Towards a Complete Framework for Virtual Data Center Embedding

M. P. GileshNational Institute of Technology Calicut

Kozhikode, Kerala, IndiaEmail: gilesh p140059cs@nitc.ac.in

Abstract

Cloud computing is widely adopted by corporateas well as retail customers to reduce the upfrontcost of establishing computing infrastructure. However,switching to the cloud based services poses a multitudeof questions, both for customers and for data centerowners. In this work, we propose an algorithm foroptimal placement of multiple virtual data centers on aphysical data center. Our algorithm has two modes ofoperation - an online mode and a batch mode. Coordi-nated batch and online embedding algorithms are usedto maximize resource usage while fulfilling the QoSdemands. Experimental evaluation of our algorithmsshow that acceptance rate is high - implying higherprofit to infrastructure provider. Additionaly, we try tokeep a check on the number of VM migrations, whichcan increase operational cost and thus lead to servicelevel agreement violations.

1. Introduction

In the last few years, cloud computing has becomethe backend of all the service oriented IT businesses.The conventional service providers (SP) are able tosignificantly reduce their capital expenditure (CapEx)by switching to virtualized IT infrastructure. Thetime to establish (ToE) infrastructures of any desiredsize has come down from several months to a fewminutes/hours of automated provisioning of virtualmachines (VMs) in physical infrastrcture providers’premises and installing the application stack on thesevirtual infrastructures [8] using tools like Puppet, An-sible, and Vagrant.

With the new model of service provisioning, thebusiness role of conventional SPs has got dividedamong infrastructure providers(InP), who expose asoftware abstraction of the underlying hardware orsoftware resources; and service providers, who usethese abstractions to build their own application stack

to offer services to the end users. Virtualization ofthe hardware is the prime technology that enabledthe cloud computing paradigm. Though the conceptof virtualization is more than two decades old, cloudcomputing has leveraged the expoitation of the poten-tial of virtualization at various levels viz. hardware,development platform and software. As of now, almostevery domain of computing infrastructure, includingcomputing, storage, network, operating systems andapplications, have been virtualized to maximize theresource utilization and reduce the ToE. The InPsmaintain a pool of resources to be abstracted andmutliple instances of user machines/ applications runon these resources, typically called slices.

Network virtualization, though late entrant in cloudcomputing, has key role in complying with the SLAbetween InP and SPs. The bandwidth requirementfor internal traffic is growing fast against that forexternal traffic in cloud data centers [10]. From thebusiness perspective, virtualizing the network is crucialbecause the cost of networking is escalating against thecost of other equipments and the ratio of network tocompute is going up, especially in big data applica-tions. Literature show that, NV is killer application forthe software defined networks (SDN) technology. Inthis paper, we address the problems associated withsharing compute and network resources of an InP, inparticular, that of a datacenter infrastructure. In multi-tenant data centers, multiple service deploy their virtualinfrastructure(VI) for service provisioning. The servicelevel agreement (SLA) defines the QoS expectations ofthe service providers and the penalty for the violationof the same. Hence, it is critical for the InP to provideisolation between these VIs, in terms of performance,disruption, and security.

In this paper we address the virtual data centerembedding (VDCE) problem in cloud data center envi-ronment [7]. In VDCE, embedding of virtual networks(VNs) and virtual machines (VM) are consideredsimultaneously. A virtual datacenter(VDC), like any

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other DC, has VMs connected through virtual switchesusing virtual links of specific bandwidth and delayconstraints. VDCE refers to the class of algorithmswhich optimally superimpose multiple VDCs on a DC,satisfying the SLA. [14], [17]. The problem is impor-tant because, many customers (i.e. SPs) try to createor migrate their topology intact (including switches)to a cloud for reasons like failure recovery, scaling oreconomic saving.

