Boosting performance for software defined networks from traffic engineering perspective
BBoosting Performance for Software DefinedNetworks from Traffic Engineering Perspective
Mohammed I. Salman
Department of Computer Science and EngineeringWright State University
Dayton, [email protected]
Bin Wang
Department of Computer Science and EngineeringWright State University
Dayton, [email protected]
Abstract —Paths selection algorithms and rate adaptation ob-jective functions are usually studied separately. In contrast, thispaper evaluates some traffic engineering (TE) systems for soft-ware defined networking obtained by combining path selectiontechniques with average delay and load balancing, the two mostpopular TE objective functions. Based on TE simulation results,the best TE system suitable for software defined networks is asystem where the paths are calculated using an oblivious routingmodel and its adaptation rate calculated using an average delayobjective function. Thus, we propose the RACKE+AD systemcombining path sets computed using R¨acke’s oblivious routingand a traffic splitting objective function using average delay. Thismodel outperforms current state-of-the-art models, maximizesthroughput, achieves better network resource utilization, andminimizes delay. The proposed system outperformed SMOREand SWAN by 4.2% and 9.6% respectively, achieving 27% betterutilization and delivering 34% more traffic with 50% less latencycompared with both systems on a G ´EANT network.
Index Terms —Traffic engineering, routing schemes, softwaredefined networking, oblivious routing, simulation, optimization
I. I
NTRODUCTION
Centralized traffic engineering (TE) has gained much at-tention following new software defined networking (SDN)developments. Large technology companies such as Microsoft[1] and Google [2] have shifted to this technology over thelast few years.Some previous studies have deviated from the standard SDNcentralization feature to improve scalability and fast adaptationto changing traffic conditions, e.g. Contra [3], HULA [4],MP-HULA [5], and DASH [6] balance load traffic entirely inthe data plane to reduce controller overhead. These solutionsprovide scalable systems with short response time, but degradeperformance, with resulting distributed solutions far fromoptimal [7].Performance can also be affected by the traffic splittingobjective function. Some TE systems balance load over somepaths by minimizing maximum link utilization (MLU) [1, 8].However, minimizing MLU does balance load and enhanceperformance for low traffic and degrades performance signifi-cantly during peak hours since it requires additional constraintsto satisfy all the demands [9]. Other TE systems use meta-heuristic [10] or heuristic [11] solutions that can provide fast routing convergence, but the solutions are sub-optimal sincethey may be only local optima. Prior to SDN, several studiesconsidered different objectives [12, 13]. To our knowledge,performance impacts from these objectives and path selectionstrategies have not been properly considered for SDN. Any TEsystem has two key ingredients: which set of paths is used forforwarding traffic, and how to split traffic over these selectedpaths. To the best of our knowledge, no previous study hasfocused on boosting performance by optimizing combinationsof these key ingredients, in contrast, previous work has focusedon either path selection algorithms or traffic-splitting objectivefunctions, but not both.Many studies suggest that a set of shortest paths should beused in TE systems to achieve reliable performance [1, 14,15]. Unfortunately, choosing shortest paths may exacerbatecongestion for topologies with high link capacity hetero-geneity. Oblivious routing strategies offer network demandindependent routing schemes, i.e., the routing scheme that isoblivious to the demands [16, 17, 18, 19]. Although obliviousrouting schemes can be devised with guaranteed congestionratio, the resulting routing scheme is static and unable to adaptto changing traffic conditions. Several studies have shownthat route allocations calculated using an oblivious routingmodel achieve comparable quality to adaptive solutions [8,20]. Selected paths from this approach are capacity-aware anddiverse, which improves not only system performance, but alsorobustness.The capacity aware concept not only applies to path se-lection only, but also to sending rates. For example, theKleinrock delay objective function [21] minimizes congestionby increasing highly utilized link costs, thus, avoiding highlycongested links. The widely used load balancing (LB) objec-tive function [1, 8, 22, 23, 24] minimizes utilization (relativeload) for all links, and can also be considered a capacity-awareobjective function. The main goal for demand aware objectivesis to mitigate proportional increases for all demands [12] byminimizing MLU. However, all source destination (SD) pairdemands do not increase at the same rate, and it is not trivialto predict future demands. Thus, sending rates should not only We use “Oblivious routing” and “R¨acke’s oblivious routing” interchange-ably a r X i v : . [ c s . N I] J a n e capacity aware, but also demand aware.Therefore, we constructed a new simulator, and motivatedby SMORE [8] and AD objective functions [23, 24, 25] wepropose RACKE+AD, a centralized, adaptive, semi-oblivious,demand aware, near optimal TE system with static routesallocated using R¨acke’s oblivious routing model [16, 18, 19]and dynamic rate adaptation by approximating the averagedelay (AD) objective function. RACKE+AD outperformedSWAN [1] and SMORE [8] for throughput, congestion, andlatency evaluated on G ´EANT and ATT topologies. Contributions.
