Virtual Network Embedding for Switch-CentricData Center Networks

Ana Laura Gonzalez RiosKamila Bekshentayeva

Maheeppartap SinghSimon Fraser University

Vancouver, British Columbia, Canada{anag, kdagilov, msa206}@sfu.ca

Soroush HaeriHuawei Munich Research Center

Huawei TechnologiesMunich, Germany

soroush.haeri@huawei.com

Ljiljana TrajkovicSimon Fraser University

Vancouver, British Columbia, Canadaljilja@sfu.ca

Abstract—Advances in software defined and data center net-works have enabled network virtualization. Virtual networkembedding increases resources utilization and reduces cost ofnetwork deployment. Its performance depends on embeddingalgorithms and data center network topologies. In this paper, weevaluate performance of virtual network embedding algorithmsbased on acceptance ratio, revenue to cost ratio, and node andlink utilizations by simulating virtual network embeddings onSpine-Leaf, Three-Tier, and Collapsed Core data center networktopologies.

Index Terms—Networks virtualization, virtual network embed-ding, software defined networks

I. INTRODUCTION

Data center networks (DCNs) are essential infrastructure forprovisioning diverse Internet services and applications [33].Software defined networks and network function virtualiza-tion technologies offer low implementation cost and optimizeDCNs resource utilization and energy efficiency [8]. Networkvirtualization integrates distributed cloud computing serviceswith physical storage, servers, and network resources byembedding multiple virtual networks (VNs) into a commonphysical substrate network (SN). This NP-hard problem witha large solution space is known as virtual network embedding(VNE) [42]. Infrastructure providers optimize VNE algorithmsto solve allocation of virtual resources (nodes and links), tosatisfy diverse quality of service (QoS) demands, and to servea large number of virtual network requests (VNRs).

VNE problem may be solved by using heuristic un-coordinated algorithms or by employing coordination be-tween embedding stages. Well-known VNE approaches in-clude Monte Carlo Tree Search (MCTS)-based algorithmsemploying Multi-Commodity Flow (MaVEn-M) and the short-est path (MaVEn-S) [19], Deterministic (D-ViNE) and Ran-domized (R-ViNE) algorithms [13], Global Resource Capac-ity (GRC) [14], GRC with Multi-Commodity Flow (GRC-M) [16]. Other approaches include: VNE based on deepreinforcement learning [37], [40], reinforcement learning al-gorithms based on historical VNRs data [39], Real-TimeDynamic Virtual Embedding (RT-VNE) algorithm for cloudnetworks [28], candidate-assisted optimal mapping algo-rithm [11], algorithms that allow substrate resource sharing

This work was supported by the Natural Sciences and Engineering ResearchCouncil (NSERC) of Canada under grant R31-611284.

when embedding requests with multiple priority classes [29],and algorithms that implement topology awareness [10].

Performance of embedding algorithms should be optimizedfor diverse substrate and virtual topologies that include server-centric and switch-centric [9], [17] DCNs. In this paper, weconsider network virtualization by embedding VNRs on Spine-Leaf, Three-Tier, and Collapsed Core switch-centric DCNtopologies. In this study, we evaluate performance of switch-centric topologies since they are more widely deployed dueto their simplicity [12], [38]. We implement the three DCNtopologies using the VNE-Sim [1], [18], a discrete event sim-ulator publicly available under the terms of MIT license. Wecompare MaVEn-M, MaVEn-S, and GRC-M algorithms withthe well-known D-ViNE, R-ViNE, and GRC algorithms thathave been reported in the literature and have been implementedin VNE-Sim [1]. The remainder of this paper is organizedas follows: The survey of related VNE algorithms and theirobjectives are presented in Section II. The description of theSpine-Leaf, Three-Tier, and Collapsed Core DCN topologiesis given in Section III. Experimental procedure and results areprovided in Section IV. We conclude with Section V.

