A Reolution Approach to a Hierarchical Multiobjective Routing Model for MPLS Networ Joé Craveirinha a,c, Rita Girão-Silva a,c, João Clímaco b,c, Lúcia Martin a,c a b c DEEC-FCTUC FEUC INESC-Coimbra International Doctoral School on Algorithmic Deciion Theory: MCDA and MOO (COST IC060 Han ur Lee, Belgium, 7- September 007
A Reolution Approach to a Hierarchical Multiobjective Routing Model for MPLS Networ Introduction and Motivation Routing in MPLS networ Modern multiervice networ routing functionalitie have to deal with multiple and heterogeneou QoS (Quality of Service requirement. Routing model have to calculate and elect one (or more route( atifying certain QoS contraint and the optimiation of route related metric. There are potential advantage in uing multiobjective formulation for the routing calculation problem in MPLS networ. Thee formulation enable the trade-off among ditinct performance metric and other networ cot function to be purued in a conitent manner.
A Reolution Approach to a Hierarchical Multiobjective Routing Model for MPLS Networ Introduction and Motivation In [Climaco et al,07] and [Craveirinha et al, 07a] an overview on multicriteria routing model for MPLS and a dicuion on conceptual and modelling iue on thi area, were preented. Alo a generic hierarchical multiobjective networ-wide routing optimiation framewor in MPLS, wa propoed in [Craveirinha et al, 07a]. Networ-wide optimiation mean that the objective function are formulated at networ level and depend explicitly on all traffic flow (eg. average total carried traffic, total expected revenue, utiliation function of the arc. The poibility of applying thi modelling framewor to a MPLS type networ, namely by conidering two clae of ervice, QoS traffic irt priority traffic and Bet Effort (BE traffic (econd priority traffic, wa a major motivation for thi wor. The flow of QoS type irt priority flow, when accepted by the networ, have a guaranteed QoS level, related to the required bandwidth, while BE traffic flow, which are treated in the model a econd priority flow, are carried in order to obtain the bet poible QoS level for the current networ routing olution. 3
A Reolution Approach to a Hierarchical Multiobjective Routing Model for MPLS Networ Decription of the Routing Model It i baed on a networ-wide multiobjective routing optimiation model: Hierarchical multiobjective routing optimiation firt level: objective function related to QoS traffic formulated at global networ level econd level: average performance metric aociated with the different type of QoS ervice plu the global networ level objective for BE traffic (expected revenue Explicit conideration of fairne objective at the two level of optimiation It conider an (approximate tochatic repreentation of the traffic flow aociated with the explicit route, enabling to etimate flow blocing probabilitie. Unlie model baed on virtual networ defined for QoS and BE traffic, it enable a complete repreentation of the interaction among all traffic flow. 4
A Reolution Approach to a Hierarchical Multiobjective Routing Model for MPLS Networ Routing optimiation model P-M-S Firt level (QoS Networ objective min {-W Q = total expected revenue of the QoS traffic} R min {B Mm Q = maximal average blocing probability among QoS R ervice} networ fairne objective Second level (QoS Service objective min {B m Q = average blocing probability for QoS flow of type } R S Q min {B M Q = maximal blocing probability among QoS flow of R type } S Q QoS ervice fairne objective (BE Networ objective min {-W B = total expected revenue of the BE traffic} R 5
where A Reolution Approach to a Hierarchical Multiobjective Routing Model for MPLS Networ W Q = S Q A c w A c : total traffic carried for ervice w : expected revenue per µ-flow of type All the objective function can be expreed in term of the traffic offered by all the flow f, A ( S Q U S B and the correponding end-to-end blocing probabilitie B. B = m Q A o B A f F B M Q = max f F {B } B Mm Q = max SQ {B m } W The B are calculated from a lin tochatic model baed on a multidimenional Erlang ytem by uing the concept of effective bandwidth. B = S B A c w 6
