Int. J. Communcatons, Network and System Scences, 2017, 10, 264-273 http://www.scrp.org/ournal/cns ISSN Onlne: 1913-3723 ISSN Prnt: 1913-3715 Dstrbuted Mddlebox Placement Based on Potental Game Yongwen L, Zhy Qu School of Informaton Scence & Engneerng, Lanzhou Unversty, Lanzhou, Chna How to cte ths paper: L, Y.W. and Qu, Z.Y. (2017) Dstrbuted Mddlebox Placement Based on Potental Game. Int. J. Communcatons, Network and System Scences, 10, 264-273. https://do.org/10.4236/cns.2017.105b026 Receved: May 3, 2017 Accepted: May 23, 2017 Publshed: May 26, 2017 Abstract In ths paper, we analyse the deployment of mddlebox. For a gven network nformaton and polcy requrements, an attempt s made to determne the optmal locaton of mddlebox to acheve the best performance. In terms of the end-to-end delay as a performance optmzaton ndex, a dstrbuted mddlebox placement algorthm based on potental game s proposed. Through extensve smulatons, t demonstrates that the proposed algorthm acheves the near-optmal soluton, and the end-to-end delay decreases sgnfcantly. Keywords Mddlebox Placement, Performance Optmzaton, Potental Game, Matchng Graph, Dstrbuted Algorthm 1. Introducton In order to manage users communcaton, mprove safety and performance the operators wdely deploy mddlebox servces n ther own network, such as deep packet nspecton (DPI), frewall, proxy, ntruson detecton and preventon (IDP), network address converson (NAT), etc. The servce chan s defned as a mddlebox sequence that should be traversed n a pre-specfed order. Recently, the academc and ndustral domans have done a lot of efforts on how to mplement the servce chan effcently [1] [2] [3]. Accordng to the predefned sequence of strateges, the routng s transmtted from one mddlebox to another. However, no matter what program s used to acheve the servce chan, there wll be such a problem that n the network where the deployment of mddlebox s placed n order to make the performance of the overall strategy for the mplementaton of overall strategy. Ths paper manly solves the problem of mddlebox deployment. In partcular, accordng to the traversal sequence of the polcy, we am to fnd the best locaton DOI: 10.4236/cns.2017.105B026 May 26, 2017
of the deployment of mddlebox. Instead of the shortest path passng from the entry pont to the ext pont, n whch traffc route from the entrance to a number of mddlebox one by one, and then ext the outlet. Obvously, the overall path wll be exaggerated, whch wll result n a long end-to-end delay. Therefore, n ths work, we consder the total end-to-end delay as the optmzaton ndex of the polcy mplementaton, whch s also adopted n [4], and use ths optmzaton ndex to evaluate the performance of proposed mddlebox deployment scheme. In the network functon vrtualzaton (NFV) [5], the problem s more meanngful snce you can easly move one form of mddlebox software runnng on commodty hardware. In NFV, you can use the deployment algorthm more often to determne the best locaton of mddlebox perodcally. In ths paper, a dstrbuted mddlebox placement based on potental game s proposed to decrease computaton complexty. Through the defnton of the servce queue mddlebox for the partcpants n the game, to mnmze the total end-to-end delay as the goal, we desgn the game strategy and utlty functon, gve the potental game proved that, and accordng to the defnton of ordnal functon and analyss of change, t can be proofed that Nash equlbrum pont exsts n the model. Based on ths potental game model, a dstrbuted algorthm s proposed. Through numercal results, the proposed dstrbuted algorthm can reduce the system end-to-end delay sgnfcantly compared wth the random placement. On average, the end-to-end delay wll be reduced by 34%. In addton, t shows that the performance of the proposed dstrbuted algorthm obtans the near-optmal soluton. 2. Methodology 2.1. System Model These G = ( SE, ) s utlzed to express underlyng network, where S denotes the swtch set, E denotes the lnk set. For each swtch sl S, Cs ( l ) represents the avalable resource of swtch s l n deployng mddlebox, and resource represents the number of avalable ports n server or the computng resources of p the server. In addton, d l1, l represents the delay from route s 2 1 to route s 2, that s the total delay of all lnks on the route. Then, a format model s gven to descrbe the strategy. The P s used to descrbe provson set of polcy, the provson of each polcy p k 1 2 n P, whch s defned as p {,,,, k k = k mk mk mk, ek} where and k e k denotes nput swtch and output swtch, respectvely, m k represents the data stream of ths polcy adopted by the -th mddlebox, and n k represents the number of mddlebox of ths polcy. Further, we use Q to represent the set of mddleboxes to be deployed, and Rq ( ) to represent the requred resource to deploy mddlebox Q. 2.2. Problem Formaton q From the above defnton, we need to determne the locaton of each mddlebox. x l, s utlzed to represent the deployment scenaro of the mddlebox. When x =, t represents that mddlebox q connected to swtch s l. Otherwse, l, 1 265
