Avaable onlne at www.scencedrect.com Proceda Engneerng 23 (20) 780 785 Power Electroncs and Engneerng Applcaton, 20 Game Based Vrtual Bandwdth Allocaton for Vrtual Networks n Data Centers Cu-rong Wang, Ku Lu, Cong Wang Department of Informaton, Northeastern Unversty at Qnhuangdao, Qnhuangdao 066004, Chna Ema: wangcr@ma.neuq.edu.cn Abstract In current data center, vrtual machnes may experence severely degraded performance due to the competng of network traffc on shared physcal lnks. Ths stuaton s manly caused by unreasonable and unfar allocaton of the bandwdth resource. Ths paper presents a schema based on the dea of non-cooperatve game theory n the feld of mcroeconomcs for dynamc bandwdth resource allocaton between vrtual networks. By modelng vrtual networks as competng players and gvng the prcng mechansm whch decded by the physcal substrate network and to guarantee effcency, the schema can acheve optmal bandwdth allocaton at the Nash equbrum pont of the game. We prove that the scheme admts a unque equbrum pont. Expermental results show that the bandwdth allocaton between vrtual networks s effcent and far. 20 Publshed by Elsever Ltd. Open access under CC BY-NC-ND lcense. Selecton and/or peer-revew under responsbty of [name organzer] Keywords: Network vrtualzaton; data center; bandwdth allocaton; game model;. Introducton In recent years, more and more data centers are beng but to provde ncreasngly popular onlne applcaton servces, such as search, e-mas, IMs, web 2.0, and gamng, etc. These data centers often host some bandwdth-ntensve servces such as dstrbuted fe systems (e.g., GFS [] ), structured storage (e.g., BgTable [2] ). There are sgnfcant networkng requrements across all these cases. The major cause of congeston n current data center s that non-coordnaton of these traffc may result n the number of packets exceed the bufferng capacty of the swtch for output. In modern data centers, especally towards the cloud computng, not all network traffc s TCP (or TCP-frendly) and not all protocols perform self-regulaton the way TCP does. In fact, a growng proporton of network traffc s not TCP-frendly such as streamng meda, voce/vdeo over IP, and peer-to-peer traffc. Although TCP s 877-7058 20 Publshed by Elsever Ltd. Open access under CC BY-NC-ND lcense. do:0.06/j.proeng.20..258
Cu-rong Wang et al. / Proceda Engneerng 23 (20) 780 785 78 self-regulatng, even a small amount of non-tcp frendly traffc can dsrupt far-sharng of swtched network resources. Network vrtualzaton has opened up new opportuntes for explct coordnaton that are smple, effectve, feasble, and complementary to swtch-level hardware support. Network vrtualzaton can extenuate the ossfyng forces of the current Ethernet and stmulate nnovaton by enablng dverse network archtectures to cohabt on a shared physcal substrate [3, 4]. In the man thought of network vrtualzaton, vrtual machnes of same applcatons n data center are parttoned nto same vrtual networks by network slcng; therefore the busness model can be two part: nfrastructure provder who buds the data center fabrc and servce provder who rents the vrtual machnes to run ther own applcatons and provdes Internet servce. Ths paper makes the case for dynamc bandwdth allocaton between vrtual lnks after the creaton of vrtual networks n the data center Ethernet to proactvely prevent network congeston and provde more agty. By leveragng the non-cooperatve game theory n the feld of mcroeconomcs, vrtual networks are modelled as competng players to run a game. We also present a prcng mechansm whch decded by the physcal substrate network to guarantee effcency and prove that the gven schema can prevent congeston and maxmze the utzaton of the physcal substrate network. The rest of the paper s organzed as follows. The basc game model s presented n Secton 2. In secton 3, we descrbe a dstrbuted mplementaton for dynamc bandwdth allocaton runnng on programmable swtches. Secton 4 presents expermental evdence va a smulaton mplementaton. Secton 5 gves the concluson. 2. Basc model The vrtual bandwdth allocaton optmzaton model n ths secton s consdered from the overall perspectve of the system whch contans vrtual networks and substrate hardware resource,.e. the bandwdth of the physcal network. Consder a substrate network wth a set L of lnks, and let C j be the capacty of substrate lnk j J. The network s shared by a set N of vrtual networks and ndexed by. Defne a vector b whch denotes the allocated bandwdth of vrtual network n lnk j. Let U ( b ) be the utty of vrtual network as a functon of hs bandwdth b. Note that the utty U ( b ) should be an ncreasng, nonnegatve, strctly concave and twce contnuously dfferentable functon of b over the range b 0. Assume further that uttes are addtve. The bandwdth control problem can be formulated as the followng optmal problem. The bandwdth control problem can be formulated as the followng optmal problem. N L MAX U ( b ) = l= P : s.. t, l, b 0, l L, b C For each vrtual network, ts bandwdth must be greater than or equal to 0, the total bandwdth of all vrtual networks n physcal lnk l does not exceed the maxmum bandwdth C l allowed by the hardware. Snce the utty functons are strctly concave, and hence contnuous, and the feasble soluton set s compact then the above optmal problem has a unque optmal soluton. P s an overall problem wth multple constrants. Consderng the fact that vrtual networks on data centers are of non-cooperatve nature n terms of ther demand for networks resources, leveragng noncooperatve game theory, let the network announce a rental prce per unt of bandwdth, then let all vrtual N l