Critical contributions from the current paperare as follows:1) We present a routing scheme that outperforms currentstate-of-the-art techniques.2) We introduce RACKE+AD, a new efficient TE simulatorthat can test many routing schemes simultaneously.RACKE+AD is optimized for testing different routeselection algorithm and objective function combinationsand can be easily extended to test future TE systems.3) We demonstrate that a TE system with static routes andadaptive traffic splitting offers many benefits, includingperformance, throughput, and resource utilization.II. S
YSTEM M ODEL
All TE systems comprise two phases: identifying a set ofpaths to be used to forward traffic (path selection), and identi-fying splitting ratios to distribute traffic over these paths (rateadaptation). Generally, routes selected in the path selectionphase are static, i.e., selected once and only recalculated whenthe network topology changes. Path selection is usually offlinebecause updating end-to-end paths may take hundreds ofseconds for wide area networks. In contrast, the rate adaptationphase must update path weights regularly due to frequentdemand changes. However, the time required to update pathweights is considerably less than the time required to updatepaths in the network. Among many techniques of paths se-lection algorithms and rate adaptation objective functions, theaim of this research is to find the best combination of thesephases to enhance network performance.
Path and Rate Adaptation Properties:
Intuitively, inde-pendently chosen paths may not provide better performancethan dependently chosen paths. However, SMORE showedthat path selection has considerable effect on performance [8].Selected paths should be low stretch to minimize latency andnaturally load balanced to provide better performance. Lowstretch motivated us to compare SMORE performance andlatency against k-shortest paths (KSP) approaches. SMOREis naturally load balanced since route computation in R¨acke’soblivious routing model is not independent and incorporatessome randomness, i.e., the obtained route set may not be thesame if we were to run the model again. Thus, we expectdifferent performance for each run. On the other hand, KSPselected paths are not capacity aware, whereas R¨acke’s modelselected paths are capacity-aware due to the natural loadbalancing. Performance can be further boosted if we use thesame concept for splitting traffic over the selected paths, and f ( y ) Piecewise Linear Approximationy/(c- y)
Fig. 1: Piecewise linear approximation of the delay function.we expect best performance may be achieved using phases,path selection, and rate adaptation.
A. Rate Adaptation Models1) Load Balance:
The load balance (LB) objective is alsoknown as minimizing MLU, Wozencraft objective [26], orminimizing congestion, where LB minimizes the load on themost congested link. Thus, the LB problem can be expressedas [24] min F ( x ) = r (1)s.t. (cid:88) p ∈ P d x dp = h d , d ∈ D (1a) (cid:88) d ∈ D (cid:88) p ∈ P d δ dpl x dp ≤ c l r, l ∈ L (1b) where: x dp is the flow on path p for demand d ; h d is thevolume for demand d ; c l is the capacity for link l ; P d is thenumber of candidate paths for demand d ; δ dpl = 0, 1 is a link-path indicator, with δ dpl = 1 if path p for demand d uses link l , and 0 otherwise.Two constraints are applied. The demand constraint (1a)ensures that all demands are satisfied over some paths. Thecapacity constraint (1b) ensures that load does not exceedthe link capacity where r ≤ , after solving (1). The linearprogram formulation above is the final form of the problemwhereas the original problem is non-linear. The reader isreferred to Chapter 4 of [24] for details on how the problemcan be converted to the current form.