II. VIRTUAL NETWORK EMBEDDING

The VNE approaches are categorized into uncoordinatedand coordinated algorithms. The uncoordinated two-stagealgorithms heuristically solve the Virtual Node Mapping(VNoM) and then proceed to solve the Virtual Link Mapping(VLiM) using the shortest path (SP) and Multi-Commodityflow (MCF) algorithms without and with path splitting, respec-tively. The approach leads to a restricted solution space be-cause it ignores preselection of node mappings [42]. The coor-dinated two-stage algorithms solve the VNoM first while con-sidering link constraints and availability [45]. The VLiM thenemploys SP or MCF techniques. The coordinated one-stagealgorithms simultaneously solve the VNoM and VLiM bycreating a suitable optimal virtual link between the nodes [43].

MaVEn-M and MaVEn-S [19] are coordinated two-stageVNE algorithms based on MCTS. They addressed the virtualnode embedding problem in terms of Markov Decision Processthat was solved using MCTS. For node and link coordinationduring node mapping and for virtual link embedding, MaVEn-S employed the breadth first search (BFS) while MaVEn-M

employed MCF. The algorithms maximized revenue becausethey searched for more profitable embeddings.

The ViNEYard algorithms (D-ViNE, R-ViNE, WiNE) [13]used a coordinated approach for node and link mapping stagesand employed deterministic (D-ViNE) and randomized (R-ViNE) rounding to solve VNE problem that was presentedas a mixed integer programming. The coordinated node andlink mapping increased the acceptance ratio and revenue whiledecreasing the provisioning cost when compared to heuristicalgorithms that separated the node and link embeddings.

To increase the revenue of infrastructure providers, anefficient heuristic GRC-VNE algorithm was designed basedon the GRC metric [14] used to evaluate the embeddingpotential of each node in the substrate network. GRC score wascalculated for substrate and virtual network nodes based on thecomputing and bandwidth resources, and it was expressed ina random-walk form. Virtual nodes were then sorted based onthe calculated GRC and embedded using the greedy algorithmwhile virtual links were then mapped using the shortest-pathalgorithm. The proposed GRC-M algorithm [16] improvedthe substrate resources utilization by adopting MCF for linkmapping that allowed path splitting.

Let Gs(Ns, Es) denote the substrate network graph, whereNs = {ns1, ns2, . . . , nsj} is the set of j substrate nodes(vertices) while Es = {es1, es2, . . . , esk} is the set of ksubstrate links (edges). Let the ith VNR be denoted bya triplet Ψi(G

Ψi , ωΨi , ξΨi), where GΨi(NΨi , EΨi) is thevirtual network graph with NΨi = {nΨi

1 , nΨi2 , . . . , nΨi

` } andEΨi = {eΨi

1 , eΨi2 , . . . , eΨi

m } denoting the set of ` virtual nodesand m virtual edges, respectively, ωΨi is the VNR arrival time,and ξΨi is VNR lifetime [19].

Performance of VNE algorithms is evaluated based on:virtual network request acceptance ratio, generated revenue,incurred cost (nodes and links), and substrate resource utiliza-tion [19]. The acceptance ratio is expressed as a probabilitypτa of accepting VNRs. It is equal to the ratio of number ofaccepted VNRs |Ψa(τ)| at a given time instance τ and thetotal number of arrived VNRs |Ψ(τ)|:

pτa =|Ψa(τ)||Ψ(τ)|

. (1)

Revenue R(GΨi) of an infrastructure provider generated byembedding VNRs Ψi is defined as:

R(GΨi) = wc∑

nΨi∈NΨi

C(nΨi) + wb∑

eΨi∈EΨi

B(eΨi), (2)

where wc and wb are the weights for CPU C(nΨi) and band-width B(eΨi) requirements, respectively. The cost C(GΨi)depends on the spent resources during the embedding process:

