SLA Adaptation for Service Overlay Networks

SLA Adaptation for Service Overlay Network Con Tran 1, Zbigniew Dziong 1, and Michal Pióro 2 1 Department of Electrical Engineering, École de Technologie Supérieure, Univerity of Quebec, Montréal, Canada con.tran.1@en.etmtl.ca, zdziong@ele.etmtl.ca 2 Department of Communication Sytem, Lund Univerity, Sweden 2 Intitute of Telecommunication, Waraw Univerity of Technology, Poland Abtract. Virtual Network Operator leae bandwidth from different data carrier to offer well managed Virtual Private Network. By uing proprietary algorithm and leaed reource diverity they can offer Quality of Service, at competitive price, which i difficult to attain from traditional data network operator. Since maximizing the profit i a key obective for virtual network operator, in thi paper we decribe a novel reource management approach, baed on an economic model that allow continuou optimizing of the network profit, while keeping network blocking contraint. The approach integrate leaed link capacity adaptation with connection admiion control and routing policie by uing concept derived from Markov Deciion Proce theory. Our numerical analyi validate the approach and how that the profit can be maximized under varying network condition. Keyword: Service Overlay Network, Economic Model, Reource Management, Quality of Service, Markov Deciion Proce. 1 Introduction With the continuing increae in popularity of the Internet, more and more application are offered. However, ince the Internet i formed by numerou interconnected Autonomou Sytem (AS) operating independently, real time application uch a Voice over Internet (VoIP), Streaming Multimedia and Interactive Game are often unable to get their required end-to-end Quality of Service (QoS) guarantee. One poible approach to overcome the problem i to ue global Service Overlay Network (SON) [1], [2], where a et of overlay router (or overlay node, ON), owned and controlled by one Virtual Network Operator (VNO), i interconnected by virtual overlay link (OL) realized by leaing bandwidth from the AS via Service Level Agreement (SLA) [3]. In general there are two approache to provide QoS in Service Overlay Network. In the firt approach, the VNO that manage the SON leae the bet effort acce to the AS. In thi cae, to enure availability of required bandwidth and QoS, the SON ha to monitor continuouly it OL etablihed over bet effort Internet and react fat in cae of ome OL quality deterioration, e.g., by rerouting the connection on the path with acceptable QoS. In the econd approach the VNO leae the overlay link I.F. Akyildiz et al. (Ed.): NETWORKING 2007, LNCS 4479, pp. 691 702, 2007. IFIP International Federation for Information Proceing 2007

692 C. Tran, Z. Dziong, and M. Pióro with appropriate bandwidth and QoS guarantee (e.g., baed on the MPLS-TE technology). In thi cae uer end-to-end QoS connection are realized through the SON admiion control and routing policy. Obviouly the VNO can ue both type of leaed bandwidth in a flexible and controlled way in order to reduce cot ince bet effort bandwidth i le expenive. The above argument indicate that Virtual Network Operator can potentially offer well managed QoS Virtual Private Network (VPN) at competitive price, by uing economically-ound SON that can be managed by ophiticated proprietary control mechanim adaptable toward the need of particular client. At the ame time the VNO can leae bandwidth from everal different operator that remove the geographical barrier and alo offer much better architecture for reliability and failure protection. Thee advantage led to creation of everal VNO like Internap (internap.com), Mnet (mnet.co.uk), Sirocom (irocom.com), Vanco (vanco.co.uk), Virtela [4] (virtela.net), Vanguard (vanguardm.com), Netcalibur (netcalibur.com). In thi paper, we focu on reource management in SON baed on leaed bandwidth with QoS guarantee (e.g., baed on the MPLS-Traffic Engineering technology). In particular, we decribe a novel framework, baed on an economic model, which allow continuou network profit optimization. The approach integrate leaed link capacity adaptation (to traffic and SLA variation) with connection admiion control and routing policie by uing concept derived from Markov deciion proce theory. The paper i organized a follow. The framework for the SON economic model i decribed in Section 2. In Section 3, we preent the reource adaptation model that contitute the main element of the economic model. Numerical analyi validating the propoed approach i given in Section 4. 2 SON Economic Framework In general, the cot of etablihing and operating a SON can be divided into three part: the initial cot of intalling ON and the maintenance center, the ongoing cot of the leaed bandwidth according to SLA, and the ongoing maintenance cot. Thee cot hould be covered by the revenue achieved from connection charge. The monetary and provided good flow between the uer, SON and AS are illutrated in Fig. 1. Service uer Revenue from connection End-to-end QoS connection SON SLA cot Overlay link bandwidth with QoS AS Fig. 1. SON economic framework To implify preentation, auming that the maintenance cot i proportional to SLA cot, we can integrate them together in the total SON operation cot expreed a a um of overlay link cot C (expreed a a cot per time unit). Further we

