An Approach to Optimizations Links Utilization in MPLS Networks

Transcription

1 An Aroach to Otimizations Utilization in MPLS Networks M.K Huerta X. Hesselbach R.Fabregat Deartment of Telematics Engineering. Technical University of Catalonia. Jori Girona -. Camus Nor, Eif C, UPC. 8 Barcelona Sain xavier.hesselbach@entel.uc.es Deartment of electronics an Circuits, Universia Simón Bolívar, Aartao Postal 89, Caracas 8-A, Venezuela mhuerta@usb.ve Institut Informàtica i Alicacions Universitat e Girona EPS P. Camus Montilivi, 77 Girona Sain ramon@silver.ug.es Abstract In this aer we resent a stuy for the otimization of the links utilization in several MPLS network toologies. This information hels in etermining the maximum link utilization require, which is a valuable knowlege in balancing loa strategies in the network. We resent mathematical moels that tune the otimal arameters for strategically routing traffic in an MPLS network. We resent the Otimal Link Utilization Moel () for ifferent toologies. rovies an aroach that woul result in otimally balance link utilization. Finally we comare the results of the moel with the interior oint an simlex algorithms. Results show that the maximum link utilization require is minimize.. INTRODUCTION In recent years there has been active research in the fiel of MultiProtocol Label Switching (MPLS) an an increasing number of networks are suorting MPLS. The remise of MPLS is to attach a short fixe-length label to the ackets at the ingress router of the MPLS omain. These ege routers are calle Label Ege Routers (LERs), while routers caable of forwaring both MPLS an IP ackets are calle Label Switching Routers (LSRs). The ackets are then route base on the assigne label rather than the original acket IP heaer. The label assignments are base on the Forwaring Equivalent Class (FEC), where ackets belonging to the same FEC are assigne the same label an traverse through the same ath across the MPLS network. A ath traverse by an FEC is calle a Label Switche Path (LSP). The Label Distribution Protocol (LDP) an an extension to the Resource reservation Protocol (RSVP) are use to establish, maintain, an tearown LSPs []. One of the most attractive alications of MPLS is Traffic Engineering (TE) []. A TE roblem in the Internet consists of setting u aths between the eges routers in a network to meet traffic emans while achieving low congestion an otimizing the utilization of network resources. In ractice, the usual key objective of traffic engineering is to minimize the utilization of the most heavily use link in the network, or the maximum of link utilization. As the maximum link utilization qualitatively exresses that congestion sets in when link utilization increases higher, it is imortant to minimize the link utilization throughout the network so that no bottleneck link exists. It is known that this roblem of minimizing the maximum link utilization can be solve by the multicommoity network flow formulation of otimal routing, which leas to slitting traffic over multile aths between source-estination airs []. The objectives of this aer are twofol. First of all, the aer aresses in etermine otimal flow allocations to alternative aths for MPLS networks, which we call the Otimal Link Utilization Moel (), consists of minimizing the loa in each link, maximize the utilization of links, subject to caacity an flow constraints. In orer to minimize the average acket elay, a common aroach has been the maximum link utilization require is minimize. The secon goal of the aer is to allocate traffic loa from source noes to target ones, in such a way that backbone resources are utilize in a balance manner. Our mathematical moel is base on ifferent MPLS networks toologies: Mesh, Ring an Tree. We assume that all links are biirectional an consier the maximum link utilization within the network as the relevant network QoS measure. In this aer we consier Interior Point Methos () an Simlex Metho (SM) for the comarison with the. The remainer of the aer is organize as follows. In Section II, we roose, escribe an analyze the Otimal Link Utilization Moel (). Section III we resent ifferent toological MPLS networks with. Section IV rovies the simulation results for evaluation urose. Finally, we resent some conclusions in Section V.