C(GΨi) =∑

nΨi∈NΨi

C(nΨi) +∑

eΨi∈EΨi

∑es∈Es

feΨi

es , (3)

where feΨi

es is the total bandwidth of the substrate edge eS

allocated to the virtual link eΨi . An objective of infrastructureproviders is to maximize the profit as the difference between

revenue R(GΨi) and cost C(GΨi). Substrate node and linkutilizations are:

U(Ns) = 1−

∑ns ∈ Ns

C(ns)∑ns ∈ Ns

Cmax(ns)(4)

U(Es) = 1−

∑es ∈ Es

B(es)∑es ∈ Es

Bmax(es), (5)

where Cmax(ns) and Bmax(es) are the maximum availableCPU in a substrate node and the maximum bandwidth of thesubstrate link, respectively.

III. TOPOLOGIES IN DATA CENTER NETWORKS

Data centers have the capability to store and processlarge data, host large-scale data-intensive applications, andoffer cost-effective solutions [24], [38], [41]. DCNs may beclassified based on the implementation of packet forwardingas switch-centric, server-centric, and hybrid topologies [31].In switch-centric topologies (Fat-Tree, F2Tree, Diamond,Spine-Leaf, Collapsed Core, and Three-Tier), switches [32]are responsible for network interconnections and performdata forwarding while servers are used for computation andstorage. There is no bandwidth bottleneck because linksand switches are equally utilized unlike in traditional tree-structured DCN topologies [20]. In server-centric topologies(BCube, DCell, FiConn, Crystal) [12], [27], [36], servers areused for data, computation, and storage. Hybrid topologies(star-wired ring) [22], [34] employ both switches and serversfor routing tasks.

The Spine-Leaf topology proposed by Cisco, shown inFig. 1, is extensively employed in scalable data centers [6],[7]. It consists of spine and leaf switches where each spineswitch is directly connected to all leaf switches and acts asan aggregation switch. Hosts are linked to leaf switches. Thetraffic path is randomly chosen so that the load is evenlydistributed among the spine-layer switches [21], [25], [30].

Fig. 1. Spine-Leaf topology with spine (aggregation) and leaf (edge) layers.It consists of 4 spine switches, 8 leaf switches, and 24 hosts.

The Three-Tier topology [15], [23], [26] is widely used. Ithas a multi-tiered architecture [4] and consists of one core, oneaggregation, and one edge layer, as shown in Fig. 2. Advan-tages include simplicity of virtual network management [35],[44], shorter downtime, and path redundancy that is requiredfor medium to large commercial DCNs.

A modified design of the traditional Three-Tier topologywhere the core and aggregation layers are merged into onelayer, is considered more practical for small enterprise net-works [5]. A Collapsed Core topology is implemented by

Fig. 2. Three-Tier topology with core, aggregation, and edge layers. It consistsof 2 core switches, 4 aggregation switches, 8 edge switches, and 24 hosts.

removing expensive core switches and by linking aggregationswitches, as shown in Fig. 3. Its purpose is lowering networkcost and increasing usage of interconnecting links while main-taining most benefits of the Three-Tier topology.

Fig. 3. Collapsed Core DCN with aggregation and edge layers. It consists of4 interconnected aggregation switches, 8 edge switches, and 24 hosts.

IV. EXPERIMENTAL PROCEDURE AND RESULTS

The algorithms are compared for a range of VNR trafficloads. Experiments are performed using Dell Alienware Au-rora with 32 GB memory and Intel Core i7 7700K processor.A discrete event simulator VNE-Sim [1], [9], [17], [18] is usedto evaluate and compare performance of MaVEn-M, MaVEn-S, D-ViNE, R-ViNE, GRC, and GRC-M VNE algorithmswhen applied to switch-centric network topologies. Spine-Leaf, Three-Tier, and Collapsed Core DCN substrate networkfiles are generated using the Fast Network Simulation Setup(FNSS) [3] while the VNRs were generated using the BostonUniversity Representative Topology Generator (BRITE) [2].Each topology contains 6 aggregation (spine) switches, 18edge (leaf) switches, and 90 hosts while the Three-Tier topol-ogy also has 3 core switches. Spine-Leaf, Three-Tier, andCollapsed Core have 198, 126, and 123 links, respectively.

