require SDN trnsponde to forwrd dt, nd on the contrry TN flows requires route to forwrd dt. Node-bsed Hybrid SDN rchitecture is bsed on the vriety of nodes (which re the trnsponde nd route in the networ) in netwo; comprtively, flow-bsed hybrid SDN is bsed on the vriety of flows in netwo. In short, node-bsed hybrid SDN system contins different inds of nodes, flows follow vrious protocols forwrding in corresponding nodes. Similrly, flow-bsed hybrid SDN system contins only one ind of node which cn forwrd ll inds of flows. At present, there hve been quite lot of reserches on SDN [4] nd trffic engineering of SDN [5], some of them introduce virtuliztion into SDN rchitecture to solve the problem of sclbility [6], some of them focus on the reserch of OpenFlow [7] technology used in SDN. However, reserches on hybrid SDN rchitecture re insufficient. Thus, we come up with the flow-bsed SDN rchitecture; discuss how to optimize flow lloction using methods of bi-level progrmming. 2. Architecture Hybrid SDN rchitecture, put forwrd to meet the complex requirement of netwo s well s to me up for the insufficient of SDN rchitecture, brings topology nd technology which re developed in trditionl netwo into SDN. Schemtic of flow-bsed hybrid SDN is shown below: 25

2 Fig. 1. Flow-bsed Hybrid SDN Architecture As cn be seen in the schemtic, flow-bsed hybrid SDN rchitecture is divided into two lye: 2.1 Physicl Networ: Switche in physicl networ support dt forwrding protocol of trditionl IP networ, besides, these switche cn be used s SDN trnsponde which follow commnd of controlle in controller lyer. As result, these switche hve to provide mple spce to store the dt-flow grphs which re generted by controlle. As stted, flow-bsed hybrid SDN rchitecture chieves the forwrding of SDN flows nd TN flows. 2.2 Controller Lyer: Controller lyer plys the role of bstrcting resources in physicl networ, it lso offe open interfce to pplictions which mes ppliction progrmming possible. Applictions in this wy cn flexibly control dt flows. Wht clls for specil ttention is tht controller lyer only controls nodes who forwrd SDN flows. 3. Model 3.1 Model Foundtion As described in the rchitecture, there re two inds of flows in the networ: SDN flows nd TN flows. Condition of flow lloction is decided by the interction of different flows. Before forwrding CN flows, we hve to consider the occupied resources by SDN flows. At the sme time, controlle commnd SDN flows forwrding, which results in new condition of resources occuption. The interction of flows forms Stcelberg Competition nd cn be represented s leder-follower gme where the trnsport plnner mes networ plnning decisions, which cn influence, but cnnot control the use route choice behvior. The use me their route choice decisions in user optiml mnner. We formulte the problem s bi-level decision problem: the lower-level, in which TN flows re the decision-mer, ims to minimize the trvel time of TN flows, considering the influence of SDN flows t the sme time. In the end, the lower level reches trditionl Wrdrop user equilibrium [8] (UE) blnce. The UE problem refe to equliztion stte in which ll the dt flows choose lnes tht cost the lest time. And we ssume tht ll the flows re entirely rtionl which mens dt flows ccurtely undetnd the sitution of the lnes. Under this equilibrium, dt flows trnsporting time is equl in ll chosen lnes between the sme origin-destintion pi (OD pi). And the time is less thn ny other lnes trnsporting time. The upper level, in which SDN flows re the decisionmer, ims to relize globl optimiztion. The controller djusts SDN flows in the networ so tht the resources cn be used effectively. Both the upper level nd the upper-level hve their own decision, but their gol ttinment is interplyed. Bsed on ll the trits described bove, we formulte bi-level progrmming model. In order to me the reserch simple nd convenient, we ppropritely simplify some terms s follows: 26

3 Demnd ssumption: we ssume tht the quntity of SDN flows nd TN flows demnded is settled. Cpcity limittion: In upper level, when optimize the globl networ, we hve to consider the influence from TN flows to SDN flows, thus we use flow lloction model with cpcity constrin, the constrined cpcity hs been nown. The stochstic user equilibrium [9] (SUE) mnner: we use the SUE mnner to describe the problem of the upper-level. We ssume tht TN flows me decisions rndomly. Further, we ssume TN flows hve undetood error bout the trnsporting time, nd the error is vrible which meets independent identiclly distributed of Gumbel. Which in return, the consequences of the decision cn be described by SUE bsed on Logit mounted. 3.2 Model Building Before formulting the bi-level model, we bstrct flow-bsed SDN into directed networ G={N, A}, nd then list some symbols used in the model: Tble 1 Symbols used in bi-level progrmming model N A R S P qsdn qtn CSDN t(x) ε x x t p f δ c Sets Set of ll nodes in the networ, represent the trnsponde in the networ Set of ll lins in the networ, represent the directed section of djoined nodes Set of ll the origins of dt flows in the networ, r R Set of ll the destintions of dt flows in the networ, s S Set of ll the lnes between R nd S(OD pir), P, represent one of the lnes between R nd S(OD pir) Prmete Given trvel demnd of SDN flows for OD pir Given trvel demnd of TN flows for OD pir The cpcity limittion of SDN flows in the trnsport networ Trvel time fuction on lne, A Rndom error of undetnd dt trnsporting time if choose lne in OD pir Vribles Flow of TN flows on section Flow of SDN flows on section Trnsport time of dt flows on section Probbility for choosing lne of OD pir Flow on lne of OD pir Associted vrible of lne nd section, δ =0 if is on The ctul trnsport time of dt flow on lne, c = r,s t (x )δ The upper-level problem: We ims to minimize the totl trvel time of entire networ, thus the upper-level problem cn be formulted s: (1) ' ' min z xt( x) xt( x) A A s.t. f 0, r R, s S, P (2) 27