2 . THE OPTIMAL LINK UTILIZATION MODEL () The roblem consists of minimizing the loa in each link, maximize the global utilization of links, subject to caacity an flow constraints. We nee to efine a esign objective function. In orer to minimize the average acket elay, a common aroach has been to minimize the maximum link utilization. In [] enote the metric of link e which takes non - negative or ositive integer values, eening on the unerlying routing rotocol boune above. Thus, the link metric system w = (w, w,,w e ) will inuce traffic flow each eman base on the rule of the routing rotocol. In the case of OSPF/IS-IS, this is governe by the shortest ath routing. If multile shortest aths are available for a eman then flow is equally slit among all shortest aths accoring to the rule know as the equal-cost multiath (ECMP) rule[]. Suose that we can etermine a set of ossible/allowable aths =,, for eman (instea of assuming which one woul be the shortest). We enote the flow on ath for eman inuce by the link metric system w by x (w) this relation is imortant to oint out ie to the eenency of the flows x (w) on ath. The link utilization on each link e is enote by Le( w) / c e.where Le is link loa of the link e. Then the maximum utilization over all links is reresente by the eenent variable r an reresent function objective. The goal of the maximum link utilization requires is minimize can be formulate as follows: Minimize r = max ( L ( w) / c ) e e e x = h =,,.D () δ e x = Le e=,,..., E () Le ce e=,,..., E () we non-negative integers Where: h is eman constraint volumes, δ e is link ath inicator, meaning it takes the value if the route for eman uses the link e, Otherwise it is an c e is caacity of link e.. IN MPLS NETWORKS.. in Mesh MPLS network A mesh network is a local area network that emloys one of two connection arrangements, full mesh toology or artial mesh toology. The Fig. shows a full mesh network with five noes. Mesh networks work well when the noes are locate at scattere oints that o not lie near a common line. The chief rawback of the mesh toology is exense, because of the large number of connections require. In some scenarios, a ring network may rove more cost effective than a mesh network. Alying link utilization an maximum throughut analysis for each link of this network we obtain (). Consiering "all with all", the total number of connections is the ouble of the number of combinations of N noes, taken from to, the number of connections can be efine as: N = N( N ) Minimize r = max e( N( N ) / ce) () x = h =,,.D (5) δ ex = N( N ) e=,,..., E (6) NN ( ) c e=,,..., E (7) f e x f f x x x 5 x7 f x5 x6 x8 x x9 Figure : Mesh MPLS networks. in Ring MPLS network The ring toology may rove otimum when system requirements are moest an noes are at scattere oints. A break in the cable of a ring network may result in egrae ata see between airs of noes for which the ata ath is increase as a result of the break. If two breaks occur an they are not both in the same section of link, some noes will be cut off from some of the others. When system reliability is a critical concern, a bus network or star network may rove suerior to a ring network. If reunancy is require, the mesh network toology may be referable. Fig. illustrates a ring network with 5 noes an 5 links. Alying link utilization an maximum throughut for each link of this network we obtain (8). For ring network the number of connections can be efine as: N(N-)/. N N Minimize r = max e / ce (8) x = h =,,.D (9) N N δex = e=,,..., E () N N ce e=,,..., E f 5 ()

3 f L5 L f 5 5 f L L f L f Where n are noes in tree network, n are noes number below the noe where it is calculate F an h is height tree. In Fig., F enotes throughout noe. A Height = Root noe Deth F Deth Figure : Ring MPLS Network. in Tree MPLS network Deth Deth Clearly the tree structure reresenting such a comutation usually grows ynamically uring the rocess of the comutation in an unreictable way. Efficient execution of these comutations on a arallel comuter requires assigning their rocesses (tree noes) to the rocessors of the unerlying arallel comuter such that every rocessor gets aroximately an equal amount of comutation loa an communicating rocesses are assigne to rocessors that are as close as ossible. This roblem is known as ynamic tree embeing roblem [5-7]. A comlete m-ary tree in which all leaves have the same eth () an all internal noes have egree m is shows in Fig.. Thus, the number of leaves at height h is m h, consequently, h of a comlete m-ary tree with n leaves is log m n [8]. The number of internal noes if a comlete m-ary tree of height h is: h h i + m+ m m = m i= To calculate utilization of links first we calculate the throughut in each noe, for it we ivie the roblem in two arts. The first art is to calculate whole loa that exists over each noe an the secon art is the loa of noes that are below lus the loa of internal connections. This gives us the result of all the ossible connections in network, which is reresente for A in the Fig. an formulate by (). The equation is multilies for taking into account that links are biirectional; this roceure is vali only for h >. In orer to calculate all