Opposites Attract: Virtual Cluster Embedding for Profit
OOpposites Attract:Virtual Cluster Embedding for Profit
Arne Ludwig , Carlo Fuerst , Alexander Henze , Stefan Schmid , TU Berlin, Germany, Telekom Innovation Laboratories (T-Labs), Germany { arne,carlo,ahenze } @inet.tu-berlin.de, [email protected] ABSTRACT
It is well-known that cloud application performance criti-cally depends on the network. Accordingly, new abstrac-tions for cloud applications are proposed which extend theperformance isolation guarantees to the network. The mostcommon abstraction is the
Virtual Cluster
V C ( n, b ): the n virtual machines of a customer are connected to a virtualswitch at bandwidth b . However, today, not much is knownabout how to efficiently embed and price virtual clusters.This paper makes two contributions. (1) We present analgorithm called Tetris that efficiently embeds virtual clus-ters arriving in an online fashion, by jointly optimizing thenode and link resources. We show that this algorithm allowsto multiplex more virtual clusters over the same physical in-frastructure compared to existing algorithms, hence improv-ing the provider profit. (2) We present the first demand-specific pricing model called
DSP for virtual clusters. Ourpricing model is fair in the sense that a customer only needsto pay for what he or she asked. Moreover, it features otherdesirable properties, such as price independence from map-ping locations.
1. INTRODUCTION
Server virtualization has revamped the server businessover the last years, and cloud computing has changed theway we think about resource allocation in the Internet.However, while cloud providers support the flexible alloca-tion of virtual machines (
VMs ) and provide the customerwith certain resource and performance isolation guarantees,networking has so far been treated as a second class citizen:until recently, cloud customers could not specify even basicnetworking guarantees to connect their virtual machines.This is problematic given the fact that the traffic gen-erated by cloud applications such as MapReduce and dis-tributed databases is not negligible. Indeed, it has beenshown that cloud applications suffer from resource inter-ference on the network, in the sense that application per-formance can become unpredictable. Longer job executiontimes also entail higher costs for the customers who arecharged on a per-VM-hour basis . [4]To overcome these problems, more powerful resourcereservation models have been proposed. [3] A common ab-straction is the
Virtual Cluster : a virtual cluster
V C ( n, b )connects n virtual machines to a virtual switch at bandwidth Copyright is held by author/owner(s). b —essentially a hose model. [4] While the resulting perfor-mance isolation guarantees are attractive, the virtual clus-ter abstraction raises two fundamental questions: (1) Howto embed virtual clusters on a given physical network? Inorder to make an optimal use of its resources and hence max-imize the profit, a provider may want to multiplex as manyvirtual clusters as possible over the physical infrastructure(while fulfilling the requested virtual cluster specification).(2) How to efficiently price virtual clusters? While today’scloud pricing models typically focus on VM hours only, thepricing of virtual clusters becomes a 2-dimensional problem:a customer requesting more bandwidth should be priced ac-cordingly. This paper addresses these two questions. Our Contribution.
We present the first pricing schemefor virtual clusters, called
DSP ( Demand-Specific Pricing ),which explicitly takes into account the different computationand bandwidth requirements. That is, unlike the dominant-resource pricing scheme
DRP presented in the literaturebefore [2],
DSP is designed according to a specification-dependent, pay-only-for-what-you-request policy : While in
DRP , the size n and the bandwidth b of a virtual clusterare strictly coupled, DSP allows customers to request vir-tual clusters
V C ( n, b ) of arbitrary and independent size n and bandwidth b , and be priced accordingly and in a fairmanner. Moreover, DSP ensures desirable properties suchas location independent pricing.Together with this pricing scheme we present anew embedding algorithm called
Tetris which is alsospecification-dependent in the sense that Tetris accountsfor differences in the node and link requirements of virtualclusters. Concretely,
Tetris is tailored to an online scenariowhere different virtual clusters
V C ( n , b ) , V C ( n , b ) , . . . are requested over time, and collocates “opposites”:computation-intensive but communication-extensive virtualclusters are mapped together with computation-extensivebut communication-intensive virtual clusters, to maximizethe number of simultaneously hosted virtual clusters overtime. Given the online nature of the problem, this is a non-trivial task. We show that our algorithm outperforms pre-vious algorithms, in the sense that a provider can host morevirtual clusters, and hence increase its profit.