4 P f q SDN, r R, s S (3) x f ' r, sr, S P, A (4) x CSDN (5) The objective function (1) represents the totl trvel time where x is determined by the lower-level SUE problem which will be presented lter. Constrint (3) (4) ensures to meet the demnd of the flows. Constrint (5) gurntees tht the totl flow does not exceed the cpcity limittion. The lower-level problem: We use SUE model bsed on Logit mounted to formulte the lower-level problem, we ssume tht the rndom error ε, r R, s S, P of undetnd dt trnsporting time is independent identiclly distributed, men vlue equls zero, nd is rndom vrible who obey Gumbel probbility distribution, then bsed on rndom utility probbility nd utility mximiztion principle we now tht probbility of lne choosing cn be given by Logit formul [10] : p exp( c) l exp( c ) lp, r R, s S,,l P In this formul, non-negtive prmeter θ represents the undetnd indetermincy of dt flows trnsporting time. The rndom error ε, r R, s S, P is Gumbel probbility vrible, therefore bigger vlue of θ mens flows nows better bout the condition of the networ, thus flows hve more ccurte estimte on the dt trnsporting time. For exmple, when θ, flows now exctly wht condition it is in the networ, they ll choose the shortest pth, which in the end reches UE blnce. The problem cn be formulted s follows: 1 min Z t ( w) dw f ln f x 0 A r, sr, S P (6) s.t. P f q TN, r R, s S, P f 0, r R, s S, P x f r, sr, S P, A 28

5 3.3 Solution Method for Model Sheffi(1985) [9] hs proved tht the Hessin mtrix of function (6) is usully not positive definite, but it will be positive definite on SUE solution point, which mens this function is strictly convex on solution point. Thus, the SUE solution point is locl minimum of the optimiztion problem. The mechnism of the model shows s follows: the lower-level obtin vrible x, which is the resources occuption sitution of CN flows under UE blnce, ccording to its objective function. The vrible then is used s the initil vlue of cpcity constrin in upper-level optimiztion problem. The upper-level obtin vrible x, which is the resources occuption sitution of SDN flows of system optimiztion blnce. The vrible directly influences the lower-level. In this pper, we use tbu serch lgorithm [11] to solve the bi-level progrmming model, nd use Bell s Logit mounted lgorithm [12] to solve the lower-level model. Bell s lgorithm does not need to enumerte the lnes, nd it tes ll the possibility into considertion. The set of lne only relted to the structure of the networ, nd hs nothing to do with the flow distribution. Tbu serch lgorithm is similr to simulted nneling lgorithm nd genetic lgorithm, its relevnt prmeter influences the opertion effect. At fit, we convert the upper-level model into n extremum without constrint; we use penlty function [13] to relize this: mx Y ( ) Z( x) {mx [0, ( x C )] } 2p (7) The bsic ide of the lgorithm is to select the initil vlue of cpcity constrin, wor out the neighborhood of the solution: N(t). Solve the lower-level model to obtin the flow of section, substitute the vlue of the flow into function (7), we then wor out the fesible solution. After tht, we serch the best solution from new strt point until we obtin the solution of bi-level progrmming model. The concrete steps re s follows: step 0. Set cpcity constrin s initil vlue is, t this time elements of vlue zero. Set τ (0) =(0,0,0,0,0), solve the problem of lower-level to obtin the vlue of x (0) nd q (0), substitute the vlues into objective function of upper-lower-level level to obtin Z(t (0) ). Set the tbu list empty, i=1. step 1. Expnd the neighborhood of ρ (i), the expnd rules re to chnge only one section s vlue ech time. If the vlue of section in ρ (i) chnges from 1 to 0, then this section does not need SDN flows to llocte the flow. Otherwise if ρ (i) chnges from 0 to 1, then rndomly generte vlue bsed on τ (i), τ (i+1) = τ (i) + δ[ j, j], prmeter δ is the step size in serch. Respectively determine x (i+1) nd q (i+1), substitute them into objective function of upper-level to obtin Z(t (i+1) ), set the vlue which me the objective mximum s cndidte solution. step 2. Judge the section flow under current stte to see if it meets the requirement of cpcity constrint. If does, then the cndidte solution is the solution we need, updte tbu list nd the optiml stte. If not, then set the optimum solution of tboo object s the solution, updte tbu list. step 3. Set mximum serching times n mx, if we cn t improve the optimum solution within n mx times, nd then stop the lgorithm. 4. Computtionl Exmples In order to verify the lgorithm vlidity, we dopt experiment networ which is designed by Suwnsiriul(1987) [14], showed in Fig. 2. There re 4 nodes, 5 sections nd 3 lnes in the networ. 29

