Application of the theory of the Multicommodity for the flows distribution in MPLS networks*

Monica Huerta’.’ E-mail: mhuerta@mat.upc.es

‘Department of Telematics Engineering. Technical University of Catalonia. Jordi Girona 1 y 3. Campus

Nord, Edif C3, UPC. 08034 Barcelona. Spain ’University Sim6n Bolivar Caracas - Venezuela

Abstract: Multicommodity network flows models are computationally challenging due to the large dimension of real instances, as those from the fields of telecommunications specifically m Multiprotocol Label Switching (MPLS) . MPLS is extends the IP destination based routing protocols to provide new and scalable routing capabilities in connectionless networks using a relatively simple packet forwarding mechanism. MPLS networks cany traffic on virtual connections called Label Switched Path (LSP). This paper considers distributed D LSP mechanism, each sub-LSP is set up on a diferent nodedisjoint route. We propose an analytical method that allows minimizing spare bandwidth using the optimization multicommodity Flows technique, specifically applying the reformulation with path flows. The results show that there is an optimization of the spare bandwidth with Distributed LSP mechanism in comparison with conventional LSP.

Keywords: Traffic Engineering, MPLS, D-LSP, Minimum Cost, Multicommodity Network Flows.

1. INTRODUCTION

Multi Protocol Label Switching (MPLS) [l] is a flexible routing mechanism for traffic flows that is based on the assignment of flows to complete end-to-end paths within an Autonomous Domain. The flexibility comes from the freedom to choose the criterion by which traffic flows will be recognized and treated as distinctive ffows. Such “traffic engineering” in the Internet is one of the primary applications envisioned for MPLS. An MPLS network consists of label switched paths (LSPs) and edgekore label switch routers (LSRs). The LSRs store the label translation tables. Core LSRs provide transit services in the middle of the network while edge LSRs provide an interface with extemal networks. The capacity to divide the traffic offers several advantages being the most important: the distribution of the flow and the optimization of the bandwidth. Studies realized in different broadband networks [ 1, 21 have demonstrated that these characteristics can be optimized by means of the usemulticommodity network Flows.

Xavier Hesselbach E-mail: xavier.hesselbach@entel.upc.es

Department of Telematics Engineering. Technical University of Catalonia. Jordi Girona 1 y 3. Campus

Nord, Edif C3, UPC. 08034 Barcelona. Spain

The problem of the multicommodity network Flows (MCNF) can be defined as a network where more than one commodity (messages among the different pair of nodes) needs to be transported from an origin node to a destination node =cording to the restrictions of capacity associated with the links. It is possible to see it as an extension of the single commodity network flow problem (SCNF) [3]. The difference lies in the existence of a set of limitations that do the problem MCNF more complex than the problem of the SCNF . The models of the MCNF have many applications, most of them in routing algorithms in networks and network design problems. The disadvantage is how to find a minimal cost for routing the flow with all the request demands that satisfy the link capacities, for example, messages of routing [4], routing of packages in virtual circuits, networks of information [SI, routing in a ring networks [6] , the design of ATM networks where the maximum load is minimized and the limitations of connection are assembled with a minimal cost [7], appear frequently in the literature of communications.

We consider the problem of Assignment of flows and the Minimization of cost in a network. That is, given a set of links in a network, we wish to determine whether a set of paths can be routed between each request pair such that very few paths use the same wire. In this article we present an analytical method that allows minimizing the spare bandwidth using the technique of optimization of the MCNF, in distributed LSP’s mechanism (DLSP) that was proposed by Kyu and Dan Keun [SI. The D-LSP is constructed by the partition of a LSP in several sub LSP and distributed in different disjoints routes, connecting an origin node with a destination node. The theoretic method proposed is evaluated in a network model with two solvers of optimization: CPLEX and LIPSOL[9].

The remainder of the paper is organized as follows. In Section 11, we describe the MPLS and D-LSP. Section I11 presents a MCNF problem description. Section IV discusses proposed model. Section V provides the simulation results for evaluation purpose. Finally, we present some conclusions and future work in Section VI.