2. BACKGROUND & MODEL
Most cloud providers today still offer virtual machine ser-vices only, charging their customers on a per-hour basis. The name of the algorithm is due to its strategy to balancedifferent resources equally, see also Figure 2 for an illustra-tion. a r X i v : . [ c s . N I] N ov owever, we witness a trend towards more network orientedspecifications (see also, e.g., Amazon Placement Groups , Amazon EBS-Optimized Instances or Microsoft Azure Ex-pressRoute ), and especially the virtual cluster abstraction isbecoming a popular model for datacenter applications. [3]In [3], a first algorithm (henceforth called
Oktopus ) wasproposed to embed virtual clusters in fat-tree datacentertopologies, and Ballani et al. [2] proposed a first pricingscheme for virtual clusters which give minimal bandwidthguarantees. Essentially, their scheme is based on
DominantResource Pricing , short
DRP . DRP provides different tem-plates for the customers, with predefined sizes n and an as-sociated amount of minimal guaranteed bandwidth b . Whilethis model is attractive for its simplicity, also in the sensethat the interface between the customer and provider maynot have to be changed, the minimal bandwidth b is a func-tion of n and cannot be chosen by the customer. As such, DRP is still 1-dimensional and does not leverage the fullflexibility of the virtual cluster model, which is described bytwo independent parameters n and b .Indeed, virtual cluster specifications are likely to comewith different requirements [1] and can be heterogeneous [4]:a latency sensitive webservice can be very different in na-ture than, say, a delay-tolerant batch processing job or anetwork-hungry database synchronization application. Oneimplication of the DRP scheme is that customers who knowtheir virtual cluster demands might suffer from the inher-ent 1-dimensionality: in order to meet their application re-quirements, customers may be forced to upgrade to the nextlarger template, increasing both resources.This paper seeks to overcome this problem by allowingcustomers to specify their computation and communicationrequirements separately. Concretely, we allow the customerto specify three parameters independently: the number ofVMs n , the computational type c of the virtual machines(e.g., small, medium, or large instances), as well as thebandwidth b . That is, we use a virtual cluster abstraction V C ( n, c, b ), where all virtual machines are of the same com-putational type c , and are connected to a virtual switch atbandwidth b .We use the following conventions in our notation. Thecomputational type c is normalized in the sense that c de-scribes the fraction of the capacity of a physical server. Sim-ilarly, we will normalize b to denote the requested fraction ofthe overall link capacity of a physical server. A central con-cept for our algorithm Tetris (improving upon
Oktopus )and pricing scheme
DSP (improving upon
DRP ) is the re-source ratio between the requested node and link resources,henceforth denoted by ρ = c/b .In general, we will assume that requests arriving in anonline fashion have to be immediately embedded or rejectedby the provider. In order to successfully embed a virtualcluster, the provider has to fulfill all its specifications.
3. PRICING SCHEME
The proposed specification-dependent pricing scheme
DSP is based on a unit price for computation, henceforth de-noted by p c , as well as a unit price for communication (i.e.,bandwidth), henceforth denoted by p b . Ideally, for a vir-tual cluster request with a per-VM computational demand c and a per-VM bandwidth demand b , a customer should be charged according to the resource proportions, e.g. P ideal = n · ( c · p c + b · p b )However, compared to a dominant resource pricingscheme, this solution can result in a lower income at theprovider, especially if requests are highly heterogeneousleading to a higher fragmentation. While this income losscould be compensated by increasing the unit prices p c , p b ac-cordingly, one has to be careful not to punish customers withan ideal resource ratio ρ = 1, who would prefer providersoffering DRP in this case. To solve this problem, in thefollowing, we propose to add a small charge for customerswith a resource ratio ρ (cid:54) = 1.But let us first revisit the DRP scheme given our nota-tion. In
DRP , a customer who requests a virtual cluster
V C ( n, c, b ), with relatively lower resp. higher computationrequirements compared to the communication requirement,is forced to upgrade the request to the next larger templatefor both resources. The corresponding formula for the DRP scheme is P DRP = n · [max { c, b } · ( p c + p b )]In order to bridge the difference between P ideal and P DRP ,we propose the following demand specific pricing scheme
DSP which introduces an extra fee for requests with an un-balanced resource ratio ρ . In this paper, we will assume alinear dependency between the extra cost and ρ , althoughother dependencies (e.g., quadratic) could also be expressedin our model. This decision is based on the assumption thatmore skewed requests are more likely to generate fragmen-tation. In summary, DSP computes the virtual cluster priceas follows: P DSP = n · ( b · p b + c · p c ) + (cid:26) ( c − b ) · p b · λ b , if c ≥ b ( b − c ) · p c · λ c , elsewhere λ c , λ b ≥ λ c , λ b = 1 implies that P DSP = P DRP . Lowerweights result in savings for the customers, and λ c , λ b = 0implies P DSP = P ideal . Given that the customers have a goodunderstanding of their specific requirements in terms of com-putation and communication—a reasonable assumption aswe argue—this pricing scheme leads to a higher providerprofit, and in a competitive market, the extra income com-pared to DRP is shared with the customers.Let us elaborate on the weighing factors λ c and λ b . Ingeneral, the factors should depend on the amount of embed-ded virtual requests as well as the current resource demandand supply. If the provider has a good estimation of thevirtual clusters that will be requested, the values can becomputed ahead of time; otherwise, the factors may be esti-mated over time, see also Section 5 for a discussion. Givena difference of ∆ between the provider profit under DRP for upgraded and non-upgraded requests, the extra incomegenerated by the lower resource consumption of the non-upgraded requests could be evenly distributed over requestsrequiring more of either one of the two resources. (Recallthat the price of requests with ρ = 1 will not change.) Thecalculation for λ b in a scenario with N virtual machines forwhich c > b and with expected requirements E ( c ) and E ( b ),is given by N · ( E [ c ] − E [ b ]) · p b · (1 − λ b ) = ∆ / ost RackAggregation Switch ToR SwitchPod Core Switch Figure 1: Fat-tree datacenter topology.
