Online Traffic Engineering using Least InterferenceOptimization

A.B Bagula, M. Botha, and A.E KrzesinskiDepartment of Computer Science

University of Stellenbosch,7600 Stellenbosch,

South AfricaTel: +27 21 8084232 Fax: +27 21 8084416

Email: bagula@cs.sun.ac.za

Abstract— Flow-based routing algorithms have recently beenproposed where the online routing process uses a priori knowl-edge of the ingress-egress pairs and an estimation of the trafficprofile to reduce LSP rejection in MPLS networks. This paperpresents a new routing scheme referred to asLeast InterferenceOptimization (LIO) where the online routing process uses thecurrent bandwidth availability and the traffic flow distribution toachieve traffic engineering in IP networks. A Least InterferenceOptimization Algorithm (LIOA)is presented which balances thenumber and quantity of flows carried by a link to achieveefficient routing of MPLS bandwidth-guaranteed label-switchedpaths (LSPs). Preliminary simulation results show that LIOAoutperforms several widely known routing algorithms includ-ing the Minimum Hop Algorithm (MHA), Shortest Path First(SPF), Constraint Shortest Path First (CSPF) and MinimumInterference Routing Algorithm (MIRA) on several performanceparameters including (1) the LSP rejection and (2) the ease ofimplementation.

Index Terms— Traffic engineering, online routing, MHA, SPF,CSPF, MIRA, LIOA.

I. I NTRODUCTION

Traffic engineering (TE) is a network management tech-nique which improves the use and efficiency of a networkby explicitly steering the traffic through a routed or switchednetwork to achieve performance goals such as delay minimiza-tion, throughput maximization, etc.

The routing algorithms currently deployed in the Internetand the extensions proposed to adapt these algorithms fortraffic engineering include the widely deployed Shortest PathFirst (SPF) and Constraint Shortest Path First (CSPF).

SPF, the most widely used algorithm for intra-domainrouting, uses by default a static model where traffic is routedbased on link costs which are inversely proportional to the linkcapacity as proposed by Cisco. This static routing model maylead to unbalanced network loading by assigning bandwidthrequests to overloaded portions of a network while leavingother parts of the network under-utilized.

This work is supported by grant numbers 2047362 and 2677 from theSouth African National Research Foundation, Siemens Telecommunicationsand Telkom SA Limited. One of the authors acknowledges a bursary from theDepartment of Labour (DoL). Opinions expressed and conclusions arrived atare those of the author and are not necessarily to be attributed to the DoL.

CSPF was proposed as an algorithm which solves theproblem of load balancing of SPF by using link costs whichreflect the current resource availability. These include costswhich are inversely proportional to the residual link capacities.However both SPF and CSPF are poorly equipped for trafficengineering support under heavy load conditions [1].

Multiprotocol Label Switching (MPLS) enables the con-struction of a connection-oriented network over the connec-tionless IP network using bandwidth guaranteed tunnels calledLabel Switched Paths (LSPs). The Minimum InterferenceRouting Algorithm (MIRA) [2] was proposed in the contextof MPLS networks as a flow-based routing algorithm whichsets up LSPs using knowledge of the ingress-egress pairs toprevent the creation of bottlenecks for flows in a network, thusreducing the rejection rate of LSP requests between a specifiedsubset of ingress-egress pairs. However, MIRA causes addi-tional routing complexity which does not necessarily translateinto equivalent performance gains.

This paper presents a Least Interference Optimization Al-gorithm (LIOA) for setting up bandwidth-guaranteed tunnelsin MPLS networks. The main contributions of this paper are

• Cost-based route optimization.We present an onlinemethod for finding optimal routes using a link costmetric which reduces the interference among competingflows by reducing the numbers and magnitudes of theflows carried on the links. Our routing algorithm has thesame complexity as classical routing algorithms such asBreadth First Search and Dijkstra’s algorithm.

• Performance improvement.Our routing model is easyto implement (and thus easily deployed by ISPs) and of-fers substantial network performance improvement com-pared to the flow-based MIRA and the packet-basedMHA, SPF, and CSPF algorithms.

The remainder of this paper is organized as follows. Section IIpresents the least interference optimization model. Section IIIcontains the performance evaluation. Our conclusions arepresented in section IV.