Figure 1. Virtual Data Center Embedding [7]

Formaly, the problem of VDCE, is defined as fol-lows. Let Gs = (Ns, Es, Cs, φsa, δ

sb , ξ

sc) be a phys-

ical DC and there is a set of VDC requests R ={Gv

u = (Nvu , E

vu, C

vu, φ

vau, δvbu , ξ

vcu) : u = 1, 2, ..m}

. Table 1 gives the description of the variables used.The problem is to find an optimal placement of VDCson DC while satisfying the SLAs with the tenantsu = 1, 2, ..m. In otherwords, find a mapping fromVDC set to DC

FCu : Cv

u → Cs′

FNu : Nv

u → Ns′

FEu : Ev

u → Ps′

for u = 1, 2, ..m where Ps′ ⊂ (Es)k, 1 ≤ k ≤

|Ns|, Ns′ ⊆ Ns, Cs′ ⊆ Cs, under the followingconditions

1) Virtual machines(VM) are mapped toservers/physical machines (PM).

FCu (c1) = c ∈ Cs′ (1)

2) Not more than one node of a virtual request ismapped to a physical (substrate) switch (pSwitch).

FNu (n1) = FN

u (n2) =⇒ n1 = n2 (2)

and hence, at most one virtual link (vLink) of arequest is mapped to a path. Moreover, virtual

Var Description< Set of serviceable VDC requestsNs Set of substrate switchesEs Set of substrate linksCs Set of serversPs Set of all paths in substrate networkNv

u Set of virtual switch of request uEv

u Set of virtual links of request uCv

u Set of VMs of the request uφsa/δ

vau

Value of PM /VM attribute aδsb/δ

vbu

Value of PSwitch / VSwitch attribute bξsc/ξ

vcu Value of PLink / VLink attribute c

qC Set of machine attributesqN/qE Set of switch/machine/link attributesPkl Set of paths in SN between k and lyuij,kln 1 if vLink ij of u ∈ < is mapped to nth path kl.xuik 1 if vSwitch i of u ∈ < is mapped to a pSwitch k, Else

0wu

ik 1 if VM i of u ∈ < is mapped to a PM k, Else 0Zu 1 if a request u is mapped. Else 0.pekln 1 if e is in the nth path of kl. Else 0

Table 1. Notations used

edge switches are mapped only to edge switchesof the physical topology.

3) Sum of capacity demands of VMs does not exceedthe total capacity of the PM to which they aremapped∑u∈<:FC

u (k)=s

φvau(k) ≤ φsa(s) ∀s ∈ Cs,∀a ∈ qC

(3)

4) Similarly, sum of capacity demands of virtualswitches (vSwitch) should be within that of thepSwitch to which they are mapped∑u∈<:FN

u (k)=n

δvbu(k) ≤ δsb(n) ∀n ∈ Ns,∀b ∈ qN

(4)

5) The sum of attribute demands of vLinks do not ex-ceed the total capacity of the physical / substratelink (pLink ) to which they are mapped.∑

u∈<:FEu (l)=p;e∈p;p∈Ps

ξvcu(l) ≤ ξsc(e)

∀e ∈ Es,∀c ∈ qE (5)

Figure 1 illustrates how two VDC requests areembedded on a physical data center.

The node mapping problem - mapping virtual nodesto physical nodes - was proven to be NP-Hard [4] [6],[18]. The problem is reducible from the famous Multi-way Separator Problem [4] which is NP-Hard. Optimalassignment of links with functional constraints, in agraph, where the nodes are already assigned, is stillNP-hard [6], [18] and is similar to Unsplittable Flow

Problem (UFP) [11] / Multi-Commodity Flow (MCF)problems. Many heuristic solutions were proposed forthe problem.

We propose a VDCE algorithm that employs suit-able technique for embedding requests depending onthe availability of DC resources. The model employsmathematical programming for embedding a group ofrequests, in one shot. Local search heuristic is used foronline embedding of requests to reduce the averagewaiting time of the requests. The online embeddingreduces the number of VM migrations by not consoli-dating the VMs, as proposed by many solutions foundin literature.

Rest of this paper is organized as follows. Section 2gives a brief review of the relevant work in this area.Section 3 explains the proposed algorithm in detail. InSection 4 we discuss experimental setup for evaluationof our algorithm and the results of these experiments.Section 5 concludes the paper.