the internal connections between chilren noes to the target noe where F is calculate an reresente for B in the Fig. an formulate by (). We roose the next equation for the total utilization: n F = ( n n) n + ( m ) m () A B Where: n h i = m i= Figure : Tree MPLS Network By means of this moel we can calculate the comlete loa that asses for each of the noes. Nevertheless it is necessary to otimize the loa in each links. The links utilization in each branch may be formulate as follows: Minimize n F = maxe ( n n) n + ( m ) / ce m () x = B =,,.D () n δex = ( n n) n + ( m ) e =,,,E m n ( n n) n + ( m ) ce e =,,,E m. RESULTS In this section, we rovie some numerical examles that illustrate the link utilization on three networks toologies. Those results are obtaine from simulations or from exact analysis. The first moel is base on the mesh network shown in the Fig., which consists of 5 noes, with links; the caacity of each link is limite between an i, j. Ingress flows f, f an f, are resectively:,, an egress flows f, f5 will be: -, -. We want to otimize the link utilization. To get it we aly the equations resente in section III, an we comare the results using well known solvers for otimization: CPLEX [9] an LIPSOL []. First we analyze link maximum utilization eening of number of noes in the network. The Fig. shows the results maximum link utilization require in function of the number of noes for ring an mesh networks acquire the () an (8) B

4 resectively. We can see that the link utilization ecreases accoring to the amount of noes in the network. Secifically, this iminish is inversely to square of the number of noes, this behaviour is similar for both tyes of networks. The Fig. 5 shows the obtaine results using three otimization methos: SM, an in Mesh network. We can see the flow istribution in each link. The loa balance is similar in all cases. The link X is aroximately saturate whereas links X, X6, X8, X9 an X are ractically free of traffic loa. In this case the moel minimizes the loa in % of the link X, istributing the loa in the links X9 an X, but it continues maintaining the loa of the links X, X6 an X8 ractically in zero. The Fig.6 shows the obtaine results consiering for a ring network which consists of 5 noes, with 5 connections; the caacity of each connection is limite between an i, j. The ingress flows f, f an f, will be resectively: 5,, an the egress flows f, f5 will be: -5, -5. We want to otimize the link utilization. To get it we aly equations, like we exlain reviously, an we will verify the results by solvers commercials of otimization CPLEX an LIPSOL,6,5,,,, Noes Mesh Ring Figure : Maximum link utilization require in function noes grown in mesh an ring network. Maximun Utilization,,8,6,, X X X X X5 X6 X7 X8 X9 X SIMPLEX Figure 5: Maximum link utilization in mesh network. In for this tye of network the roose moel is more efficiently than SM an, it istributes the traffic more uniformly in each network link. Also in this grah we can observe that in SM there is only one link at maximum loa (X5) an another without loa (X), balancing the loa in the rest of the links. For the case of the some links on t have loa, it is the case of X, X5, X8 an X. But it suorts the rest of the links with fair loa. This behaviour is smoothe by the roose moel ().,,8,6,, X X X X X5 X6 X7 X8 X9 X Figure 6: Maximum link utilization in ring network. SIMPLEX The table shows how the network grows eening on the number of branches an of the eth of the tree network, in articular for,,, 5 an 6 branches. We can observe that the growth is exonential resect to eth. For number of noes calculation in tree network, we assume that it s symmetric; in other wors, the root noe slit in m branches, an the chilren noes also woul slit in others m noes. For examle, we consier the tree toology resente in figure with four height an m = in each noe, also we consiere others networks with m = an m = an height 5. For the analysis of the utilization of the links in a network tree, is consiere a toology with noes an biirectional connections; the caacity of each connection is limite between an (i, j). We want to otimize link utilization. To get it we will aly equations, like we exlain reviously, an we will verify the results by solvers commercials of otimization CPLEX an LIPSOL. The results are shown in Fig 7. There we can see the istribution of the loa in each of network links using the three methos in evaluation. In general the behaviour is similar in the neighbourhoo of the root noe links, but as we move to the inferior branches of the network where the loa is smaller than in the suerior ones we see that link utilization is aroaching to zero an therefore they are less congeste. Nevertheless the roose moel has a better balance of loa than an SM in the inferior branches of the network. If esigning an otimal tree is a comlex roblem, maintaining this tree otimality after changes in the noes grou may be even more comlex. The table shows the results obtaine for function objective. The evaluation was one for the three network toologies using 7, 5, an 6 noes. It is necessary to highlight that this function is ientical when evaluate three methos (SM, an ).