SLA Adaptation for Service Overlay Network 693 aume that thi total cot hould be covered from the operating profit Pˆ and that the obective of the virtual operator of SON i to maximize thi profit expreed a: ˆ Rˆ C = λ rˆ (1) P = S J S C where: Rˆ : SON average revenue rate, λ : average rate of admitted cla connection, rˆ : average revenue (price) for cla connection, S : et of overlay link, J : et of uer connection clae. In thi formulation the maximization of the revenue profit can be achieved by leaed bandwidth adaptation that influence the admiion rate λ and cot C, and by aduting the ervice price rˆ. Note that a change of ervice price can influence the ervice demand [] expreed in our model a the average rate of connection arrival λ. The profit maximization hould be done in uch a way that the connection blocking probabilitie B of all clae do not exceed the contraint B. In general, the demand for SON ervice i variable due to factor like periodic variability in cale of a day, week, month, year, and variability caued by trend of increaing (decreaing) demand for certain ervice. Alo bandwidth price in SLA can fluctuate due to competition and market trend. Since the leaed bandwidth amount within SLA can be adapted from time to time or even dynamically (on line), it i natural that the VNO need a mechanim that can indicate when and how to adapt the SLA to maximize profit while repecting the required blocking contraint. In thi paper we decribe a framework for uch an approach. The propoed framework i baed on integration of a model for SLA adaptation with a model for CAC (call admiion control) and routing that i baed on Markov deciion proce. A it will be explained in Section 3, thi integration provide two key advantage. Firt, the CAC and routing algorithm take into account the cot of SLA and therefore the reource utilization i maximized taking into account their cot. Second, ome tatitic of CAC and routing parameter provide information indicating which SLA hould be adapted in order to maximize the profit. It i important to emphaize that, a decribed in [6], in the propoed framework, beide the concept of revenue from connection, rˆ, we alo ue very imilar concept of reward from connection, r. In general the reward from connection i a more general concept ince it doe not have to have monetary meaning and it can be treated a a control parameter. In our framework we firt ue the reward concept to maximize the reward profit from the network expreed a: P R C = λ r (2) = S J S C Then we determine rˆ a a function of r. The reaon for thi dual approach i that it allow decompoition of the original problem (1) into two ub-problem. The firt i c

694 C. Tran, Z. Dziong, and M. Pióro optimal link bandwidth allocation for given connection arrival rate λ and blocking c contraint B, that i olved by uing the reward formulation (2). The outcome of reolving thi ub-problem i a et of link bandwidth allocation and a et of connection reward parameter. The econd ub-problem i to optimize rˆ a a function of r. In the implet cae, one can aume that r ˆ = r. Neverthele the demand for ervice ( λ ) can be influenced by the choice of rˆ. In particular if the demand i ignificantly reduced for r ˆ = r, one may need to reduce the revenue parameter in order to maximize the revenue profit (1). An approach to olve the econd ubproblem i dicued in [6]. In the balance of thi paper we concentrate on a olution of the firt ub-problem. In particular we preent a baic model for bandwidth adaptation auming that connection reward parameter are given. 3 Reource Adaptation In thi ection we decribe a model for reource adaptation for given connection arrival rate. In Section 3.1 the applied CAC and routing policy baed on Markov deciion theory i preented. In Section 3.2 the mechanim for bandwidth adaptation i decribed for given reward parameter. Finally, in Section 3.3 we dicu the iue of adaptation of reward parameter in order to achieve the required blocking contraint. While the propoed framework i applicable to multi-cla ervice with different bandwidth requirement, in thi paper we will conider a network with homogeneou connection where all clae have the ame bandwidth requirement and the ame mean ervice time. 3.1 CAC and Routing Policy For a network with given link dimenion and reward parameter, optimizing profit i realized with efficient ue of available reource, through a CAC and routing policy which admit the connection on the mot profitable route. The policy ued i a tate dependent CAC and routing baed on Markov Deciion Proce (MDP) theory [7]. In addition to dynamic link cot, defined in [7] a hadow price, we integrated the cot of the SON phyical overlay link, C, in the model. A hown in [7, 8], for given reward profit rate, one can find an optimal CAC and routing policy that maximize the average profit by uing one of the tandard MDP olution algorithm. In thi paper, thi exact approach i called the MDP CAC and routing model. In the MDP model, the network tate pace i uually too large in realitic network example. To overcome thi problem, a decompoition technique, called MDPD, decribed in [7, 8], i applied. The technique ue a link independence aumption to decompoe the network reward proce into eparable link reward procee. The decompoed proce i decribed eparately for each link by the link tate X=(x :=1,2, ) (where x i the number of cla connection admitted on the link), the link arrival and ervice rate λ, µ, and the link connection reward parameter r.