* Thiswork FEDER

is partially supported by the “Ministerio de Ciencia . y Tecnologia” of Spain under project TIC2003 0 8 12pC02, which is partially funded by

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II. MPLS AND DLSP

A. Mpls Fundamentals

The traffic engineering in Intemet is one of the primary applications foreseen for MPLS [lo, 111. A MPLS network is composed of MPLS routers: LSR (Label Switched Router) that represent the core of the network (backbone) and the LER (Label Edge Ibuter) that are the interface between MPLS domain and other networks. The MPLS network is connection oriented, where each connection or LSP Fabe1 Switching Path) are is established among each couple of LER (Ingress and Egress LER), as shown in Fig. 1

Network backbone

ACCfJSS Netwak

Fig. 1. Core and edge nodes in an MPLS network. A distributed LSP.

MPLS is an advanced framework for fast label switching. The basic premise behind MPLS is quite simple: The main idea is to attach a short fixed length label to packets at the ingress to an MPLS domain. Throughout the interior nodes of the MPLS domain, the labels rather than the original packet headers are used to make forwarding decisions. The assignment of labels to packets is based on the concept of forwarding equivalence class (FEC). A FEC is a group of packets that share some of the same characteristics for its transport; they will receive the same treatment in its toward the destination [l]. According to this concept, packets belonging to the same FEC are assigned the same label at an ingress node to an MPLS domain and generally traverse through the same path (or multi-path) across the MPLS network

The tools of aggregation of flows and the explicit routing make MPLS the ideal protocol to carry out Traffic Engineering. An important aspect of MPLS is the classification in the LER of the incoming traffic. So a FEC is assigned for the incoming traffic.

B. Analytical approaches to MPLS trafjc engineering

We now tum our attention to analytical modelling of the MPLS traffic engineering problem. These activities are mostly concemed with the third and fourth phases of the traffic engineering process model. There are many sub problems involved in the performance optimization of

operational MPLS networks. Three of the most significant problems include: (1) constraint-based routing, (2) traffic partitioning and assignment, and (3) restoration. It should be noted that even though these problems are well known in other application domains, they are still in a state of infancy conceming MPLS, and much remains to be done. Accordingly the literature addressing these areas is somewhat limited, at this time. The problem of constraint- based routing deals, in general, with the computation of paths for LSPs subject to various types of constraints. The constraints themselves may be inherent to the network (e.g., available bandwidth) or they can be administratively specified (e.g., affinities and resource class attributes, and diversity requirements for protection and restoration). The computational aspects of constraint-based routing can be performed online or offline. Generally, these problems are NP-complete. This is a MCNF problem which involves flow conservation and bundle constraints plus some side constraints related to the installation of the new facilities. The objective function may be nonlinear or general discontinuous stepincreasing.

C. Distributed LSP (DLSP)

The DLSP is constructed by the partition of a LSP in several sub LSP and distributed in different nodes of “disjoint routes”. The stream of traffic that arrives is distributed on the subLSP in the ingress node. An additional backup sub-LSP is established on a different route from that of its primary sub-LSPs. We assume that every link in the network has the same capacity. The backbone network can provide sufficient routes to any pairs of LER’s and each LER is connected with a sufficient number of backbone LSRs in order to access to any disjoint node routes. Route is shared by the same number of D LSPs. We assume that each disjoint node routes has the same number of hops. Each LER is connected with the same number of backbone LSRs. Network model is defined and the architecture of a D-LSP is represented with a MPLS network model. Fig.1 shows an example of a DLSP established in the MPLS network model. The DLSP is originated from ingress LER and is destined for an egress LER. A DLSP is partitioned into sub-LSPs and spread over the disjoint node routes. Each disjoint node routes should not serve two or more sub-LSPs belonging to the same D-LSP [ 81.

111. MCNF PROBLEM DESCRIPTION

The multicommodity network flow problem is defined over a network where more than one commodity needs to be shipped from specific origin nodes to destination nodes according to the capacity constraints associated with the arcs. It extends the single commodity network flow (SCNF) problem in a sense that if we disregard the bundle constraints, the arc capacity constraints that tie together flows of different commodities passing through the same arc, a MCNF problem can be viewed as several