782 Cu-rong Wang et al. / Proceda Engneerng 23 (20) 780 785 networks play a non-cooperatve game, the resultng bandwdth allocaton at the Nash equbrum pont of the game solves the above optmal problem P. 3. Dstrbuted mplementaton As mentoned above, the soluton for vrtual bandwdth allocaton n data center s stl a global problem. It s mpossble to manage vast amounts of vrtual nodes n large-scale network, because a centralzed soluton whch requres real-tme access to all physcal swtches wthn the physcal network to get vrtual bandwdth consumpton and also need a large-scale computng s obvously unrealstc. There s no gan n usng the local nterpretaton unless we can devse a local way to solve the problem. In ths secton, we present a dstrbuted framework whch runnng on the rack swtches n data centers to mplement the bandwdth control game. The overall optmzaton problem P can be splt nto several dstrbuted problem. Recall the problem n the prevous secton, each b n vector b = ( b, l L) denotes the allocated bandwdth for vrtual network n lnk l. For any set of vrtual network lnks L we have L L. Takng nto account of the dversfcaton and varabty of vrtual network topologes, we need to regulate all dmensons of L and make t equal to the dmenson of L. Let L be the new lnk set of vrtual network, the two under sets are equvalent. L =, f l L; L L, l L, () L = 0, f ; l L L = 0 means that the bandwdth allocated for vrtual network on lnk l s 0. Then the overall optmal problem P can be rewrtten as: N L L N U b U b = = l= l= = MAX ( ) ( ) N N N = U ( b ) + U ( b ) +... + U ( b ) = = 2 = L From equaton (2) we can see the P can be transformed nto L sub optmzaton problems on each network port of rack swtches. When the bandwdth allocaton for every vrtual network on each port of the rack swtches n the physcal network s optmal, the overall optmzaton problem P can be solved smultaneously. Ths dstrbuted soluton n large-scale data center network was feasble, and can be easy acheved. Then we can get the sub optmzaton problems on each network port of rack swtches: MAX U ( b) n = st.., b 0, n b C Where n s the number of vrtual networks, b denotes the allocated bandwdth for vrtual network. U ( b ) s the utty functon dscussed n the prevous secton. Then we can bud the non-cooperatve game model for bandwdth allocaton accordng to sub optmzaton problem (3). Gvng the utty functon of each vrtual network: F( ω, b) = u ( b) ω (4) l (2) (3)
Cu-rong Wang et al. / Proceda Engneerng 23 (20) 780 785 783 Where ω s a wlngness-to-pay (also called a bd) announced by vrtual network to the substrate network, u ( b) s the utty functon of vrtual network lkes U (). After collectng each ω, the substrate network chooses a bandwdth allocaton strategy bb (, b2,..., b N ). If the substrate network always seeks to allocate the entre lnk capacty, then prce s calculated as follows: n = l p = ω C (5) Assumng that all vrtual networks on lnk l are ratonal and do not know the bd of any other vrtual networks, then equaton (4) and (5) defne a non-cooperatve game, at the Nash equbrum pont of the game the bandwdth allocaton s optmal. We then proof there exsts a unque Nash equbrum pont n the game defnte by (4). Proof: From equaton (5) we can calculate the allocated bandwdth for vrtual network : b = ω p. Then rewrte the utty functon of each vrtual network: ω F( ω, ω ) = u ( c) ω (6) n ω Where ω = ( ω, ω,... ω, ω ) reflects the effect to vrtual network accordng to the demand of other + n vrtual networks. For the game defnte by equaton (6), there exsts a Nash equbrum pont only f for any vrtual network, when there s no change on the bd of other vrtual networks, there s a fxed * strategy ω meet: * * * F( ω, ω ) F( ωω, ) (7) = Let W = ω, substtute t nto (6) and calculate the frst order dervatve: k k cw F = u (8) 2 ( W + ) ω Snce u () s a twce dfferentable concave functon, u c s strctly decreasng n b 0. Obvously, 2 cw ( W + ω ) s strctly decreasng n ω 0. So F < 0,.e. F s also a twce dfferentable concave functon, so there exsts a unque ω * maxmze the functon F, thus the game has a unque Nash equbrum pont. At the equbrum pont the proft of each vrtual network s maxmzed, so the vrtual bandwdth allocaton strategy s far and effcent 4. Performance Evaluaton We mplemented the dstrbuted vrtual bandwdth allocaton schema dscussed n Secton 3 usng OpenFlow VM [5] envronment. For the lmtaton of the current software, we made a smple but suffcently persuasve experment as shown n Fg., where PC has two ports, eth and eth2 and PC 2 has one port connect to the OpenFlow Swtch.