2. Related Work

Virtual Network Embedding problem, for efficientplacement of virtual networks on physical network,is being studied for several years . Algorithm toefficiently map virtual nodes to the physical nodes, tosatisfy various objectives had been studied. Single shotembedding of both nodes and edges were also studied[5] [9]. In practice, exact algorithms for the problemapply for small networks only. A comprehensive sur-vey of classic virtual network embedding techniquesis given by Belbekkouche et al. [5] and Fischer et al.[9]. Fischer et al. [9] proposed a taxonomy for VNEand classified them as centralized vs distributed, staticvs dynamic and redundant vs concise. The centralized,dynamic and redundant algorithms are particularly ofinterest because they apply to the present day data cen-ter networks, especially the software defined networks

The VDCE problem is different from VNE be-cause the latter cares about the efficient palcementof VMs with multiple constraints. Efficient placementof VMs on servers is an independent problem byitself. To the best of our knowledge, there are onlya few proposals for VDC resource allocation in cloudcomputing centers. Sivaranjini et al. [16] and Correaet al. [7] give surveys on the existing virtual datacenter embedding algorithms. Papagianni et al. [12]proposed a VNE for cloud computing environment viz.Networked Cloud Mapping (NCM), that handle bothcompute and network node assignments. The mixedinteger programming (MIP) model attaches multipleproperty vectors for the nodes including the type ofnodes, capacity etc.

Zhani et al. [20] proposed a VDC planner to embedvirtual data center network and machines on a substratedata center. The primary consideration of the pro-posal is migration-awareness. There are three scenariosconsidered in the proposal - an initial deployment,handling up/down scaling of VDC and a dynamic con-solidation (reoptimzation) for power saving. The exper-imentations are carried out on the VL2 topology [10].Three stage virtual data center embedding algorithmby Rabbani et al. [13] maps virtual machines, switchesand links in sequential stages. The heuristic algorithmreduces the server fragmentation, communication costand the resource utilization.

Amokrane et al. [3] give a resource allocation tech-nique for virtual data center spanning over distributedsubstrate data centers. The proposed method has twostages - a VDC partitioning and a partition embedding.In partitioning, the VDC requests are partitioned tominimize the inter-data center bandwidth. In the sec-ond phase, the partitions are mapped to data centerssatisfying capacity constraints. The integer linear pro-gram (ILP) formulation of both phases ensures exactsolution for reduced bandwidth. Venice is a reliabilityaware VDC embedding algorithm proposed by Zhanget al. [19]. The authors proved that computing theavailability of VDC is a hard problem. The reliability-aware embedding is handled using a heuristics and aconsolidation to handle the frequent entry and exit ofrequests. Wang et al. [17] proposed a heuristic frame-work for the VDCNE problem - Presto. The frameworkuses Blocking Island (BI) paradigm for improvingthe accuracy and speed of embedding. However, thelink and node embeddings are uncoordinated and theheuristic based solutions are sub-optimal.

Our survey shows that algorithms are either exactalgorithms that suffer from sluggishness or heuristicalgorithms which leave the DCs under-provisioned. Asuboptimal embedding might be possible using heuris-tics. But, such an embedding may lead to rejectionof other peer requests, resulting poor QoE (Qualityof Experience) of customers. Moreover, most of theheuristics fail if the residual resources are spread overmultiple fragments. Hazzles of live VM migrationdismiss the possibility of frequent remapping of theincumbent nodes. There had been solutions whichuse VM migrations to find optimality, neglecting thecost of migration. So, we believe that, a well coordi-nated hybrid technique can find an optimal solutionin less time. We propose a mixed approach withsuitable modes from mathematical programming andlocal search heuristics to maximize the resource usagewith limited VM migrations.