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independent SCNF problems. This dissertation will focus on min-cost MCNF problem. Hereafter, when we refer to the MCNF problem, we mean the min-cost MCNF problem. The existence of the bundle constraints makes MCNF problems much more difficult than SCNF problems. For example, many SCNF algorithms exploit the sngle commodity flow property in which flows in opposition direction on an arc could be cancelled out. In MCNF problems, flows do not cancel if they are different commodities. The malcflow min-cut theorem of Ford and Fulkerson in SCNF problems guarantees that the maximum flow is equal to the minimum cut [3]. Furthermore, with integral arc capacities and node demands, the maximum flow is guaranteed to be integral. None of these properties

I can be extended to MCNF, except for several special planar graphs [12l, or two-commodity flows with even integral demands and capacities. The total unimodularity of the constraint matrix in the SCNF LP formulation guarantees integral optimal flows in the cases of integral node supplieddemands and arc capacities. This integrality property also can not be extended to MCNF LP fomlations. Solving the general integer MCNF problem is NP-complete [ 131. In fact, even solving the two-commodity integral flow problem is NP-complete [14].

and each column represent a network link. The equation 4 describes one limitation of individual flow in relation to link (i, j) capacity ukz, for each individual flow o f commodity k.

For study's case we select a group of price-directive decomposition, we used the approximation called "Column Generation" specifically the reformulation path flow because it is the most appropriate to resolve flow assignation and minimization of cost problems in communication network applications such as Ahuja R. & Magnanti T. [3] suggest.

Analyzing the studied cases: the conventional LSP and the distributed mechanism LSP, we can verify that in the D LSP the spare bandwidth is more optimized, for the fact of make the division of the LSP and to establish it for disjoint routes, this technique leaves less margin for the bandwidth than it is not used and when applying the technical optimization t even decreases more. It is necessary to highlight that the methods of Multicommodity Flow outlined in this research are newly using for assignment of flows and routing in Multipath networks, as well it is it MPLS.

IV. THE MODEL A. MCNF Formulations

Given a directed graph, G = (N, A) let N denote the set of all nodes in G, A the set of all arcs, and K the set of all commodities. For commodity k with origin sk and destination tk, c.. represents its per unit flow cost on arc

(i, j) and xi the flow on arc (i, j). Let b: be the supply/demand at node i, and 9 be the total demand units of commodity k. Let uij be the arc capacity on arc (i, j). Without loss of generality, we assume each unit of each commodity consumes one unit of capacity from each arc on which it flows.

This notation is formulated the MCNF is follow

k

k

Function Objective (Z) M~~ C ckxk

Constrains: 15kSK

mk = b k fork = 1, 2, ..., K (3) 05 $ SU: (i, j) E E and all k = 1, 2,.., K (4)

The group o f conditions that are described in the equation 2 reflects thc restriction of the total flow of all the commodities of the link (i, j) with relate to the total capacity o f thc link. The equation 3 is a set of K constrains of load balance where bk IS the available quantity o f the bandwidth for each of them commodities k, to model in each commodity [k = 1, 2... . . K) flow. HIS a representation of the incidence matrix [3], each row representing a node

We propose a network with N nodes (routers), the nodes (m, n ) are connected in m+n way with equivalent bandwidth AB(m, n) in (bit / sec). The number of link is equal to the number of (m, n) couples with AB (m, n) > 0 we designate L to this. We suppose that in the network for each n node it could be linked by all m nodes, in consequence, according to T. Ott[ 131 :

N I L 2 N(N-1) ( 5 )

To represent traffic demand we define a matrix [qi, ,)I, where 4i,,) represents quantity of traffic that enter in the network by the node i and leave by node j. We assume that AB,,, ,,) and d(i,j) are constant on time and all flows are fluid flows, that is, it don't have losses. The load of link (m, n) is X (m,n) and xo, ,)(,,,, ,,) represents flow of traffic of couple of nodes (i, j) in link (m, n). The flow is defined by selected traffic route and assigned traffic to this route, total flow of one route will be:

*(w) = C x ( i j g I n ) (6)

i,i

This equation interprets that the total flow is the sum of each flow that goes by the connection, that is to say, for each connection on pass information of several couples (i, j), and also in each connection we have the limitation:

(7)

The proposed model is based on the networks shown in the Fig. 1, where we want to optimize the spare bandwidth. To make it we can apply the equations of the MCNF, for the

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Distributed LSP system, for the conventional LSP system and to compare both results.