784 Cu-rong Wang et al. / Proceda Engneerng 23 (20) 780 785 PC PC 2 Lnk 3 P P2 P3 OpenFlow Swtch Fg.. Smple topology for evaluaton In PC, we use two perf clents to generate a TCP flow and a UDP flow wth destnaton to PC 2. We test each flow s assgned bandwdth wth and wthout bandwdth allocaton schema to verfy the farness. Note that n the experment wth the allocaton schema, lnk 3 s slced nto two vrtual lnks. VN VN 0.8 VN 2 0.8 VN 2 0.6 0.6 Bandwdth (Gb/s) 0.4 0.2 Bandwdth (Gb/s) 0.4 0.2 0 0 5 0 5 20 25 30 Tme (s) 0 0 5 0 5 20 25 30 Tme (s) Fg. 2. (a) No bandwdth allocaton case (b) Wth the bandwdth allocaton schema For non-vrtualzed case as shown n Fg.2 (a), when UDP flow was sent, the bandwdth assgned to TCP flow dropped serously. In Fg.2 (b), for the substrate network was slced nto two vrtual networks, and wth the dynamc bandwdth allocaton schema, both flow s QoS s guaranteed. They farly share the bandwdth when they oversubscrbed the lnk smultaneously under same wlngness-to-pay. Ths can confrm the truth of that network vrtualzaton can provde an effcent mechansm to prevent congeston n data center network whch full of vrtual machnes, and also a more agty way for QoS guarantee. 5. Concluson Ths paper ntroduced a bandwdth allocaton schema base game theory to allevate congeston problems n data center networks. We present a overall optmal problem and gve a dstrbuted mplementaton approach. Maybe there s a certan dstance from a practcal fully mature system, we beleve that network vrtualzaton and dynamc bandwdth allocaton are more sutable for the future data center networks, especally n the context of mult-tenancy mechansm of cloud computng. References
Cu-rong Wang et al. / Proceda Engneerng 23 (20) 780 785 785 [] Ghemawat S, Gobo H, Leung S. T. The Google FeSystem. In Proceedng of the nneteenth ACM symposum on Operatng systems prncples, New York; 2003: 29-43. [2] Fay C, Jeffrey D, Sanjay G, et al. Bgtable: A Dstrbuted Storage System for Structured Data. In Proceedngs of The 7th conference on usenx symposum on operatng systems desgn and mplementaton, Seattle; 2006: 205-28. [3] Shmonsh H, Ish S. Vrtualzed network nfrastructure usng OpenFlow. In Proceedngs of the 200 IEEE/IFIP Network Operatons and Management Symposum Workshops, Osaka; 200: 74-79. [4] Wang Y, Keller E, Bskeborn B, et al. Vrtual routers on the move: Lve router mgraton as a network-management prmtve. In Proceedngs of the SIGCOMM 08, Seattle; 2008: 23-242. [5] Yakoums Y, Kobayash M. Innovatng n Your Network wth OpenFlow: A Hands-on Tutoral. In Proceedngs of the 8th Annual Symposum on Hgh Performance Interconnects, Mountan Vew; 200: 2-22.