II. T HE LEAST INTERFERENCEOPTIMIZATION MODEL

Consider a network represented by a directed acyclic graphG(N ,L) whereN is the set of nodes andL is the set of links.Let C` denote the capacity of link and letPi,e denote theset of feasible paths connecting the ingress-egress pair(i, e).Assume that a request to establish an LSP tunnel of bandwidthdi,e units between an ingress-egress pair(i, e) is received andthat future demands concerning LSP requests are not known.

The routing problem consists of finding the best feasiblepathp∗ ∈ Pi,e such that

0 < f` < C` (1)

di,e ≤ min`∈p∗

(C` − f`) (2)

Lp =∑

`∈p

L`(I`, f`) (3)

Lp∗ = minp∈Pi,e

Lp (4)

where L`(I`, f`) is the cost of link ` when carrying I`flows, f` is the total flows on link` and Lp is the cost ofpathp. Equations (1), (2), (3) and (4) express respectively thefeasibility of the flows, the feasibility of the path, the additivityof the path cost function and the optimality of the routingprocess.

A. The Minimum Interference Routing Algorithm

The objective of MIRA is to find a path between a pair ofnodes that blocks the least amount of available flow betweenall other source-destination nodes.

The link penalty function

MIRA uses the link penalty function expressing costs whichdetermine the relative importance of the ingress-egress pairs.In MIRA, computing the link costs reduces to finding the setof critical links for all ingress-egress pairs where the set ofcritical links belong to min-cut sets computed using the currentresidual link capacity. The link penalty function is

L` =∑

(s,d ):`∈Cs,d

1/θs,d (5)

whereθs,d is the max-flow between pair(s, d ) andCs,d is theset of critical links between the pairs(s, d ) as determined bythe max-flow algorithm.

The MIRA routing algorithm

Consider a demand fordi,e bandwidth units between twonodesi and e. MIRA uses the link penalty function definedin equation (5) above and executes seven steps in routing thisdemand

1) Compute the max-flow valuesθs,d for all (s, d ) pairsexcept(i, e).

2) Compute the set of critical links for all (s, d ) pairsexcept(i, e). A link is critical for a given ingress-egresspair if that link belongs to any min-cut for that ingress-egress pair.

3) Compute the link costsL`.4) Compute the reduced network. Eliminate all links

with residual capacities less thandi,e to form a reducednetwork whose links have sufficient spare capacity tocarry the demanddi,e.

5) Find the new least cost path.Use Dijkstra’s algorithmto find the new least cost pathp∗ from i to e in thereduced network using the link costsL`.

6) Route the traffic demand. Assign the traffic demanddi,e to the pathp∗.

7) Update the link flows. For each link` ∈ p∗ : f` :=f` + di,e.

B. The Least Interference Optimization Algorithm

The objective of LIOA is to find a path between a pair ofnodes that minimizes the number and the magnitude of theflows carried by the links on the path.

A power-based penalty function

The link penalty function is

L`(I`, f`) = Iα` /S1−α` (6)

where the link interferenceI` is the number of flows carriedon the link, the link slackS` = C` − f` whereC` is the linkcapacity,f` is the traffic carried by a link and0 ≤ α ≤ 1 isa parameter representing the trade-off between LIO and CSPFrouting.

The link penalty function (6) is minimized by minimizingthe the link interferenceI` and maximizing the link slackS`. By dispersing traffic flows over the network throughinterference minimization, this link cost will minimize thenumber of LSPs blocked under congestion. Note that

L`(I`, f`) =

1/(C` − f`) α = 0 CSPF routing1/C` α = f` = 0 SPF routingI` α = 1 LIO routing

When 0 < α < 1 the link penalty function yields a mix ofLIO and CSPF routing. The impact of the parameterα on thelink penalty function is discussed further in Section III.

A log-based penalty function

A link penalty function based on the logarithm of the power-based penalty function (6) is given by

L`(I`, f`) = α log(I` + 1) + (1− α) log(k/(C` − f`))

where0 < α ≤ 1, 1 ≤ k/(C` − f`) ≤ (I` + 1)α/(1−α) andk = max` C` avoids negative link costs.

The LIO routing algorithm

Consider a demand fordi,e bandwidth units between twonodesi ande. LIOA executes four steps in routing this demand

1) Compute the link costs

L(I`, f`) ={

∞ C` − f` ≤ di,eIα` /(C` − f`)1−α C` − f` > di,e.

2) Find the new least cost path.Apply Dijkstra’s algo-rithm to find the least cost pathp∗ ∈ Pi,e.