3. Proposed Algorithm

The proposed algorithm works in two differentmodes - online mode or batch mode - based on therate of fragmentation of resources with in data center.Different techniques are used to perform batch embed-ding and online embedding. If suffiecient resources areavailable, individual arriving requests are embeddedimmediately with local search method to avoid reopti-mization of the entire mapping. Online embedding isdone also when one or more embedded requests exitand if the total residual resources are above a threshold(t1) defined in terms of the smallest pending request. Online embdding is attempted in case of failure ofhardware components also. Frequent reoptimization ofthe entire embedding or consolidation may cause manyVM migrations. It may cause unprecedented delayin the communication within a virtual network, if atenant vSwitch is mapped to a farther pSwitch afterreoptimization. Batch embedding of multiple requestsis performed by a mixed integer programming model.Batch embedding is performed if there are sufficientresources to embed multiple VDC requests or the totalfragmented resources are above a threshold vector t2

defined in terms of the resource requirement of thelargest pending request. Threshold vector has valuest2c , t

2n, t

2e the residual values of servers, switches and

links.Initially, the residual resource vectors tc, tsn, tse

are initialized with the capacity vectors of the datacenter. If there are multiple pending requests and thetotal demand is less than tc, tsn, tse we try a batchembeding. If the sum of resource demand vectorsof all requests exceed tsn, tse for nodes and linksrespectively, and multiple requests can be embedded,then a batch embedding is attempted on a selectedsubset request. The subset has the high priority jobs.Deatils of the online embedding and batch embeddingalgorithms are give below.

3.1. Online Embedding

Online embedding is the most common occurencein our model. In online mode, an embedding is at-temped whenever arrival of a new request or an exitof embedded request happens. Specifically, an onlineembedding is attempted when:

(i) a new request arrives and the local remapping canenable the embedding of the request; or.

(ii) there is failure of some servers, nodes and linksand VDC components already mapped to thefailed part of the substrate requires a remapping;or

(iii) a mapped virtual data center requires scalingup and free resources are not available in theneighbourhood.

online embedding attempts to find a local solution withminimum modification to the existing mappings. Ifthere are multiple waiting requests, we prioritize the re-quests based on the time to expiry, size of the VDC andexpected time of incumbancy. If a fragment (connectedcomponent) of the DC graph has sufficient resources toembed the selected request then, an embedding is at-tempted by simple heuristics. We use a local search andswap technique to do online embedding. A temporarymapping of the new request is made in the followingorder - VMs, Switches, Links. The temporary mappingis allowed to have capacity violations. Then swappingis attemped between already mapped VMs/Switchesin locations where the temporary mapping has leastviolations. If a solution is derived by few number ofswappings (limited by the number of swaps required)the temporary mapping is made permanent. If neitherof the above are possible the algorithm tries to embedthe next request.

3.2. Batch Embedding

Batch embedding is attempted when a set of requestsare available for the first time or when there are enoughfragmented resources for embedding a new/defferedrequest for which it is hard to find a local solution. Inour algorithm we focus on maximizing the acceptancerate of requests which positivley affects the revenueof InP and availability of the cloud service. The batchembedding algorithm works as follows.

Figure 2. Data Center Topology

We formulated the batch embedding problem asa mixed integer program (MIP). The model restrictsat most one VSwitch of a request on an PSwitch.However, this restriction does not apply to embeddingof VMs on PMs. Multiple VMs can be embedded ina single PM. An edge switch of a VDC request inembedded on an edge switch of the substrate topology(Figure 2). Any VLink is embedded on a single pathbetween the nodes onto which the end virtual devices

are mapped. The MIP model for batch embedding isas follows

Equation (6) tries to maximize the number VDCsembedded, while minimizing the number of VM mi-grations, subject to the constraints (7) - (16)

Maximize∑u∈<

Zu − r1 −r2f

(6)

where r1 and r2 are the normalized migration distancesof VMs and vSwitches already embedded. Parameter fdecides the weight of penalty for vSwitch migrationrelative to VM migration.

Constraint (7) and (8)ensures that when a VDCu is embedded all its vSwitches and VMs are alsoembedded.∑

k∈Ns

xuik = Zu ∀i ∈ Nvu , u ∈ < (7)∑

k∈Cs

wuik = Zu ∀i ∈ Cv

u, u ∈ < (8)

As per the definition, at most one vSwitch of virtualrequest in embedded on a pSwitch. Constraint (9)affirms this rule.∑

i∈Nvu

xuik ≤ 1 ∀k ∈ Ns, u ∈ < (9)

To ensure that a virtual link is embedded only onceand not split across multiple path, constraint (10) isused. There can be exponentialy many paths betweenany two nodes of a graph. We consider paths of lengthutmost 4 and other paths are not included in Pkl.∑kl∈{Ns∪Cs}×{Ns∪Cs}

∑n∈Pkl

yuij,kln = Zu ∀ij ∈ Evu, u ∈ <

(10)The linking constraint (11) ensures that, whenever apair of vSwitches are mapped, the vLink between themare mapped to at most one path between the selectedpSwitches.