SLA Adaptation for Service Overlay Network 69 In thi paper, thi approach i called the MDPD CAC and routing model. In thi model, to integrate monetary link cot into the CAC and routing policy, we propoe to divide connection reward into link connection reward proportionally to the ued reource cot: r = r. ( C N) ( o S k Co No) (3) where N : link capacity (max number of connection) k S : et of link on path k Then, analogouly to.(2) the link expected profit i: P = R C = J λ r C (4) where λ i the rate of admitted cla link connection. In the MDPD model, a link net gain g (X ) i defined a the expected link reward increae from accepting an additional connection of cla. A tate dependent link hadow price i then defined a the difference between the link reward and net gain. It repreent the cot of accepting the cla call on link in tate X: p ( X ) = r g ( X ) () During network operation, the link hadow price can be calculated baed on meaurement of link connection arrival rate [7], [8]. Then the optimal CAC and routing policy will chooe the connection path with the maximum poitive net gain: g = max [ r k p ( X )] (6) max k W S If no path produce a poitive gain, the connection i reected. 3.2 Link Bandwidth Adaptation for Given Reward Parameter With changing network condition, uch a traffic level or leaed bandwidth cot, SON parameter hould be adapted to continuouly realize the reward profit maximization obective. A mentioned, the SON operator can control overlay link capacitie (by modifying the SLA) and reward parameter r. In thi ection, we concentrate on overlay link capacity adaptation with given reward parameter. Profit Senitivity to Link Capacity. In the MDPD model the network profit enitivity to a link capacity can be approximated by the link profit enitivity to the link capacity. Following equation (4) we have: P N = ( R N ) ( C N ) (7) It ha been hown in [8] that the average reward enitivity to link capacity can be approximated by the average link hadow price of a connection cla with unit bandwidth requirement, ( R N ) p ( N ). The value of the average link hadow price can be calculated or meaured during execution of the CAC and routing algorithm. In the econd term of (7), auming that C i a linear function of N, we

696 C. Tran, Z. Dziong, and M. Pióro have C = cn where c i the bandwidth unit cot. Subtituting in (7), the link profit i maximized when P N = 0, i.e. at the olution for the following equation, which contitute the bae for the capacity adaptation procedure: p ( N ) c = 0 (8) Bandwidth Adaptation Model. An iterative procedure i ued to converge to the olution for (8), giving the optimized link capacity. In our cae, we ue Newton ucceive linear approximation, in which the capacity new value N n+1 at each n i given by (link index i omitted to implify the notation): p c N 1 N n n+ = n (9) [ ( p( N) c) N] Approximating the derivative in equation (9) at iteration n: ( p ( N) c) N= p( N) N ( pn pn 1) ( Nn Nn 1) (10) and ubtituting (10) in (9), the new capacity will be: N n+ 1 = Nn ( Nn Nn 1)[( pn c) ( pn pn 1)] (11) Link capacity adaptation i then realized by executing periodically the following tep for each link: a. Etimate new average link hadow price p n baed on CAC and routing algorithm link hadow price. b. Calculate new value of link bandwidth: Nn + 1 = Nn + α ( Nn+ 1 Nn) (12) where N n+1 i from (11) and α i a damping factor ued to improve convergence. c. Round N n+ 1 to the nearet value available from SLA and, if Nn +1 Nn exceed the threhold of importance, ue it a the new link capacity. It i important to underline that the bandwidth adaptation procedure and the CAC and routing procedure (ection 3.1) are integrated by the fact that link hadow price obtained in the latter procedure are ued in the capacity adaptation. In turn, CAC and routing policie adapt to change in link capacitie and in bandwidth unit cot. 3.3 Reward Parameter Adaptation to Meet the Blocking Contraint The CAC algorithm reect connection requet when bandwidth i not available or the connection i not profitable. The reulting blocking probabilitie can be defined for each connection cla a: B = ( λ λ ) λ = 1 ( λ λ ) (13) We define the network average blocking probability a: BT = ( λ λ) λ = λb λ = 1 ( λ λ) (14)