3) Route the traffic demand. Assign the traffic demanddi,e to pathp∗.

4) Update the link flows and interference.For each link` ∈ p∗ : I` := I` + 1; f` := f` + di,e.

The original MIRA algorithm [2] required as many max-flow computations as the number of ingress-egress pairs whereeach max-flow computation has O(N3) complexity for anetwork of N nodes. Improved versions of MIRA knownas S-MIRA and L-MIRA use approximations of the linkinterference [4]. These improvements result in a lower LSPrejection compared to the original MIRA algorithm but resultin additional complexity which can outweigh the advantagesoffered by the approximations.

The complexity of LIOA is determined by the shortestpath computation which has complexity O(N +L) or O(N2)depending on whether shortest paths are found using a BreadthFirst Search or Dijkstra’s algorithm.

III. PERFORMANCEEVALUATION

We conducted simulation experiments using a fictitiousrepresentation of a South African network illustrated in fig-ure 1 to compare the performance of five routing algorithms(1) Minimum Hop Algorithm (MHA) (2) Least InterferenceOptimization Algorithm (LIOA) (3) Shortest Path (SPF) (4)Constraint Shortest Path (CSPF) and (5) Minimum Interfer-ence Routing (MIRA). The test network has 23 nodes with88 unidirectional links. The dark thick links have capacity48 units and the light thin links have capacity 12 unitscorresponding respectively to OC-48 and OC-12 links. In oursimulation experiments, each node is used as an ingress andegress node, leading to 506 ingress-egress pairs.

Beaufort West20

De Aar 19

Upington18 Kimberley17Bloemfontein16

Klerksdorp 15

Mafikeng14Johannesburg13

Pretoria12

Pietersburg/Polokwane11

Messina

10

Nelspruit 9

Kroonstad 8

Pietermaritzburg 7Durban 6

Bisho 5

East London 4

Port Elizabeth 3Mosselbaai 2Cape Town 1

Saldanha21

Springbok22

Richards Bay23

Fig. 1. A South African network

The relevant performance metrics are LSP rejection undercongestion (heavy load conditions) and the quality of the pathsfound by the different algorithms. The first parameter waschosen to compare how algorithms such as LIOA, Minimum

Hop Algorithm (MHA), Shortest Path first (SPF) and Con-straint Shortest Path First (CSPF) compare versus the MIRAalgorithm. The second metric reveals the impact of bandwidthallocation on future admission control. LSP rejection refersto LSP requests which were not accepted due to randomfluctuation of the bandwidth availability.

A. LSP rejection

We conducted simulation experiments to analyze (1) thebehavior of the different algorithms (2) the impact of theLIOA calibration parameterα on the network performanceand (3) the performance difference resulting from using themultiplicative and additive versions of the LIOA cost function.

Different algorithms

We simulated two LSP setup modes: static and dynamic. Inthe static mode, LSP requests were long-lived while the dy-namic mode assumed that LSP requests are offered randomly,are kept for a random time period and finally torn down. Eachsimulation experiment consists of 20 trials.

In the static case, the link capacities were scaled by 30. 4500LSP setups each requesting between 1 to 6 units of bandwidthwere simulated.

In the dynamic case, the link capacities were scaled by 30.3500 long-lived LSPs were first loaded. Thereafter 2000 moreshort-lived LSP requests were simulated. The LSP requestswere for 1-6 units of bandwidth.

Figure 2 compares the performance achieved by MIRA,SPF, MHA, CSPF and LIOA in dynamic mode. Figure 2reveals that LIOA rejects fewer LSP requests compared to thethree other algorithms.

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Fig. 2. Network optimality: dynamic mode

The results illustrated in figure 3 are found when MIRA,SPF, MHA, CSPF and LIOA are compared in static mode.These results reveal that LIOA rejects fewer requests comparedto the three other algorithms.

The calibration parameterα

We conducted simulation experiments in dynamic mode toevaluate the impact ofα as a parameter expressing the trade-off between LIO and CSPF routing. Figure 4 reveals the lowestLSP rejection is obtained forα = 0.5, a value balancing LIOand CSPF routing.