x l, = 0. Then, the followng constrants are obtaned. xl, = 1, q Q. (1) sl S Rq ( ) xl, Cs ( l), sl S. (2) q Q xl, = 0, q Q, sl S \ S. (3) Condton (1) ensures that each mddlebox s only deployed n a swtch condton (2) guarantees that the total resource requrements n a local deployment mddlebox do not exceed resource performance. Condton (3) ndcates that mddlebox wth specal requrements can only be deployed n a specfc area. a) Inducton problem usng matchng graph The man problem of ths paper s how to deploy the mddlebox to mnmze the system delay. Ths paper manly uses the matchng graph to explan how to deploy mddleboxed, as shown n Fgure 1. Where ω q, s represents the weght of mddlebox q located n swtch s, whch s defned as sum lnk delay from the mddlebox q to the next hop. When the last hop of mddlebox q s the end node, the ω q, s contans the lnk delay of startng node to q. From the above defnton, the overall delay of the system s: tot D = ωq, s, (4) q where the weght ω q, s s related to the matchng of other mddleboxes, whch are determned by the decson varables x l,. b) Analyss of the reasons for the problem dffculty From the above analyss based on matchng graph, we can observe that f the matchng poston of any mddlebox q changes, and the weght value of other mddleboxes may vary wth unchanged matchng poston. The edge weght of the matchng graph s nfluenced by each other, thus t becomes very dffcult to obtan the maxmum matchng problem as shown n Fgure 1. Furthermore, we can see that f mddlebx q changes ts matchng poston, then the weght of edges, whose next hop s q, also changes. Therefore, we modfy the defnton of weghts, and use the growth trend to desgn dstrbuted algorthm. Swtch Mddlebox Fgure 1. Problem model wth matchng graph. 266
2.3. Defnton of Potental Game Potental game (PG) [6] s an effectve model for the change of the trend, and the most mportant one s the defnton of utlty, the effectve polcy space and the defnton of the optmal polcy. 1) Accordng to the above analyss, the game model s defned as = (,, ), where represents the number of game players, represents strategy space, and represents network performance of any player. From the above analyss, the utlty of mddlebox q s related to the start edge and the weght of the next hop edge, so the utlty of any player s defned as: = x ω + I d, (5) q, l q, sl pk, q pk, q sl pk q Compared wth ω q, s, ths defnton ncreases the weght of the edge wth the next hop to the mddlebox. Here I ab, s the ndcatve symbol that f a = b, I ab, = 1, or I ab, = 0. 2) It s clear that the feasble strategy space of any mddlebox q s to select some swtch, whch also meets the constrant of the swtch port capacty. Defnton 1: The optmal strategy of the partcpants. The optmal polcy for any mddlebox q s the mnmum utlty that can be obtaned n a feasble space when the locaton of the other mddlebox s not changed, that s max U ( x, x ), n, (6) xn n n n where n represents mddlebox, x n represents strategy of n, x n represents the strategy of other mddlebox except n. The above formula represents the best strategy for the current mddlebox, whch s based on the same locaton of the other mddlebox. 3) Accordng to the defnton of the above utlty functon and the strategy space, we also need to prove that ths game model s a potental game. Theorem 1: The game model defned as = (,, ) s a potental game. Proof: We frst defne the ordnal functon as F( x) x ω. Then, we prove that any varyng n the layout of the = q sl l, q, s l mddlebox wll brng a change n ts own utlty functon and change the value of ordnal functon wth the same trend. Assumng that the layout of a mddlebox q has changed, from the swtch s l to swtch mddlebox varys as follows: = x ω + I d q q, l q, sl pk, q pk, q sl pk q x ω I d, l q, sl pk, q pk, q sl pk q = x ω x ω sl l, q, sl l, q, sl sl U1 + I d I d pk, q pk, q pk, q pk, q pk q pk q U2 s l, the utlty functon of the (7) 267