SLA Adaptation for Service Overlay Network 697 A mentioned in Section 2, blocking probabilitie hould not exceed the network c and/or cla blocking contraint BT and B c. To achieve thi obective we propoe an adaptation of reward parameter, ince in general the increae of r will caue decreae of B and B T, and vice vera. Note that a change of r may influence the optimal olution for link bandwidth allocation. Therefore the adaptation of a reward parameter hould be integrated with adaptation of link bandwidth. One poible relatively imple olution i to apply the two adaptation algorithm iteratively, a illutrated in Fig. 2. Network blocking contraint can be met by multiplying all cla reward parameter {r } by a common factor γ. Fig. 2. SON adaptation algorithm Once network contraint ha been met, cla blocking probabilitie can be readuted, a required to meet cla contraint, by varying relatively the cla reward parameter between them (while preerving the average network reward parameter). In thi paper, we only conider meeting the network blocking contraint. Let rt = λ r λ and r = λ r λ = λ r λ be the current c average network and link reward parameter. To achieve equality B T ( rt ) = BT, one can apply Newton iteration with an approximation for the derivative BT rt. At each iteration n, the new network reward parameter will be: c n n+ 1 n BT B r T T = rt + (1) n n ( BT rt ) Since adaptation multiplie all cla reward parameter by the ame factor γ, all reward parameter relative differential will be equal: Uing (16) in the differentiation of (14) give: r r = rt rt = r r (16) BT rt = 1 λ ( λ r rt B ) r (17)

698 C. Tran, Z. Dziong, and M. Pióro To implify calculation for B r, we ue the one moment performance model baed on the link independence aumption, where link blocking probability B applie to all connection clae on the link. Then, connection path k and cla blocking probabilitie are: k B = 1 Π k (1 B ) (18) S k B = Πk W B = Πk W [ 1 Π k S (1 B )] (19) Differentiation of cla blocking probability (19) give: B r = {[ \{ }(1 (1 ))]* ( (1 )) * } B k k W Π o k \{ } o W k Π B S Π B S t S t (20) r r r To find link blocking probability derivative B r, we can ue the formulation of the link average hadow price given in [8], which at optimal network profit (8) equal the bandwidth unit cot c: p = c = λ λ )[ E( λ, N 1) E( λ, N )] J k r ( λ (21) where E( λ, N) i the Erlang B formula. Baed on (21), for a given c, differential δn required to maintain optimal profit condition correponding to differential δr, i determined uing the following: [ E( λ, N 1) E( λ, N)] r E(, N + N 1) E( λ, N + N ) = r + r λ (22) Uing δn, link blocking probability derivative i then approximated a: B r = [ E( λ, N + N ) E( λ, N )] r (23) The adapted network reward parameter (1), obtained uing (17), (20), (23), allow for determination of multiplier γ to be ued for cla reward parameter. 4 Numerical Analyi In thi ection, we preent numerical reult for our reource adaptation model. Adaptation reult are obtained baed on each of the two cae of CAC and routing model (ection 3.1): MDP and MDPD. The MDPD cae allow for adaptation in realitic ize network, while the MDP cae provide exact olution which can be ued to verify the approximate MDPD cae. In both cae, the network performance evaluation (cla blocking probabilitie and flow ditribution among the path) i baed on an exact model with exact network tate. The advantage of uing thi exact performance model i that we can concentrate on key iue of profit optimization without being affected by the noie of an event-driven tatitical imulation. The obviou limitation i that the network example ize i quite mall due to the number of network tate. In the future, we will preent reult baed on event driven imulation that can handle realitic ize example.