2) Average Delay:
For this objective function, delay forany network link can be modeled as y/ ( c − y ) , as shown in(Figure 1, solid line). Similar to the LB objective, the originalAD problem is non-linear and cannot be formulated directlyas a linear program. Thus, the delay function is a piecewiselinear approximation (2) (Figure 1, dotted line) ( z ) = (3 / z for ≤ z < / / z − for / ≤ z < / z − for / ≤ z < / z − for / ≤ z < / z − for / ≤ z < / z − for z ≥ / (2) The linear program for this AD problem is min F = L (cid:88) l =1 r l c l (3)s.t. P d (cid:88) p =1 x dp = h d , d = 1 , , ..., D (3a) D (cid:88) d =1 P d (cid:88) p =1 δ dpl x dp = y l , l = 1 , , ..., L (3b) r l ≥ y l , l = 1 , , ..., L (3c) r l ≥ y l − c l , l = 1 , , ..., L (3d) r l ≥ y l − c l , l = 1 , , ..., L (3e) r l ≥ y l − c l , l = 1 , , ..., L (3f) r l ≥ y l − c l , l = 1 , , ..., L (3g) r l ≥ y l − c l , l = 1 , , ..., L (3h) x dp ≥ , p = 1 , , ..., P k , d = 1 , , ..., D (3i) y l ≥ , l = 1 , , ..., L (3j) which is considerably more accurate [24] than the Fortz etal. [27] approximation. B. Paths Selection Algorithms1) R¨acke’s oblivious routing model:
R¨acke’s oblivious rout-ing model iteratively computes a distribution over randomizedrouting trees using an approximation algorithm. Link weightsare adjusted for each iteration based on how much the linkhas been utilized in previous routing tree sets. A routing treehas leaves corresponding to nodes in the original topology.Thus, a path can be obtained between nodes u and v in theoriginal graph by finding corresponding leaves for u and v inthe routing tree.However, paths for R¨acke’s oblivious routing model arecomputed without considering demands, thus, they do notoverfit to a specific scenario [8]. Similar to SMORE, we alsoadopt the simple mechanism used to impose the number ofpaths for each SD node pair. We use 4 paths for each SD pairof nodes that have the highest weights.
2) K-shortest paths:
The proposed KSP algorithm is basedon Yen’s algorithm, the most commonly used algorithm forTE. KSP is a generalization of the shortest path routingproblem. The algorithm returns loopless k shortest pathsordered from shortest to longest. We use four paths for eachSD pair, i.e., k = 4 . III. S IMULATOR F RAMEWORK
We built a simulator to model and test different TE sce-narios, with particular attention to efficiency, simplicity, andextendibility. Although many network simulators have beenproposed previously [28, 29, 30, 31], they are generally notoptimized for modeling TE approaches and/or do not provideease of use or extendibility. The proposed simulator was builtin Python and can test many TE models in parallel whilerecording statistics in the background. We use Gurobi opti-mization [32] to solve the linear programming problems, byintegrating it with Python. The framework, data and R¨acke’soblivious routing model implementation are all available on-line .Simulator inputs, (e.g. topology, demands, path selectionalgorithms, objective functions, etc.) are all specified in aPython script or configuration file. The simulation producesvisualized throughput graphs for each TE system. The graphsare updated periodically as throughput data becomes available.Three time-series metrics for each TE system are recorded inthe background during simulation: overall throughput, con-gestion per link, and latency per path. Topology and trafficmatrices are provided as input files, where the user providesthe location to these files in the configuration file. If thelocations are unavailable, random topology and traffic matriceswill be generated according to provided parameters, includingnumber of nodes N , number of links L , and traffic distributionmatrix. IV. S IMULATION S ETUP
A. Evaluating Routing Scheme Quality
We evaluate TE systems based on congestion, throughput,and delay. Congestion reflects how a TE system utilizesnetwork resources, and we mostly care about congestionwhen traffic demand exceeds link capacity. Thus, avoidingcongestion can be considered as preserving as much residualcapacity as possible, which is important for unexpected trafficsurges that could cause bottlenecks. Congestion has negativeimpact on delay due to queuing. We measure path delayby summing queuing delay for each link along that path, l/ ( c − l ) , where l is the absolute link load and c is the linkcapacity. Throughput is the proportion of total demand that issuccessfully delivered to the destinations. B. Simulation Settings
Path selection algorithms.