To obtain total bandwidth of a distributed LSP, we added the bandwidth with which we are working plus spare bandwidth. The total bandwidth (AB) comes given for.

A B i t a r ='':are +AB:abajo (8)

@pa?%? = ec* (9)

To obtain the DLSP spare bandwidth and work bandwidth we multiply the bandwidth for the total number of DLSP that exists in the network.

= C * ( m - 1 ) (10)

Where erepresents the number of DLSP from source node until destination node through m parallel routes and C* it is the equivalent bandwidth of a sub-LSP in which n flows are added. Substituting and regrouping terms, we have:

= em,* (1 1)

To optimize this equation we apply the theorem of the MCNT, equations 1 - 4, giving this result.

Under the restrictions of the equations 2 and 3, and assuming that all the direct routes are inside the distributed mechanismway.

mk = d k Para k =1,2, ..., K (14)

For the conventional LSP system, each LSP requires a quantity C of bandwidth, the work bandwidth required by the network will be c! . The quantity of spare bandwidth for LSP main backup is (Q+min(R,l))C and for the secondary backup it is QC, where Q and R are respectively the quotient and the residual, when dividing !among m, starting from this we can deduce that the total bandwidth requested by the network

AB,,I = (1 + (2Q + min (R,1 )) ) C

Min A @ ~ , ~ , x ~ Para ( i d E E (16)

(15)

Applying the equations of optimization just as it was made for the D-LSP mechanism

I&SK

Min ((l+(2Q+min(R,1)))C)*Xk (17) I&<K

In the equations 12 and 17 we can see the effects of the mechanisms of optimization applying the technical MCNF. Comparing both equations you can verify that there is a reduction of the bandwidth according to the parameters settled down in the network.

V. EVALUATION AND RESULTS

In this section, we provide a number of numerical examples that illustrate the flows 'allocations, and probe important aspects such as the effect the cost inside the network. Numerical results are obtained from simulations or exact analysis, when available.

The model is based on the network shown in the Fig. 2, which consists of 12 nodes, with 21 connections; the capacity of each connection is limited between 0 and 5 ? i, j. The ingress flows fl, f2 and D, will be respectively: 5, 2, 3 and the egress flows f4, f5 and f6 will be: -4, -3,-3; we assume that the cost of each connection = 1; (i, j). with di = S; we want to optimize the assignment of flow to one LSP and to one D-LSP. To get it we will apply MCNF equations, like we explain previously, and we will verify the results by solvers commercials of optimization CPLEX and LIPSOL [9].

The assignment of the flow will be evaluated in each connection of the network by the algorithms mentioned before for the LSP and for the DLSP, using MATLAB simulations and the free version of GAMS and both methods will be compared to know if the proposed model is optimum in the assignment of flow in LSP.

Table 1 contains results obtained of the evaluation of the CPLEX algorithm and the evaluation of the LIPSOL algorithm in the proposed model for a conventional LSP.

As can be observed from the data obtained by the CPLEX algorithm, connections that are underutilized exist because the flow that pass through it is zero, it cause that some connections are in their maximum capacity. The LIPSOL algorithm demonstrates a better distribution of the flows between connections.

F1

F6

F4 + F5

Fig. 2. MPLS network model to evaluate

B~ =dk Parak=1,2, ..., K

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TABLE 1: FLOW IN EACH CONNECTION THE MODEL PROPOSED EVALUATED WITH BOTH ALGORITHMS FOR LSP

CONVENTIONAL link CPLEX LIPSOL link CPLEX LIPSOL

XI4 0.00 2,4928 X59 5,OO 1,4317

XIS 5,00 2,5072 X68 0,OO 1,2862

X24 0,OO 0,573 X69 0.00 1,1795

XZS 2,00 0,5874 X710 0.00 2,02

X26 0.00 0.83% X711 0,OO 0,9911

X35 3.00 12739 X810 4,OO 1.98

X36 0,00 1,6261 X811 1.00 0,951

x47 0.00 1,5128 X812 0,OO 1,4466

X48 0,00 1,5529 X911 2.00 1,0578

x57 0.00 1,4984 X912 3,OO 1,5534

X58 5,00 1,5385

The distribution of the flows obtained in table 1, gives us a visualization of the distribution of the flows in the different connections of the proposed model evaluated by the CPLEX algorithm. It indicates that the connections X i s , Xs y X s 9 are totally busy, while exist 12 connections completely unused.