The factor λ c can be computed similarly. In both cases, c > b and b > c , a similar difference for E [ c ] and E [ b ] alsoleads to similar fees. This is fair, as one type of request onlygenerates more profit because of the other one.Also note that DSP keeps the desirable location inde-pendence of
DRP [2]. However, unlike
DRP , DSP isspecification-dependent, i.e., a customer only has to pay forwhat he or she specified.
4. EMBEDDING ALGORITHM
In order to fully exploit differences in the virtual clusterspecification and in order to maximize the resource utiliza-tion (and hence provider profit), a new embedding algorithmhas to be devised: the state-of-the-art virtual cluster em-bedding algorithm, Oktopus [3] (as well as its variants [6]),are based on an aggressive collocation strategy, which turnsout to be suboptimal in settings where requests can haveresource ratios ρ (cid:54) = 1.In the following, we propose Tetris , a virtual cluster em-bedding algorithm which leverages the virtual cluster spec-ification details. The algorithm is tailored toward fat-treedatacenter topologies (cf Figure 1), the standard architec-ture today. In a nutshell, hosts (or equivalently: servers)which are connected to the same top of rack (ToR) switch,constitute a rack. Racks connected to the same aggregationswitch form a pod. The fat-tree depicted in Figure 1 con-sists of two pods, containing three racks each; there are twohosts per rack.We will compare our embedding algorithm
Tetris to the
Oktopus algorithm [3].
Oktopus is designed to embed ar-bitrary virtual clusters efficiently and is not limited to anytemplates. Hence it can also directly be used as an embed-ding algorithm for
DSP , without any modifications. To findan embedding,
Oktopus traverses the different hierarchicallevels of the fat-tree. It tries to embed the virtual cluster onsingle hosts first, and if no solution is found, it continues onthe rack level. This process is repeated until a solution isfound or
Oktopus failed to find a solution over the entiresubstrate. As a result of this approach, the resulting em-beddings are dense and use low amount of bandwidth. Theproblem of such dense embeddings is that requests with aresource ratio ρ (cid:54) = 1 are collocated which wastes physical re-sources. Figure 2 ( left ) illustrates this point. For Oktopus , V C is embedded on the right three hosts. The residual ca-pacity in terms of VM slots on each host is 1 / V C , only utilize 50% of their bandwidth, buthave no remaining VM slots.
30 30 30 03 03 03 22 22 22 11 11 11
Oktopus Tetris
Figure 2: Embedding behavior of Oktopus andTetris. Six hosts are connected to a switch.Two
V C s are requested:
V C (9 , / , / and V C (9 , / , / . The numbers in the circles represent VMs of V C which are mapped to the correspondinghosts, the numbers in the squares represent VMs of V C . The core idea of our algorithm
Tetris is to distributeskewed
V C s over multiple hosts, without increasing thebandwidth costs compared to
Oktopus . Similar to
Ok-topus , Tetris also traverses the hierarchical levels (short: (cid:96) ) of the fat-tree, but instead of collocating as many
VMs ona single host as possible,
Tetris distributes the
VMs overphysical machines (short: p ) depending on the ratio of theresidual resources per host. This is described in Algorithm 1. Algorithm 1
Tetris
Require:
Fat-tree T , virtual cluster V C for (cid:96) ∈ { host( T ), rack( T ), pod( T ), root( T ) } do for v ∈ V C do
3: find p ∈ (cid:96) with highest ratio of residual resourcesafter embedding of v if ∀ v embedding found then return embedding6: return ⊥ In our example in Figure 2, using
Tetris results in adistributed embedding of both
V C s. While all resources onthe left three hosts are utilized, the right three hosts havespare capacities, both in terms of bandwidth and VM slots.Hence subsequent requests can more likely be accepted.Note that the current design of Tetris only considersthe bandwidth on the access level. Hence, it can fail tofind a feasible solution if the other layers of the fat-treeare oversubscribed. Therefore our current implementationtreats
Tetris as an extension to
Oktopus and falls back toregular
Oktopus behavior if no solution was found.