6 We suppose tht the quntity demnded is 100, forwrding time function of section is t (x ), nd we use function BPR who dds prmeter y : t x y t x c y 0 4 (, ) [1 0.15( / ( )) ] t 0 is free trvel time of section, x is flow of section, c is mximum trffic cpcity of section, y is dded trffic cpcity vlue of section. Objective function is: Fig. 2. Experiment networ D t ( x ( y), y ) x ( y) 1.5 h ( y ) 2 The vlues nd prmeter h re shown in Tb. 2. Tble 2 Free trvel time, mximum cpcities nd prmeter sections prmete t (0)/min c /(pcu h-1) h Here re two tbles(tb. 3nd Tb.4) which show the results before nd fter the flow lloction optimiztion. Tble 3 Results before flow lloction optimiztion Before x1 x2 x3 x4 x5 UE Logit-SUE In order to clerly show the results, we show the improved proportion of the optimiztion. Its computing method is: Improved proportion= D 0 D D 0 100% D 0 is the vlue of objective function before the optimiztion, D is the vlue fter optimiztion. Tble 4 Results fter flow lloction optimiztion After y1 y2 y3 y4 y5 D0 D improved proportion UE % SUE % 30

7 From the dt bove we now tht the bi-level progrmming model optimized the flow lloction of the networ. 5. Conclusion In this pper, we hve built bi-level progrmming model in flow-bsed hybrid SDN, found out the pproprite rithmetic to solve the model. The model hs ccurtely described the interction of SDN nd TN flows in flow-bsed hybrid SDN. The rithmetic used in this pper hs n dvntge over other ones. We chieve our im to optimize the whole networ. Acnowledgments This wor ws supported by the Nturl Science Foundtion of Chin(NO ), Nturl Science Foundtion of Shndong Province, Chin(NO. ZR2012MF013) nd Socil Science Fund Project of Chin(NO. 14BTQ049). Author Mingchun Zheng is Corresponding Author. References [1]S. Sezer et l. Are We Redy for SDN? Implementtion Chllenges for Softwre-defined Netwo. IEEE Communictions Mgzine, July [2]Stefno V et l. Opportunities nd Reserch Chllenges of Hybrid Softwre Defined Netwo. CCR, [3]Open Networing Foundtion. Outcomes of the Hybrid Woring Group [4]C. Y. Heng, S. Kdul, R. Mhjun et l. Achieving High Utiliztion with Softwre-driven Wn. in SIGCOMM, [5]S. Agrwl, M. Kodilm, nd T. Lshmn. Trffic engineering in softwre defined netwo. INFOCOM, [6]McKeown N, Andeon T, Blrishnn H et l. OpenFlow: Enbling innovtion in cmpus netwo. ACM SIGCOMM Computer Communiction Review, 2008, 38(2): [7]Blzs Sonoly, And Fulys. Integrted OpenFlow Virtuliztion Frmewor with Fexible Dt. Controlnd Mngement Function. IEEE INFOCOM(Demo) Orlndo, Florid, USA, Mr [8]Wrdrop J. Some Theoreticl Aspects of Rod Trffic Reserch[C]//Proceedings of the Institution of Civil Enginee, Prt Ⅱ, 1952: [9]Sheffi Y. Urbn Trnsporttion Netwo: Equilibrium Anlysis with Mthemticl Progrmming Methods[M]. Prentice Hll, [10]Chief-Hu Wen, Frn S Koppelmn. The Generlized Nested Logit Model[J]. Trnsporttion Reserch Prt B, 2001, 35(7): [11]Thmilselvn R, Blsubrmnie P. A Genetic Algorithm with Tbu Serch for Trveling Slesmn Problem[J]. Interntionl Journl of Recent Trends in Engineering, 2009, 1(1): [12]Bell M G H. Alterntives to Dil s Logit Assignment Algorithm. Trnsporttion Reserch, 1995b, 29B, [13]Bzr M, Sherli H D, Shetty C M. Nonliner Progrmming: Theory nd Algorithms (2nd ed). 1993, New Yor: Wiley. [14]Suwnsiriul C, Friesz T L, Tobin R L. Equilibrium Decomposed Optimiztion: A Heuristic for the Continuous Equilibrium Networ Design Problem[J]. Trnsporttion science, 1987, 21(4):