A Reolution Approach to a Hierarchical Multiobjective Routing Model for MPLS Networ Foundation of the reolution approach The hierarchical multiobjective alternative routing problem in quetion i highly complex a a reult of the trong interdependencie among all objective function (via the B, and the interdependencie between the objective function parameter and the (dicrete deciion variable R (networ route plan. Concerning overall complexity it can be aid that the implet, degenerated ingle objective verion of the problem, correponding to the ingle objective function W Q, one ingle ervice and no alternative routing i NPcomplete in the trong ene. Thi and the interdependencie among the objective function, are a trong indication of extreme intractability of the problem. Concerning the poible conflict between the objective function in P-M-S, it can be aid that in many ituation, the maximiation of W Q entail a deterioration on B, S Q, for mall intenity traffic flow A which tend to increae B M Q and, a a reult, B Mm Q. 7
A Reolution Approach to a Hierarchical Multiobjective Routing Model for MPLS Networ Foundation of the reolution approach The heuritic developed for problem P-M-S i baed on the calculation of olution of a bi-objective hortet path problem. In thi problem the path metric to be minimied will be the marginal implied cot (a defined according to the following analyi and blocing probabilitie. The implied cot c u reulting from the acceptance of a call of flow f u in lin l i a powerful mathematical concept in routing optimiation in circuit-witched networ, originally propoed by [Kelly,88] for ingle-rate traffic networ. It wa extended to ingle route (i.e. without alternative routing multirate traffic networ in [Farago et al,95] and [Mitra et al,99]. It can be defined a the expected value of the lo of revenue in all networ traffic flow which may ue lin l reulting from the acceptance of a call from f u aociated with the decreae on the capacity of thi lin. Therefore the implied cot meaure the noc-on effect on all networ route (of all traffic flow reulting from the acceptance of a call from f u in a lin l. 8
A Reolution Approach to a Hierarchical Multiobjective Routing Model for MPLS Networ Foundation of the reolution approach The auxiliary bi-objective hortet path problem to be olved will have two poible configuration: the firt one will ue a lin cot coefficient m =c Q when one intend to obtain candidate olution to improve the revenue of the QoS traffic, the econd one will ue m =c B when one ee to improve the revenue aociated with the BE traffic: Problem P ( r min D n m (r = m l r n= ; where m =-log(-b and m =c Q(B, and D i the et of feaible loople path for flow f, reulting from traffic engineering contraint. n 9
c Q(B u = A Reolution Approach to a Hierarchical Multiobjective Routing Model for MPLS Networ Foundation of the reolution approach ( ( Q(B Q(B Q(B Q(B + c + λ + c u r r S f :l r f :l r Q(B -B ζ λ r r ζ Q(B r u Q(B r = = = L w w Q(B (d Q(B,ρ,C l r l r j j d c u c Q(B j Q(B j L ( L Q(B r r (d,ρ,c ( where w Q(B α Q(B ]0.0;.0[ Q B α +α =.0 =α Q(B w and the coefficient atify the normaliation condition 0
A Reolution Approach to a Hierarchical Multiobjective Routing Model for MPLS Networ Foundation of the reolution approach Fixed point equation reult from the traffic model and contitute a ytem of implicit non-linear equation enabling the calculation of the blocing probabilitie of f on l, B, in term of lin capacitie, matrix C [C ], the offered traffic matrix A [A] and the current networ routing plan R : B = β(b,c,a,r ( with =,, L ; =0,, S - and B [B]. Q(B The calculation of c through the ytem of equation ( implie the olution of a ytem of equation of the form: Q(B c (c,b,c,a,r = α (3 Q(B with c [c ]. The numerical reolution of thee ytem (-(3 (in thi order i performed by fixed point iterator, for given and and. C A R
A Reolution Approach to a Hierarchical Multiobjective Routing Model for MPLS Networ Eential Feature of a Firt Heuritic Approach The core of the heuritic i the generation of candidate olution (r, r for each f, where the path are defined according to certain rule and are obtained through a contrained bi-objective hortet path algorithm, previouly developed, MMRA-S ee [Martin et al,06]. Having in mind the networ topology and the need to mae a further ditinction between real-time QoS ervice (video and voice ervice and non-real time QoS ervice (uch a premium data ervice pecial rule were defined for the election of candidate firt choice route r. For a decription of thee rule, ee the Report [Craveirinha et al,07b]. The propoed procedure for earching and electing the path to be ued by the call of each node-to-node traffic flow combine a weighted um of the two objective function and the definition of priority region obtained from preference threhold concerning acceptable and requeted value for each objective function.