We use three approaches for pathselection (i) paths selected using R¨acke’s oblivious routingmodel, (ii) paths selected using KSP algorithm, and (iii) selectall available simple paths. We refer to these RACKE, KSP, andOPTIMAL, respectively.
Rate adaptation objective functions.
We use two objectivefunctions for rate adaptation: AD and LB. We refer to a routingscheme with paths selected using KSP and rate adaptationusing LB objective function as KSP+LB. Similarly, modelswhere the routing scheme selects all available paths and rate https://github.com/MohammedSalman/TE-SIMULATOR daptation uses AD is referred to as OPTIMAL (AD), etc. TheRACKE+LB routing scheme parallels that used in SMORE[8], and KSP+LB is an approximation to the SWAN scheme[1]. Table I shows the TE systems used in our experiment.TABLE I: Implemented TE algorithms TE System DescriptionKSP+LB k-Shortest
Paths (KSP) for paths, LB for weightsKSP+AD k-Shortest
Paths (KSP) for paths, AD for weightsRACKE+LB R¨acke’s oblivious routing for paths, LB for weightsRACKE+AD R¨acke’s oblivious routing for paths, AD for weightsOPTIMAL(LB) a All paths, LB for weightsOPTIMAL(AD) b All paths, AD for weights a The best load balance is achieved with this system. b The best average delay is achieved with this system.
Path budget.
Similar to SMORE and SWAN, and to ensurea fair comparison, we use 4 paths to evaluate any routingscheme. If the R¨acke’s oblivious routing model produces arouting scheme with SD pairs that has more than 4 paths, weuse the 4 highest weight paths, similar to SMORE.
Traffic matrix generation.
We use the gravity model togenerate the traffic matrix (TM) [8, 17]. The gravity modelapproximates real-world TMs for a production network [33].TMs are deduced based on incoming/outgoing flow for eachforwarding device. Since that information is not available, weuse a capacity based heuristic rather than incoming/outgoingflow information [17].
Topologies.