5 TABLE GROWNING OF TREE NETWORK h m= m= m= N N F N N F N N F 7 8 D 6 D 5 D 6 D 7 85 D 86 D 5 D D 65 D 56 D 9 7 D 8 8 D 6 6 D 688 D D D 78 D D 7 6 D D 78 D D D 8 D 6 69 D 85 D 56 D D 66 D 89,8,7,6,5,,,, X X X7 X X X6 X9 X X5 X8 X Figure. 7 Maximum link utilization in tree network TABLE OBJECTIVE FUNCTIONS OF THE THREE ALGORITHMS 7-Noe Network 5-Noe Network OUL SM OUL SM Mesh Ring Tree -Noe Network 6-Noe Network OUL SM OUL SM Mesh Ring Tree ACKNOWLEDGMENTS This work was suorte by the National roject CICYT TIC-89-C uner a grant from the Sanish Eucational Ministry, an the COST Action 9 Graal. 5. CONCLUSIONS A mathematical moel to etermine the otimal arameters for strategically routing traffic in an MPLS network has been resente. We have roose an aroach for otimal link utilization moel () for three toologies: ring, mesh an tree. The aroach rovies a solution that woul result in otimally balance link utilization. The behaviour we get using this algorithm is similar to what we get with the X X7 X X X6 X9 X5 X55 SM X58 solver. Finally we comare the results of theoretical moel with the interior oint an simlex algorithms using the GAMS an CPLEX solvers. The results show that minimize maximum require link utilization with resect to an SM. But, the resulting function objective is the same for the three algorithms in the toologies evaluate. As a future work, we want to use the moel in others network toologies, traffic istribution, an routing constraints on network caacity. We will consier ho count restriction in this moel. 7. REFERENCES [] E. C. Rosen, A. Viswanathan, an R. Callon, "Multirotocol label witching architecture." RFC, January. [] M. Huerta an X. Hesselbach, "Alication of the theory of the multicommoity for the flows istribution in MPLS networks,". LANMAN. The th IEEE Worksho on,,. 9-. [] M. Pioro an D. Mehi, Routing, flow an Caacity Design in Communications an Comuter Networks. San Francisco: Morgan Kaufmann Elsevier,. [] A. Iselt, A. Kirstater, A. Parigon an T. Schwabe, "Resilient routing using MPLS an ECMP," High Performance Switching an Routing, HPSR-. [5] K. Li, "On ynamic tree growing in hyercubes " in Proceeings of the 997 ACM symosium on Alie comuting San Jose, California, Unite States ACM Press, [6] K. Li, "Asymtotically otimal ranomize tree embeing in static networks," resente at Parallel Processing Symosium, IPPS/SPDP,998. [7] H. Shen, K. Li, Y. Pan, G. H. Young, an S. Q. Zheng, "Performance analysis for ynamic tree embeing in k-artite networks by ranom walk," 997. I-SPAN '97 [8] T. H. Cormen, C. E. Leiserson, an R. L. Rivest, Introuction to algorithms, secon e,. [9] CPLEX, "CPLEX User's Manual," ILOG, 999. [] Y. Zhang, "Solving Large-Scale Linear Programs by Interior-Point Methos Uner the MATLAB Environment," Technical Reort TR96-, Deartment of Mathematics an Statistics, University of Marylan, Baltimore County, July 995.