For the LIPSOL algorithm, the analysis for flows distribution obtained in the table 1 indicates that the distribution of the flow for the different connections established through to network, of the proposed model is more balanced, all the connections requirements are spread over the network and there are not underutilized connections, see figure 3.

The table 2 contains results obtained of the evaluation of the CPLEX algorithm and the evaluation of the LIPSOL algorithm in the model proposed for a D-LSP

TABLE 2: FLOW IN EACH CONNECTION THE MODEL PROPOSED EVALUATED WITH BOTH ALGORITHMS FOR

DISTRIBUTED LSP mk CPLEX UPSOL link CPLEX LIPSOL

X24 3.00 0,46273 X69 0,OO 0,9514

)a5 1.80 0,4568 X711 1,20 0,8235

X26 0,W 0,807 X8ll IS0 0,9254

X47 050 1,1128 X911 2 0,9654

X58 5.00 1.1385

The table 2 presents the distribution of the flows in each connection the model proposed evaluated with both algorithms for distributed LSP. For CPLEX algorithm the connections X58 is totally busy, while through 2 connections (X26 and &) are not used. For the LIPSOL algorithm, like in case of conventional LSP, the analysis for the distribution of the flows obtained in the table 2, indicates that the distribution of the flow for the different connections, of the proposed model is more balanced. Representing these data in the network, in the fig. 4, all the connections do not end up occupying the total of their capacity and there are not underutilized connections.

We observe in the table 3 that the flows of every link is minor for the case of the D-LSP that for the conventional LSP. The comparisons of the values obtained of the proposed model improve substantially the distribution of flows in every link, which go of a minimal difference of 0,0256 up to a maxi mum value of 0,2281

TABLE 3: COMPARISON THE FLOW THE MODEL PROPOSED FORD LSP AND LSP

Rk LSP D l S P link LSP D-LSP

X24 0,573 0,46273 X69 1,1795 0,9514

X25 0,5874 0,4568 X711 0,9911 0,8235

X26 0,8396 0,807 X811 0,951 0,9254

X47 1,5128 1,1128 X911 1,0578 0.9654

XS8 1.5385 1.1385

We can deduce that the evaluation camed out by the LIPSOL algorithm distributes in an uniform way the capacity of the connection among all the connections possible of the network, on the other hand CPLEX while optimizing some connections, it overload some others while others are in little use. The values obtained of the optimization and distribution of flows applying the theory of the MCNF to the proposed model is showed in the figure 5.

IECRLX n w d

L*W.

Fig. 3 Assignment ofthe fkw in the connections of the proposed model in P conventional LSP

Fig. 4 Assignment of the flow in the connect” ofthe proposed model 111

a D-TSP

123

Mb

Fig. 5 Comparison flow in the links of the proposed model in a D -LSP and conventional LSP

The table 4shows the results obtained for the function objective. It is necessary to highlight that this function is identical when evaluated both algorithms. It can be seen a substantial decrease, with a relationship 1:6 of the spare bandwidth when comparing the result of the objective function of a conventional LSP and D -UP.

TABLE 4. OBJECTIVE FUNCTION OF THE PROPOSED MODEL FOR A LSP AND A D-LSP

CPLEX LlPSOL LSP 3l 30 D l S P 5 5

VI CONCLUSIONS AND FUTURE WORKS

In this paper, an analytical mdel has been presented, that use of Multicommodity Network Flows to optimize the spare bandwidth of Label Switching Path (LSP) in MPLS networks, specifically, in a distributed mechanism of LSP. For the analysis of the optimization of proposed model, the equations were applied to a DLSP mechanism and to a conventional LSP verifying that really optimize the spare bandwidth in the DLSP. Since the flow to have a better distribution in comparison with the conventional LSP, this methodology were evaluated doing a comparison of the same method applying two different algorithms, the use of these techniques derive of having modeling by means of multicommodities. We showed the effect of optimization mechanism by some numeric examples. This study can be extended a new line of research among the conventional technique of optimization used in networks of multipath communication, specifically in MPLS networks. Future works will lead to use this analytic method of optimization in flows control, routing and bandwidth allocation in MPLS networks.

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