We evaluate many TE systems for ATT andG ´EANT production topologies. The G ´EANT network (Euro-pean academic network) contains 38 nodes and 104 directedlinks with heterogeneous capacities. Fig. 2 shows the linkcapacity distribution for this network. Different TE systemsmay behave differently depending on link capacity distribu-tions. Shortest-path TE systems may introduce a bottleneck inheterogeneous link capacities as many SD pairs compete forthe same resources. li n k s Fig. 2: Capacity distribution for G ´EANT network (log scaled).V. R
ESULTS
We evaluated multiple routing schemes using criteria fo-cused on: • how each TE system performs regarding throughput andcongestion, and • SMORE and KSP TE system impacts on latency. A. Throughput
Performance for many TE systems were evaluated onG ´EANT and ATT networks with path budget = 4 for a faircomparison with SMORE. Figures 3a and 3b show through-put and corresponding throughput distribution for G ´EANT net-work, respectively. Rate adaptation using AD objective func-tion significantly increases throughput, achieving 4.2% and9.6% improvement over SMORE and KSP+LB, respectively,which confirms path selection effectiveness using R¨acke’soblivious routing algorithm. T h r o u g h p u t ( % ) Performance
OPTIMAL (LB)OPTIMAL (AD)RAEKE+LB (SMORE)RAEKE+ADKSP+LB (SWAN)KSP+AD (a) Throughput C D F ( f r a c t i o n o f T M s OPTIMAL (LB)OPTIMAL (AD)RAEKE+LB (SMORE)RAEKE+ADKSP+LB (SWAN)KSP+AD (b) Throughput distribution
Fig. 3: Throughput for G ´EANT topologySimilar to G ´EANT topology, a higher throughput wasachieved for ATT topology using the AD adaptation rateobjective function. KSP had slightly better throughput thanR¨acke’s oblivious routing path selection algorithm (Figs. 4aand 4b).R¨acke’s oblivious routing model with LB adaptation rateperformed 1.14% better than KSP on average. This may
10 20 30 40 50 60 70Time82.585.087.590.092.595.097.5 T h r o u g h p u t ( % ) Performance
OPTIMAL (LB)OPTIMAL (AD)RAEKE+LB (SMORE)RAEKE+ADKSP+LB (SWAN)KSP+AD (a) Throughput
82 84 86 88 90 92 94 96 98Throughput(%)0.00.20.40.60.81.0 C D F ( f r a c t i o n o f T M s OPTIMAL (LB)OPTIMAL (AD)RAEKE+LB (SMORE)RAEKE+ADKSP+LB (SWAN)KSP+AD (b) Throughput distribution
Fig. 4: Throughput on ATT topologyconfirm that AD favors shortest paths when all links have thesame capacity. However, there is no guarantee that SMOREwill always outperform (or underperform) KSP under thesame conditions due to oblivious routing scheme randomness.Figure 5 shows throughput distributions for KSP+AD witha different R¨acke’s oblivious routing TE systems obtained byrepeatedly calculating the oblivious routing scheme. Outputfrom KSP+AD remained constant since KSP+AD is determin-istic. R¨acke’s oblivious routing scheme outperformed KSP for5 runs and underperformed for 1 run. Thus, there is a worstcase scenario where KSP may perform better than SMORE.The best run had 2.29% higher throughput than KSP+AD.Therefore, a network operator may choose to run R¨acke’sscheme several times and choose the best outcome.
B. Congestion
Figures 6a and 6b show network congestion for G ´EANTtopology using AD and LB. The AD objective function sched- uled link loading differently from LB. Figure 6a shows themaximum congested link over time. All TE systems scheduledlink loads that exceeded specific link capacities since wedeliberately fed the system with high volume demands toinvestigate TE system performance well under stressed condi-tions. AD (Fig. 6a) seems to have higher MLU whereas Fig.6b) shows that the AD objective utilizes link loads much betterthan LB. TE systems with LB caused a bottleneck for morethan 40% of links whereas TE systems with AD objectivecaused a bottleneck for 13% of links. This low congestionratio for AD is the main reason for the higher throughput(Fig. 3).The LB objective always distributes traffic perfectly acrossthe available routes, in the sense that all paths are used and allnodes send and receive traffic with quite similar link utilization(relative load) for all links. Thus, all links might be over-utilized under high demands when the system is not feasible.On the other hand, AD deals more with delay and throughput,but generates worse MLU than from LB. However, MLU isnot a true network metric as it only considers congestion fora single link rather than the whole network. Thus, congestiondistribution seems like a more reasonable metric, and we onlymeasured MLU to make that point since it is heavily used inthe literature.Thus, two factors contributed to better throughput and lesscongestion: routes selected using R¨acke’s oblivious routingalgorithm, and using the AD objective. Similar results wereobtained for ATT topology (Figs. 7a and 7b).