where U1 represents the delay varyng of the edge wth q as the startng pont and U2 represents the delay varyng of the edge wth q as the next hop. Smlarly, the ordnal functon of the change s shown below: F( x) F ( x) = x ω x ω U1 l, q, sl l, q, sl q sl q sl = xl, ωq, s x l, lωq, s + F l sl sl where F22 ndcates the edge delay of next hop as q for all of the strateges, as the delay of other edge ndependent of q wll not change, F2 = U2. Therefore, t s proved that the game model defned as = (,, ) s a potental game. Accordng to the above defnton, t can be concluded that ths model exsts Nash equlbrum. 2.4. Dstrbuted Algorthm Based on the above potental game, t can be seen that any mddlebox can choose ts best strategy to reduce the system delay. The specfc algorthm can be depcted extensvley as follows (Algorthm 1): In the algorthm, each mddlebox selects ts best strategy n a random order. In each teraton, the system unformly randomly chooses one mddlebox q, the selected mddlebox obtans ts best strategy from Defnton 1. If no new strategy s obtaned from all mddlebox, the stop flag s set to be 0, and the Algorthm 1 ends. From the analyss of these algorthms, t can be seen that any mddlebox can reduce system latency only consderng ts utlty, therefore, savng the overall (8) Algorthm 1. Dstrbuted algorthm based on potental game. 268
optmzaton of the system overhead, and overcome the convergence problem of heurstc algorthm (such as reference n the lterature of the smulated annealng algorthm [4]). 2.5. Proof of Convergence Theorem: the proposed dstrbuted algorthm certanly converges to the Nash equlbrum pont. Proof: Each a teraton of the algorthm generates a new strategy by adoptng the best response strategy. Snce there are only a lmted number of mddlebox, the maxmum number of polces for each mddlebox s lmted. Therefore, the system can acheve the fnal strategy by fnte teraton wth probablty 1. 3. Results In ths secton, we evaluate the performance of the proposed algorthm for mddlebox layout. In the evaluaton, we ntroduce random layout for comparson. Random placement does not consder the mpact of mddlebox placement on system delay, and only guarantees that the constrant condtons are satsfed. In the desgn of network topology and servce chan strategy, the prevous works [2] [7] used well known topology (such as Ablene and FatTree) n strategy executon due to the lack of openly avalable nformaton. In ths paper, we choose the Ablene [8] network as the reference; Ablene s the core network of Internet 2, whch s the rregular topology of the network (lke most ISP network). The network has 11 nodes, 14 lnks. We adopted the same approach as the lterature [2] and [7] to generate polcy rules. Specfcally, we assume that there are dffeent number of applcatons, and the traffc flow requred for each applcaton s requred through multple mddlebox. We gave each applcaton a random assgnment of a mddlebox sequence. Then, a number of applcatons are randomly selected for the traffc flow between the two swtches to generate the polcy requrements. We dstrbuted the lnk delay accordng to the unform dstrbuton. Based on the lnk delay, the network controller wll select the shortest path passng from one swtch to another through route. In the evaluaton, we generated a total of 400 smulaton scenaros. In each scenaro, we randomly selected the value of each parameter from the parameter set n Table 1, and generated the network settngs and polces. The cumulatve dstrbuton functon (CDF) assocated wth the optmal value s as shown n Fgure 2. As shown n the graph, the performance gap between the dstrbuted algorthm and the optmal soluton s very small. Specfcally, the performance gap of the dstrbuted algorthm for 92.5% of the smulated scenaros s less than 20%. In addton, there s a large gap between the dstrbuted algorthm and random layout, whch shows that the proposed algorthm greatly mproves the performance of the strategy. On average, the dstrbuted algorthm reduces the end-to-end delay of 34% compared to random placement. In order to further nvestgate the effect of dfferent layout schemes on the performance, we studed the dstrbuton of end-to-end delay of each strategy. 269