Generated substrate and virtual networks parameters areshown in Table I. Virtual network requests are generated forvarious traffic loads. We assume that the VNRs arrivals area Poisson process with a mean arrival rate of λ requests perunit time. Their life-times are exponentially distributed with amean 1

µ yielding to a VNR traffic of λ× 1µ Erlangs. Duration

of each simulation scenario is 50, 000 time units [19]. (Weassume that the constant VNR arrival rate of 1 request per 100time units yields to traffic load of 10 Erlangs.) Computationalbudget (number of simulations) β is the number of evaluatedaction samples per selection cycle, which affects performanceof the MCTS algorithms [19].

Simulation results shown in Fig. 4 indicate that GRC andMaVEn-M algorithms have the lowest and the highest process-ing times, respectively. Increasing the computational budgetmay improve the performance of MaVEn-M and MaVEn-Swhile increasing the processing time [19].

TABLE IPARAMETERS OF SUBSTRATE AND VIRTUAL NETWORKS

Substrate network DistributionCPU 100 unitsLink bandwidth 100 unitsVirtual network DistributionCPU [2, 20] units uniformLink bandwidth [1, 10] units uniformLink splitting rate 0.1Lifetime mean rate 1,000 exponentialNumber of nodes [3, 10] uniform

Fig. 4. Processing times for various VNE algorithms and DCN topologies.

Performance results shown in Fig. 5 indicate that acceptanceratio, revenue to cost, node utilization, and link utilization arethe best for the Spine Leaf topology. Collapsed Core topologywith multiple switch blocks exhibits similar performance toThree-Tier while having reduced number of layers and withoututilizing expensive core switches. In most cases, MaVEn-Mand MaVEn-S outperform other algorithms. MaVEn-M showshigher acceptance ratio and average node and link utilizations.However, MaVEn-S and D-ViNE outperform other algorithmsin terms of revenue to cost ratio. D-ViNE exhibits the lowestacceptance ratio for all three topologies. GRC-M shows slightimprovement over GRC by employing the MCF algorithm.However, its revenue to cost ratio is slightly lower due to thehigher likelihood of embedding virtual nodes onto substratenodes that are located further apart. While high acceptanceand high revenue to cost ratios are desired, at higher VNRtraffic loads fewer substrate resources remain thus leading tomore costly VNR mappings [16].

V. CONCLUSION

In this paper, we evaluated performance of MaVEn-M,MaVEn-S, D-ViNE, R-ViNE, GRC, and GRC-M VNE algo-rithms by implementing Spine-Leaf, Three-Tier, and CollapsedCore data center network topologies using the VNE-Simsimulator. Performance evaluation was based on revenue tocost ratio, acceptance ratio, resources utilization, and averageprocessing time. In most cases, MaVEn-M and MaVEn-Soutperformed other algorithms. Simulation results illustratedthe effect of substrate network topology on performanceof VNE algorithms. Selecting an appropriate switch-centrictopology is a trade-off between network implementation costand performance of a VNE algorithm.

Fig. 5. Comparison of Spine-Leaf (left column), Three-Tier (middle column), and Collapsed Core (right column) DCN topologies. Shown are acceptanceratio, revenue to cost ratio, and average node and link utilization as functions of VNR traffic load. Acceptance ratio, revenue to cost, node utilizations, andlink utilization are the best for the Spine Leaf topology. In most cases, MaVEn-M and MaVEn-S outperform other algorithms. Observed performance ofD-ViNE, R-ViNE, GRC, and GRC-M algorithms is similar to previously reported study using other switch-centric topologies [9]. The lower acceptance ratiofor D-ViNE results in a less congested substrate network. Hence, the algorithm is able to use fewer substrate resources by placing virtual nodes closer to eachother thus resulting in higher revenue to cost ratio.

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