C. Latency
Figure 8 shows link delay distribution with respect totraffic delivered within that delay for G ´EANT and ATTtopologies. Latency for each path was computed by summingthe link delays to obtain the path delay. Including AD selectionoutperforms LB, achieving significantly lower latency. Figure
90 92 94 96 98Throughput(%)0.00.20.40.60.81.0 C D F ( f r a c t i o n o f T M s KSP+ADRAEKE+AD (run-1)RAEKE+AD (run-2)RAEKE+AD (run-3)RAEKE+AD (run-4)RAEKE+AD (run-5)RAEKE+AD (run-6)
Fig. 5: Throughput distribution for ATT topology for 1 KSPand 6 R¨acke schemes
10 20 30 40 50 60 70Time1.21.41.61.82.02.22.42.62.8 M a x C o n g e s t i o n Performance
OPTIMAL (LB)OPTIMAL (AD)RAEKE+LB (SMORE)RAEKE+ADKSP+LB (SWAN)KSP+AD (a) Max link congestion, G ´EANT topology C D F ( f r a c t i o n o f e dg e s ) OPTIMAL (LB)OPTIMAL (AD)RAEKE+LB (SMORE)RAEKE+ADKSP+LB (SWAN)KSP+AD (b) CDF of link congestions, G ´EANT topology
Fig. 6: Max link congestion and links’ congestion distributionon G ´EANT topology8a shows that LB and AD TE systems different considerablyfor G ´EANT topology. TE systems with AD objective initiallydeliver approximately 34% traffic more than those with LBobjective, which also has latency 50% lower latency thanTE systems with AD. RACKE+AD routing delivered slightlymore traffic than OPTIMAL(AD) since OPTIMAL(AD) goalis to reduce total delay rather than throughput. Figure 8bshows that routing schemes with AD also delivered moretraffic than those with LB for ATT topology. However, thegap between the two groups is somewhat smaller than forG ´EANT topologies (Fig. 8(a)) because ATT network linksare heterogeneous, hence smaller performance differencesbetween individual links. M a x C o n g e s t i o n Performance
OPTIMAL (LB)OPTIMAL (AD)RAEKE+LB (SMORE)RAEKE+ADKSP+LB (SWAN)KSP+AD (a) Max link congestion, ATT topology C D F ( f r a c t i o n o f e dg e s ) OPTIMAL (LB)OPTIMAL (AD)RAEKE+LB (SMORE)RAEKE+ADKSP+LB (SWAN)KSP+AD (b) CDF of link congestions, ATT topology
Fig. 7: Max link congestion and links’ congestion distributionon ATT topology VI. R
ELATED W ORK
The classic approach for TE problems is to solve them as alinear program (LP) [24, 26], referred to as a multi-commodityflow problem, where the objective function usually minimizesMLU. The approximation of AD objective function is not aswidely as used. However, this classical approach does notconsider decoupling TE system phases because all availablepaths are provided as inputs. Choosing all available paths hastwo limitations: more paths means more decision variables inthe LP, and forwarding devices, such routers and switches,have limited TCAM memory, hence fewer number paths isalways preferable to keep the routing table as small as possible.The conventional approach adjusts link weights to find agood routing scheme that can increase throughput or minimizecongestion in the network [27, 34]. However, OSPF cannever reach optimal because it uses the equal cost multi-path
200 400 600 800 1000 1200Delay (ms)0.00.10.20.30.40.50.60.70.8 C D F F r a c t i o n o f t r a ff i c d e li v e r e d OPTIMAL (AD)OPTIMAL (LB)KSP+ADKSP+LB (SWAN)RAEKE+ADRAEKE+LB (SMORE) (a) G ´EANT topology. C D F F r a c t i o n o f t r a ff i c d e li v e r e d OPTIMAL (AD)OPTIMAL (LB)KSP+ADKSP+LB (SWAN)RAEKE+ADRAEKE+LB (SMORE) (b) ATT topology.