A Reolution Approach to a Hierarchical Multiobjective Routing Model for MPLS Networ Eential Feature of a Firt Heuritic Approach r min D l r Q( B c l r( f c acc ( ( Q(B Q(B Q(B ε (( log( B + ε (c B C c req ( A B c * ( f log( B * ( f log( B req ( l r ( f log( B log( B acc ( 3
A Reolution Approach to a Hierarchical Multiobjective Routing Model for MPLS Networ Eential Feature of a Firt Heuritic Approach A general idea of the heuritic i to ee, for each ervice, a routing olution R( which may lead to a better performance in term of W B, B m Q and B M Q, hence leaving networ reource available for traffic flow of other ervice o that the olution elected at each tep may enable an improvement on the higher level objective function W Q, B Mm Q. Succeive application of MMRA-S to every traffic flow doe not lead to an effective (even le robut reolution approach to the networ routing problem P-M-S. The eential reaon for thi i an intability phenomenon that arie in uch path election procedure, expreed by the fact that the route et R tend to ocillate between certain olution ome of which may lead to poor global networ performance under the precribed criteria. 4
A Reolution Approach to a Hierarchical Multiobjective Routing Model for MPLS Networ Eential Feature of a Firt Heuritic Approach The bai of the heuritic approach (imilarly to MODR-S [Martin et al,06] i to earch for the ubet of the path et R a = U S = 0 R a (: R the element of which hould be poibly changed in the next route updating cycle. Detailed analyi and extenive experimentation led u to a pecific criterion for chooing candidate path for poible routing improvement by increaing order of a function ξ of the current (r, r. F c Q(B C Q(B r = ξ = = l r F L (n c Q(B a F n ( = Q(B C c' {(r Q(B F c' = L L r L,r + c Q(B r Q(B r,f c = n F Q(B r l r c } Q(B 5
A Reolution Approach to a Hierarchical Multiobjective Routing Model for MPLS Networ Eential Feature of a Firt Heuritic Approach In ome cae, overload condition led to the elimination of the alternative path, through a pecial mechanim, APR (Alternative Path Removal. Q(B Q(B c >α d z and -log(-b > log(0.7z l r When the alternative path i removed, Q(B Q(B F = c F L = Lr C r APR l r ( APR A econd point to be tacled by the heuritic procedure i to pecify how many of the route with maller value of ξ hould poibly be changed by applying MMRA-S once again. For thi purpoe the effect of each candidate route, in term of the relevant objective function i anticipated by olving the correponding analytical model. A decription of thi heuritic can be een in the Reearch Report [Craveirinha et al,07b]. 6
A Reolution Approach to a Hierarchical Multiobjective Routing Model for MPLS Networ Application of the Model Thi heuritic wa applied to a networ ued in a benchmaring cae tudy on routing with two ervice clae. Thi cae tudy refer to a routing model [Mitra et al,0] that conider a lexicographic optimiation formulation baed on a MCF (Multicommodity Flow, uing a determinitic repreentation of traffic flow a well a bandwidth traffic plitting and admiion control of the BE traffic. Thi reference model upplie ideal optimal value for W Q which may be conidered a upper bound for the W Q value obtained by the heuritic MOR-S. For comparion purpoe we conidered the adaptation of the model to a tochatic environment correponding to 3 node-to-node traffic matrice. 7
A Reolution Approach to a Hierarchical Multiobjective Routing Model for MPLS Networ Application of the Model Tet networ Arc capacitie 8
A Reolution Approach to a Hierarchical Multiobjective Routing Model for MPLS Networ Application of the Model Service feature on the tet networ The initial routing olution of MOR-S conider only firt choice route, hortet path and if there i more than one hortet path, the one with the maximal bottlenec bandwidth i choen. 9
A Reolution Approach to a Hierarchical Multiobjective Routing Model for MPLS Networ Application of the Model Objective function value for the initial and the final olution for MOR-S on the tet networ The value for all the objective function for all value of α are improved through the heuritic. The QoS traffic revenue can be conidered good a they tand for approximately 99% of the ideal optimal value in [Mitra et al,0]. MOR-S ha managed to find an adequate good compromie routing olution to the routing problem P-M-S. In fact thee experimental reult how that the expected QoS revenue obtained with our heuritic i never le than 98.7% of that upper bound while a ubtantial improvement on the other objective function could be obtained with repect to the initial olution, uing only hortet path firt choice routing (typical of Internet routing algorithm. 0
A Reolution Approach to a Hierarchical Multiobjective Routing Model for MPLS Networ Concluion and Further Wor We briefly decribed a new bi-level multiobjective routing model in MPLS networ formulated within a general modelling framewor developed by [Craveirinha et al,07a], auming that there are two clae of ervice (and different type of traffic flow in each cla, namely QoS and Bet Effort (BE ervice. The routing model conider the poibility of uing alternative routing when that i advantageou to the firt priority objective function. Feature of thi model: hierarchical optimiation with two optimiation level, including fairne objective; approximate tochatic repreentation of the traffic flow in the networ, baed on the ue of the concept of effective bandwidth and on a generalied Erlang model for etimating the blocing probabilitie in the arc. The tructure of a firt verion of a heuritic procedure for reolving the problem wa preented. Thi heuritic i baed on a contrained bi-objective hortet path model, of which the objective function are QoS or BE marginal path implied cot and path blocing probabilitie. The preliminary reult preented for a benchmaring cae tudy eem quite encouraging concerning the potential performance of a multicriteria routing model of thi nature.