SLA Adaptation for Service Overlay Network 699 In thi analyi, we focu on the two important profit optimization proce iue: a. Link bandwidth adaptation to maximize profit, both in the MDPD model and the exact MDP model. b. Reward parameter adaptation to meet the blocking contraint. 4.1 Analyzed Network Example To be able to proce the exact analytical model, we limit network tate pace by uing two imple network example called 3L and L, where link capacitie are alo limited. Each network ha three connection clae, each connecting a pair of node over direct or indirect path. Connection clae arrival rate are λ 1, λ2, λ3, all have the ame bandwidth requirement (1 unit), ervice rate (μ=1) and reward rate (r =r=1). Bandwidth unit cot are 0.2 in network 3L and 0.1 in network L. The network are repreented in Fig. 3 and 4, with connection cla 1 hown. In network 3L, connection clae 2 and 3 imilarly connect repectively ON2-ON3 and ON3-ON1. In network 4L, connection clae 2 and 3 connect ON0-ON2 and ON0-ON3. λ 1 Cla 1 direct connection ON1 ON2 OL1 OL2 OL3 Cla 1 indirect connection ON3 Cla 1 direct connection λ 1 ON0 OL3 OL1 ON1 OL2 OL4 ON3 Cla 1 indirect connection ON2 OL Fig. 3. Network 3L Fig. 4. Network L 4.2 Link Bandwidth Adaptation for Given Reward Parameter Link Bandwidth Adaptation Convergence. To illutrate the convergence we ue network 3L with initial link bandwidth et to N 1 = N2 = N3 = 3 and connection arrival rate et to λ 1 = λ2 = λ3 = 3. The link bandwidth adaptation procedure (with the damping factor et to one) i performed to obtain maximized network profit. The reult are hown in Fig.. For both model, MDPD and MDP, the convergence to optimal link capacitie of 6 i reached very fat after two iteration. Then we change arrival rate to λ 1 = 4, λ2 = 3, λ3 = 2 and the adaptation i performed again. The reult are hown in Fig. 6 and 7 for MDPD and MDP model repectively. Both model converge to the ame optimal value (N 1 =7, N 2 =6, N 3 =4). Numerical reult for example network L, hown in Fig. 8, confirm the good convergence of the model to the optimal network profit.

700 C. Tran, Z. Dziong, and M. Pióro 7 6 bandwidth MDP profit MDPD profit 0.4 0.3 0.2 4 3 1 2 3 0.1 0-0.1 MDP dp/dn MDPD dp/dn 1 2 3 Fig.. Network 3L bandwidth adaptation, λ = λ = λ 3 1 2 3 = 4.9 N=(7,6,4) 0.1 0.0 network profit 4.8 4.7 4.6 4. N=(7,6,) N=(6,6,6) 1 2 3 dp/dn 0-0.0-0.1-0.1 1 2 3 link 1 link 2 link 3 Fig. 6. Network 3L adaptation, MDPD, λ =, λ = 3, λ 2 1 4 2 3 =.3 N=(6,6,4) N=(7,6,4) 0.1 network profit.2.1 N=(6,6,) N=(6,6,6) 1 2 3 4 dp/dn 0-0.1-0.2 link 1 link 2 link 3 1 2 3 4 Fig. 7. Network 3L adaptation, MDP, λ =, λ = 3, λ 2 1 4 2 3 = network profit. 4. 4 3. N=(,,,0,0) N=(4,4,4,0,0) N=(7,7,7,0,0) N=(3,3,3,3,3) 1 2 3 4 dp/dn 0.6 0.4 0.2 0-0.2 1 2 3 4 link 1 link 2 link 3 link 4 link Fig. 8. Network L adaptation, MDP, λ 1 = λ2 = λ3 = 3