Fig. 8: Latency distributionapproach that splits traffic evenly among available shortestpaths without rate adaptation. Furthermore, optimizing linkweights is an NP-hard problem.Potentially centralized TE approaches recently became vi-able due to software-defined networking (SDN) developments,that clearly decouple the two TE phases. SWAN [1] distributestraffic over a set of k-shortest paths using an LP that reserves asmall amount of scratch capacity on links to apply updates ina congestion-free manner. SOL [22] uses a greedy approachto randomly select paths with the promise that this randomselection will help load balancing traffic across the network.This latter approach is somewhat similar to valiant loadbalancing [35] but can lead to unnecessarily long paths andconsequently increased latency.Oblivious routing [16, 17, 18] has also been proposed tofind a routing scheme that performs well under all possibledemands. The R¨acke oblivious routing model [16] guarantees a congestion rate that is never worse than O (log n ) of optimal,where n is the number of nodes in the graph. However, despitethe guaranteed congestion ratio, this approach cannot outper-form systems like SWAN since it considers all possible trafficdemands. On the other hand, the oblivious routing approachhas inspired several studies (including the current study) toinvestigate a careful path selection approach. SMORE [8] wasinspired by R¨acke’s oblivious routing model to carefully selectpaths that increase TE system performance and robustness.Paths selected this way have low stretch, which is importantto decrease latency, and are capacity aware, which is importantfor load balancing. The proposed approach in this paper sug-gests that careful route selection is not sufficient performanceenhancement to reach the expected maximum performance.However, a different objective function from the commonlyemployed LB could further enhance performance. Hence wewere inspired to compare LB and AD objective functionperformance, and subsequently propose the RACKE+AD TEsystem using oblivious routing for path selection with AD toachieve better link delay and network performance.VII. D ISCUSSION
This section discusses the reason behind the high gapin performance and delay between LB and AD objectivefunctions and one potential limitation for this work. The LBobjective function tends to make the relative load the same forall links when all SD pairs are sending and receiving traffic.This can enhance performance to some extent but causesbottlenecks between some SD pairs under stressed conditionsand unpredicted demands, with consequential congestion loss.On the other hand, the AD objective function increases thecost for highly utilized links to avoid utilizing them if otherless heavily utilized links are available. Thus, AD is moredemand aware than LB and hence offers better contribution toperformance. However, solving LP for LB is much faster thanfor AD, particularly for larger networks due to the increasednumber of constraints and decision variables.VIII. C
ONCLUSION
Although a few TE systems have been optimized previouslyusing different path selection algorithms, few studies have in-vestigates performance enhancement by testing many objectivefunctions for splitting traffic. These phases have only beenstudied in isolation previously, with no prior studies testingall possible combinations to find a routing scheme with thebest available performance.This paper proposed RACKE+AD TE system and validatedits performance advantages by testing many possible combi-nations. RACKE+AD selects routes using R¨acke’s obliviousrouting model and the average delay objective function. Al-though the intuitive AD goal is to minimize network delay, italso provides surprisingly better throughput than minimizingMLU (commonly known as load balancing).Simulations confirmed the proposed RACKE+AD systemoutperformed state-of-the-art routing TE systems in terms ofthroughput, congestion, and delay. We discussed a caveathen running R¨acke’s oblivious routing model, where k-shortest paths may give better performance due to randomnessin oblivious routing, and also discussed the importance ofexcluding the maximum congestion metric when evaluatingTE systems, particularly system that split traffic not based onthe LB objective function.A
CKNOWLEDGMENT
We would like to thank the anonymous reviewers for theirhelpful comments and suggestions. We also would like tothank Praveen Kumar from Cornell University for addressingall the questions we had regarding the SMORE traffic engi-neering system. R
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