∑n∈Pkl

yuij,kln − xuik xujl = 0 ∀ij ∈ Evu, u ∈ <

(11)For any server in the DC, there is one (Figure 2) ora constant number of switches in the neighbourhood.The topology in use has only one neighbour. Hencethe constraint for embedding a (vSwitch, VM) link isgiven as ∑

kl∈Es∩(Ns×Cs)

yuij,kl1 − xujl wuik = 0

∀ij ∈ Evu ∩ (Nu

v × Cuv ), u ∈ < (12)

The constraint (13) assures that the sum of resourcedemands of VMs mapped to a PM does not exceed itscorresponding resource capacity.∑u∈<

∑i∈Cv

u

wuik φa(i) ≤ φa(k) ∀k ∈ Cs,∀a ∈ |qC |

(13)Similarly, constraint (14) ensures that the sum of

resource demands of vSwitches mapped to a pSwitchdoes not exceed its corresponding resource capacity.∑

u∈<

∑i∈Nv

u

xuik δb(i) ≤ δb(k) ∀k ∈ Ns,∀b ∈ |qN |

(14)Similar to the above the sum of link resource demandsof all vLinks, mapped to a pLink, should be less thanthe capacity of the substrate.∑

u∈<

∑ij∈Ev

u

yuij,kln pekln ξc(ij) ≤ ξc(e),

∀e ∈ Es,∀c ∈ |qE | (15)

Following constraint put bounds on values that thevariables can assume.

Zu ∈ {0, 1}, yuij,kln ∈ {0, 1}, xuik ∈ {0, 1}, wuik ∈ {0, 1}

(16)Apart form the constraints given above, VDC re-

quests may have specific demands on other QoS pa-rameters like latency, location, distance between VMsetc. The following set of constraints apply to thoserequests which are in need of such special consid-eration. If the VDC requests u ∈ <′ ⊂ < want tolimit the maximum latency between adjacent nodes(switch/VM) to du, the following constraint (17) isadded in respect of them.( ∑

vw∈Pkln

dvw

)yuij,kln <= du ∀ij ∈ Ev

u, ∀u ∈ <′ ⊂ <

(17)where dvw is the delay of a physical link (v, w)

A vital requirement of VDC placement in cloudenvironment is the freedom to specify the location forembedding a VM. Customarily, the need arises fromthe locality of other nodes, ease of access etc. Thisis a major requirement in virtual clusters performingbig data processing, to improve computation time.The following constraint is used to specify the exactsubstrate node k on which a virtual node i should beembedded.

wuik = Zu (18)

A more flexible method would be specify a possiblesubset of PMs to embed a given VM. Optional con-straint (19) limits the embedding VM i on a PM from

a set of servers Cs′ ⊂ Cs∑k∈Cs′

wuik = Zu (19)

As and when needed, batch embedding is donefor compaction of the unusable fragmented resources.Such a re-embedding of incoming and mapped VDCrequest is VM migration aware and hence tries to mini-mize/limit the cost of changes in the existing mapping.We assume that virtual machines of different sizes havevarying cost of migration. Hence costly migrations areavoided to the extent possible. If remapping a VSwitchis necessary, the new PSwitch, to which the mapping isdone, is not far from the already mapped PSwitch. Thisfeature keeps a check on the number of VM migrationand the extra internal traffic.

Variable ValuesPM CPU Cores 8PM Memory 16384pSwitch memory 100pLink bandwidth (core - aggregation) 10000pLink bandwidth (edge - aggregation) 1000pLink bandwidth (edge - server) 1000No of VMs 40 - 100VM cores 1 - 2VM Memory 256 -512No of vSwitches 5 - 20vSwitch memory 10 - 25vLink bandwidth 5 - 200Duration of incumbancy 10 - 90

Table 2. Simulation parameters

4. Preliminary Results

We developed the simulation environment in python,with FNSS toolchain [15] and NetworkX library inthe backend, for managing the substrate and virtualnetworks . The batch embedding is implemented witha commercial solver, CPLEX [1]. Our algorithm in-terfaces with CPLEX using python concert API ofCPLEX. Online embedding heuristic is implementedwith python, using NetworkX library.