SLA Adaptation for Service Overlay Network 701 The preented reult indicate good convergence of the propoed model. Alo it i important that the approximate MDPD model converge to the ame olution a exact MDP model with comparable convergence peed. Convergence Improvement. Baed on the hape of the profit enitivity curve P ( N ), we noticed that, to improve convergence peed, the damping factor for N poitive derivative hould be > 1, and the one for negative derivative hould be < 1. More profound analyi of thi iue will be given in a future publication, with experiment baed on event driven imulation of larger network example. 4.3 Reward Parameter Adaptation to Meet the Blocking Contraint In thi ection, analyi reult for uing reward parameter adaptation to control network blocking probability are given. In the derivative computation, we ued imple linear interpolation to etimate fractional link capacitie blocking probability. The adaptation algorithm i applied to network 3L with cla arrival λ={4, 3, 2}. For blocking contraint et at 2%, reult are repreented in Fig. 9 while Fig. 10 how the cae when blocking contraint i et at 1%. reward parameter, blocking probability(%) 6 4 3 2 1 reward parameter network blocking Lambda=(4, 3, 2) SLA unit cot = 0.2 1 2 3 4 network profit 20 1 10 N=(8,6,) N=(8,6,) N=(7,6,) N=(7,6,) N=(7,,4) 1 2 3 4 Fig. 9. Network 3L reward parameter adaptation, block contraint=2% reward parameter, blocking probability(%) 6 4 3 2 1 0 reward parameter network blocking Lambda=(4,3,2), SLA unit cot = 0.2 1 2 3 4 network profit 3 30 2 20 1 10 N=(8,7,) N=(8,6,) N=(8,6,) N=(8,6,) N=(7,,4) 1 2 3 4 Fig. 10. Network 3L reward parameter adaptation, block contraint=1% Thee reult how that the adaptation algorithm can fulfill the blocking contraint in a few iteration.

702 C. Tran, Z. Dziong, and M. Pióro Concluion In thi paper, we propoed an economic framework for operating Service Overlay Network with the obective of network profit maximization ubect to blocking contraint. The framework ue Markov deciion theory for integration of the CAC and routing model with the link bandwidth and reward parameter adaptation model. The key element of thi integration i the concept of link hadow price that provide conitent economical framework for the whole problem. Preliminary numerical reult validate the propoed approach by howing good convergence, although network example are of limited ize due to the exact analytical model ued for network performance evaluation. Therefore, in a forthcoming publication, we will preent a tudy baed on event driven imulation uing realitic ize network. In thi cae the meaurement and prediction will be ued to feed the MDPD baed model. We will alo tudy reward parameter adaptation to meet individual cla blocking contraint. Acknowledgment. Thi work i upported in part by grant from NSERC. Reference 1. Li, B., et al.: Guet Editorial, Recent Advance in Service Overlay Network. IEEE Journal on Selected Area in Communication, vol. 22, no. 1, (2004), p 1-2. Sen, Arunabha, et al.: On Topological Deign of Service Overlay Network. Lecture Note in Computer Science, Vol. 32, Quality of Service IWQoS 200: 13 th International Workhop, IWQoS 200 Proceeding (200), p 4-68 3. Duan, Z., Zhang, Z.-L., Hou, Y.T.: Service Overlay Network: SLA, QoS, and Bandwidth Proviioning. IEEE/ACM Tranaction on Networking, vol. 11, no. 6, (December 2003), p 870-883 4. Allen, D. Virtela IP VPN Overlay Network. Network Magazine, (January 2002). Fulp, E.W., Reeve, D.S.: Bandwidth Proviionning and Pricing for Network with Multiple Clae of Service. Computer Network, vol. 46, no. 1, (September 2004), p.41-2 6. Dziong, Z.: Economic Framework for Bandwidth Management in Service Overlay Network. Technical Report. École de Technologie Superieure, (July 2006) 7. Dziong, Z., Maon, L.G.: Call Admiion and Routing in Multi-Service Lo Network. IEEE Tranaction on Communication, vol. 42, iue 234, part 3, (February/March/April, 1994), p 2011-2022 8. Dziong, Z.: ATM NETWORK RESOURCE MANAGEMENT. McGraw-Hill, New York, (1997)