1 0.9 0.8 0.7 random placement dstrbuton algorthm 0.6 P[rao<x] 0.5 0.4 0.3 0.2 0.1 0 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 rato to optmal Fgure 2. CDF of end-to-end delay wth dfferent placement over optmal results. Table 1. Parameters settngs n the performance evaluaton. Parameter Dstrbuton Mean Var Lnk delay(ms) Unform 1, 1.5, 2, 2.5 0.4, 0.5, 0.6, 0.7 Avalable swtch ports 1, 2, 3 N/A N/A The number of mddleboxes to deplay 7, 8, 9, 10 N/A N/A The number of mddleboxes n each polcy 3, 4, 5, 6 N/A N/A The number of total applcatons 5, 10, 15 N/A N/A The results of a scenaro are shown n Fgure 3. These results clearly ndcate that the layout scheme has a sgnfcant mpact on the system performance. Mddlebox placement by proposed dstrbuton algorthm can obtan near optmal performance, about 70% of end-to-end delay of strategy s less than 100 ms. However, Mddlebox deployment accordng to random arrangement s only 25%. In the schemes generated by dstrbuton algorthm, 100% of the delay of the strategy s less than 150 ms, and there s only 65% n the schemes generated by randomly placement. The performance results for each swtch wth the number of avalable ports varyng are descrbed n Fgure 4. In ths smulaton, each polcy conssts of 5 mddlebox. As shown n Fgure 4, the performance s mproved wth the ncensement of the number of avalable ports. Ths s because those more avalable ports provde more feasble strategy for each mddlebox. We observe that that the dstrbuted algorthm has can utlze the ncreased resources more effcently. Fgure 5 provdes a comparson of computaton complexty between the dstrbuted algorthm and the optmal placement algorthm. It can be clearly ob- 270
1 0.9 0.8 0.7 optmal placement random placement dstrbuton algerthm P[end-to-end delay<x] 0.6 0.5 0.4 0.3 0.2 0.1 0 0 50 100 150 200 250 300 end-to-end delay(ms) Fgure 3. CDF of end-to-end delay of each polcy. 140 120 dstrbuton algorthm random placement 100 average end-to-end delay(ms) 80 60 40 20 0 1 2 3 # of avalable ports on each swtch Fgure 4. Average end-to-end delay varyng the number of avalable ports on each swtch. served that the dstrbuted algorthm reduces the computaton complexty sgnfcantly from two aspects. One s to reduce the number of overall teratons, the other s to share the computng tasks among all swtch. 4. Concluson In ths paper, we manly analyze the optmzaton of mddlebox deployment to mnmze the end-to-end delay. The matchng graph was utlzed to formulate 271
Fgure 5. The number of teraton when varyng the number of mddleboxes. the problem, whch s proved as a potental game and exsts the Nash equlbrum. Thus, a dstrbuted algorthm s proposed based on potental game. Through extensve smulatons, t s proved that the proposed algorthm can reduce the end-to-end delay effectvely and obtan the near-optmal soluton. Acknowledgements The authors would lke to acknowledge all the members that partcpaton n the exhaustve feld measurement campagn for ther valuable effort. Thanks also anonymous revewers for ther perspcacous comments. References [1] Grllo, G., Joseph, D.A., Tavakol, A. and Stoca, I. (2008) A Polcy-Aware Swtchng Layer for Data Centers. Proc. ACM SIGCOMM, 51-62. https://do.org/10.1145/1402958.1402966 [2] Qaz, Z.A., Tu, C.-C., Chang, L., Mao, R., Sekar, V. and Yu, M. (2013) Smple-Fyng Mddlebox Polcy Enforcement Usng Sdn. Proc. ACM SIGCOMM, 27-38. https://do.org/10.1145/2534169.2486022 [3] Zhang, Y., Behesht, N., et al. (2013) Steerng: A Soft- ware-defned Networkng for Inlne Servce Channg. Proc. IEEE ICNP, 1-10. https://do.org/10.1109/cnp.2013.6733615 [4] Lu, J., L, Y., Zhang, Y., et al. (1939) Improve Servce Channg Performance wth Optmzed Mddlebox Placement. IEEE Transactons on Servces Computng, 1-1. [5] Sdn and Openflow World Congress Introductory Whte Paper, Network Functons Vrtualsaton. https://portal.ets.org/nfv/nfvwhtepaper.pdf,2012. [6] Hu, X.H., Gao, H.W., Wang, D.Y., L, Y.M. and J, Z.H. (2013) Two Classes of Potental Games and the Solvng Method of the Equlbra. Informaton Engneerng Research Insttute, USA. Proceedngs of 2013 Internatonal Conference on Intellgent Materals and Mechatroncs (IMM 2013). Informaton Engneerng Research Insttute, 5. 272
[7] Sekar, V., Eg, N., Ratnasamy, S., Reter, M.K. and Sh, G. (2012) Desgn and Implementaton of a Consoldated Mddlebox Archtecture. Proc. USENIX NSDI, 323-336. [8] Ablene Core Topology. https://tservces.stanfo-rd.edu/servce/network/nternet2/ablene Submt or recommend next manuscrpt to SCIRP and we wll provde best servce for you: Acceptng pre-submsson nqures through Emal, Facebook, LnkedIn, Twtter, etc. A wde selecton of ournals (nclusve of 9 subects, more than 200 ournals) Provdng 24-hour hgh-qualty servce User-frendly onlne submsson system Far and swft peer-revew system Effcent typesettng and proofreadng procedure Dsplay of the result of downloads and vsts, as well as the number of cted artcles Maxmum dssemnaton of your research work Submt your manuscrpt at: http://papersubmsson.scrp.org/ Or contact cns@scrp.org 273