A Reolution Approach to a Hierarchical Multiobjective Routing Model for MPLS Networ Concluion and Further Wor The major limitation of thi type of model i it inherent great complexity and the aociated computational burden, which contitute the revere of it ambitiou feature. Thi mae, at preent, it potential practical application retrained to networ with a limited number of node, uch a the core and intermediate (metro-core level networ of low dimenion. The model could alo be ued a the bai of a periodic type dynamic routing method. Further wor: Search for improvement in the heuritic procedure, through enitivity analyi of the preent verion; Development of metaheuritic for thi very complex networ routing problem; Extenion of the model to broader routing principle uch a probabilitic load haring or traffic plitting; Development of a dicrete event imulation platform enabling a more exact evaluation of the reult of the heuritic in a tochatic dynamic environment cloer to real networing woring condition.
A Reolution Approach to a Hierarchical Multiobjective Routing Model for MPLS Networ Reference [Climaco et al,07] J. C. N. Clímaco, J. M. F. Craveirinha, M. M. B. Pacoal. Multicriteria routing model in telecommunication networ Overview and a cae tudy. In Advance in Multiple Criteria Deciion Maing and Human Sytem Management, Y. Shi et al. (Ed., 7-46, IOS Pre, 007. [Craveirinha et al,04] J. Craveirinha, L. Martin, J. N. Clímaco. Dealing with complexity in a multiobjective dynamic routing model for multiervice networ A heuritic approach. In Proceeding of the 5th Mini-EURO Conference on Managing Uncertainty in Deciion Support Model (MUDSM 004, Coimbra, Portugal, Sep. -4 004. [Craveirinha et al,07a] J. Craveirinha, R. Girão-Silva, J. Clímaco. A metamodel for multiobjective routing in MPLS networ. Accepted for publication in Central European Journal of Operation Reearch, 007. [Craveirinha et al,07b] J. Craveirinha, R. Girão-Silva, J. Clímaco, L. Martin. A hierarchical multiobjective routing model for MPLS networ Analyi and reolution approach. Reearch Report, INESC-Coimbra, 007 (alo preented at the 3rd IFIP TC 7 Conference on Sytem Modelling and Optimization, Cracow, Poland, July 3-7, 007. [Farago et al,95] A. Faragó, S. Blaabjerg, L. At, G. Gordo, T. Hen. A new degree of freedom in ATM networ dimenioning: Optimizing the logical configuration. IEEE Journal on Selected Area in Communication, 3(7:99-06, Sep. 995. 3
A Reolution Approach to a Hierarchical Multiobjective Routing Model for MPLS Networ Reference [Kelly,88] F. P. Kelly. Routing in circuit-witched networ: Optimization, hadow price and decentralization. Advance in Applied Probability, 0(:-44, Mar. 998. [Martin et al,03] L. Martin, J. Craveirinha, J. N. Clímaco, T. Gome. Implementation and performance of a new multiple objective dynamic routing method for multiexchange networ. Journal of Telecommunication and Information Technology, 3:60-66, 003. [Martin et al,06] L. Martin, J. Craveirinha, J. Clímaco. A new multiobjective dynamic routing method for multiervice networ: Modelling and performance. Computational Management Science, 3(3:5-44, July 006. [Mitra et al,99] D. Mitra, J. A. Morrion, K. G. Ramarihnan. Optimization and deign of networ routing uing refined aymptotic approximation. Performance Evaluation, 36-37:67-88, 999. [Mitra et al,0] D. Mitra, K. G. Ramarihnan. Technique for traffic engineering of multiervice, multipriority networ. Bell Lab Technical Journal, 6(:39-5, Jan. 00. 4