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PSfrag replacements

α = 0.2α = 0.5

α = 0.8

Fig. 4. The calibration parameterα

Power-based versus log-based metrics

Figure 5 compares the two cost metrics (power- and log-based) using different values of theα parameter for the twometrics in dynamic mode. The figure shows that the two costmetrics achieve approximately the same performance whenα = 0.5 for the power-based metric andα = 0.2 for the log-based metric. This reveals for the test network being simulated,our routing scheme is relatively insensitive to the compositionrule of the link penalty function: an additive composition ruleperforms as well as a multiplicative composition rule.

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Fig. 5. Power- versus log-based metrics

B. The quality of the paths

We conducted simulation experiments in dynamic mode tocompare the quality of the LSP pathsets found by LIOA andMIRA. A trial of 5500 events was used for each experiment.

Let PL andPM denote the sets of paths found by LIOAand MIRA respectively. The pie chart in Figure 6 presentsa graphical view of the correlation between the pathsetsPLandPM . The slice labelledPL ∩ PM (strong) represents theLSPs common to bothPL andPM whose LIOA and MIRAflow values differ by less than 5%. The slice labelledPL ∩PM (weak) represents the LSPs common to bothPL andPMwhose LIOA and MIRA flow values differ by more than 5%.The slice labelledPL \ PM represents the LSPs discoveredonly by LIOA and the slice labelledPM \ PL represents theLSPs discovered only by MIRA.

With reference to Figure 6 we see that 55% of the paths inLIOA and MIRA are strongly correlated (LL∩LM (strong)),29% are weakly correlated (LL∩LM (weak)), 7% of the LSPswere found only by MIRA (LM \ LL), and 9% of the LSPswere found only by LIOA (LL \ LM ).

PSfrag replacements

LL ∩ LM(strong)

LL ∩ LM(weak)

LL\LM

LM\LL

Fig. 6. LSP correlation between MIRA and LIOA

In general we observe that LIOA achieves lower rejectioncompared to MIRA. This relative efficiency results from theset of weakly correlated LSPs where flows are more efficientlydistributed by LIOA.

IV. CONCLUSION

This paper presents an efficient routing algorithm usingthe least interference optimization (LIO) concept to achieveonline traffic engineering in IP networks. A new cost metricwhich balances the number and intensity of flows offered toa network is presented. We show that this metric achievesnetwork optimization under heavy traffic load profiles. Thiscost metric may be implemented using either a power versionbased on a multiplicative composition rule or a logarithmicversion based on an additive composition rule with the sameefficiency.

For the network model under consideration, simulation re-sults reveal that the Least Interference Optimization Algorithm(LIOA) requiring neither a priori knowledge of the ingress-egress pair nor the estimation of the traffic profile outperformsthe widely known Minimum Hop Algorithm (MHA), Shortest

Path First (SPF), Constraint Shortest Path First (CSPF) andMinimum Interference Routing Algorithm (MIRA) algorithmson several performance aspects including the simplicity of theimplementation and the optimization of the network.

REFERENCES

[1] I.W. Widjaja, I. Saniee, A. Elwalid, D. Mitra, “Online TrafficEngineering with Design-Based Routing”,15th ITC Specialist Seminaron Internet Traffic Engineering and Traffic Management, Wurzburg,Germany, July 2002.

[2] K. Kar, M. Kodialam, T.V. Lakshman. “Minimum Interference Routingwith Application to MPLS Traffic Engineering”,Proc. IEEEINFOCOM, Tel-Aviv, Israel, March 2000.

[3] J. Stevens. “Spatial Reuse through Dynamic Power and RoutingControl in Common-Channel Random-Access Packet RadioNetworks”, SURAN Program Technical Note (SRNTN) 59, Richardson,TX:Rockwell Inc., August 1988. Available from Defense TechnicalInformation Center (DTIC).

[4] M. Kodialam, T. V. Lakshman. “MPLS Traffic Engineering UsingEnhanced Minimum Interference Routing: An Approach Based OnLexicographic Max-Flow”,Proceedings of Eighth InternationalWorkshop on Quality of Service (IWQoS), Pittsburgh, USA, June 2000.

[5] S. Suri, M. Waldvogel, P. Warkhede “Profile-based Routing: A newFramework for MPLS Traffic Engineering”,Quality of Future InternetServices, Lecture Notes in Computer Science, Vol 2156, September2001.

Antoine Bigomokero Bagula obtained the MEng in Computer Engineeringfrom the Universite Catholique de Louvain in Belgium and the MSc inComputer Science from the University of Stellenbosch. He is currently alecturer and a PhD student in the Department of Computer Science at theUniversity of Stellenbosch.