We use the fat tree topology [2] shown in (Figure 2)to represent the substrate data center. For simplicity,we consider bandwidth of links and memory capacityof switches as the attributes for the network. Numberof CPU cores and Memory are considered as theattributes of Servers and VMs. VDC requests haverandom sized tree/fat tree topolgy - a most commoncase in big data processing clusters. The topologieswere generated using the topology generator of FNSStoolchain [15]. Simulation parameters are randomlydistributed with ranges as as given in Table 2. The

arrivals of VDCN requests are determined by a Poissondistribution ranging from 1 to 10 requests per 100 timeunits.

The acceptance rate with respect to varying rateof arrival is shown in Figure 3. The figure clearlyexposes the advantage of our strategies over MIP orheuristics solution used singly. Poor acceptance rate ofheuristic can be accounted to the sub optimal solutionsof heuristic methods. This leaves a lot of resourcesin data center unused. MIP solutions are applied inbatches and hence the acceptance largely rely on theinstantaneous availability of resources whereas, the re-sources remain unused between successive embeddingsessions.

Number of VM migrations is a measure of quality ofthe VDCE solutions. Figure 4 shows that our algorithmreduces the rate of VM migrations. Higher number ofmigrations in pure MIP solutions is intuitive from thenature of the algorithm. Every time a new batch isembedded, the existing VMs get migrated with highestprobability, to reach optimality. With pure MIP modelit is hard to achieve optimal solution without VMmigration in datacenter with fragmented resources. Theremapping in heuristic algorithms are due to the peri-odic consolidation of resources, which is inevitable.

5. Conclusions

Our algorithm is suitable for optimaly embeddingvirtual data centers on a physical data center. TheVDCE problem is important in placement of VMswith or without specific topology demands. The pro-posed multi-mode algorithm maximizes the resourceutilization over time by the online embedding, withoutwaiting for embedding in batches. In case fragmen-tation is high, an MIP based batch re-embedding isapplied to alleviate the same. Sluggish ILP-based exactalgorithm for batch embedding is the major limitationof our proposal. We are looking for faster mathematicalprogramming techniques or near-optimal heuristics thatcan overcome the limitation.

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Algorithm 1 Virtual Data Center Embedding1: procedure VDC EMBED(Gs,<)2: tsc = residual server resource vector3: tsn = residual switch resource vector4: tse = residual link resource vector5: while |<| 6= 0 do6: Initialize the set <′

7: Calculate the thresholds (t2c , t2n, t

2e) and

(t1c , t1n, t

1e)

8: if (tsc, tsn, tse) ≥ (t2c , t2n, t

2e)) then

9: call batch embedding(Gs,<′)10: else if ((t1c , t1n, t1e) ≤ (tsc, tsn, tse) <

(t2c , t2n, t

2e)) then

11: Priority sort thet set <.12: Select Gv

u ∈ < s.t. tuexp ≤ tcurr + TD13: call online embedding(Gs, Gv

u)14: end if15: end while16: end procedure

17: procedure BATCH EMBEDDING(Gs,<′)18: Formulate the MIP (Section 3.2)19: Solve the MIP (with a solver)20: for VDC u not embedded do21: Add u back to <22: end for23: end procedure

24: procedure ONLINE EMBEDDING(Gs, Gvu)

25: if residual resource(C) ¿ requirement(Gvu) then

26: Create temporary VDC placement C27: Confirm the embedding if possible with local

search.28: else29: Select servers with least capacity violation.30: Find the vi the amout of violations.31: Select smallest set of VMs with capacity ≥ vi32: Swap with VM group where the difference33: in capacity is atleast vi34: end if35: end procedure

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Figure 3. Acceptance rate for varying arrival rates

Figure 4. % of VM migrations for different arrivalrates

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