5. SIMULATIONS
In order to study the benefits and limitations of
DSP and
Tetris in different settings, we implemented a discreteevent simulator. As the pricing results also depend on theembedding algorithm, we study three combinations: we in-tegrated
DRP with
Oktopus , DSP with
Oktopus , and
DSP with
Tetris . To ensure a fair comparison, we use thesame parameters and methodology as in [3] and [2].
Requests.
The virtual cluster requests arrive accordingto a Poisson process with exponentially distributed dura-tions, chosen to induce a system load of around 80%. Bydefault, the mean size of a
V C is n = 49, c and b are cho-sen uniformly from { / , / , / } . The templates ( c, b ) of DRP are (1 / , / , (1 / , / , (1 / , /
2) and the customeris bound to select the next larger template for requests with (cid:54) = 1. For each parameter set, we request 80 k virtual clus-ters. To avoid artifacts related to the initially empty dat-acenter, we start evaluating our metrics after 10 k requests.The remaining values are omitted from the dataset. Physical Setup.
We model our datacenter as a three-layer fat-tree (Figure 1 illustrates a small fat-tree). 40 hostsform a rack, 40 racks form a pod. In total we have 10 pods.Given that each physical element has a capacity of 8 VM units, this leads to a total capacity of 128 k small VMs. Bydefault we assume that the links between the ToR switchesand the aggregation switches are oversubscribed by a factorof 4, while the links between the aggregation switches andthe core are not oversubscribed. Metrics.
Various works have used the acceptance ratioof an embedding algorithm in order to measure its perfor-mance. This metric however, is biased to prefer algorithmswhich accept a large number of small requests instead offewer bigger ones. Therefore, we decided to evaluate the sumof the embedded virtual resources in both dimensions: band-width and VM slots. A request
V C (10 , / , /
8) will havea resource sum of 10 for bandwidth and 20 for VM slots.Note that even though we will embed a V C (10 , / , /
4) for
DRP , the bandwidth sum remains 10, as the customer doesnot benefit from the over-provisioning. lllllllllllllllllllllllllllll . . . . Oversubscription Ratio V M S u m lllllllllllllllllllllllllllll lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll 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Figure 3: Embedded VM slots for Tetris with DSP( left ), Oktopus with DSP ( middle ) and Oktopuswith DRP ( right ) as a function of the oversubscrip-tion. Figure 3 shows the impact of the oversubscription factoron the embedded number of virtual machines. For all over-subscription ratios, we can observe that
Tetris with
DSP outperforms the other combinations, while
DSP is superiorto
DRP in combination with
Oktopus . While the differ-ences are small for an oversubscription factor of 1, we see anincrease of the difference with the oversubscription factor; itdiminishes after an oversubscription factor of 5, where theresults become stable.Naturally, we can only reap the full benefits of
DSP and
Tetris in highly utilized datacenters, as shown in Figure 4:While first marginal effects can be observed at a load of0 .
4, the benefits of
DSP are visible starting at 0 . Tetris at 0 .
6. The effects increase until a loadof 1. Given that highly utilized datacenters are a realitytoday and the key to provider benefits, these results areencouraging.To analyze the benefit of the pricing model, we considerour default scenario: The mean resource sum for
DSP with
Oktopus is 15% higher than for
DRP with
Oktopus . Thismeans that the amount of concurrent active guarantees is llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll . . . . . Load V M S u m llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll 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TetrisOktopusDRP0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Figure 4: Embedded VM slots for Tetris with DSP( left ), Oktopus with DSP ( middle ) and Oktopuswith DRP ( right ) as a function of datacenter load.
15% larger. Using
Tetris with
DSP yields another 5%improvement, resulting in a total benefit of 20%. Similarnumbers apply for the bandwidth resource sum.Assuming p b = p c and a uniform distribution of acceptedrequests (i.e., an equal amount of embedded VM s of each( c, b ) tuple), inserting the 20% as a ∆ in Section 3 leadsto savings of 27% for customers with skewed requests. Thecorresponding values of λ c and λ b are 1 /
6, i.e., customershave to be charged for about 17% of the resource differenceto
DRP s templates in order to keep the revenue for theprovider constant.
6. CONCLUSION
This paper has presented the first specification-dependentpricing scheme for virtual clusters, the standard abstrac-tion of cloud applications today. Together with the pricingscheme, we also developed a new virtual cluster embeddingalgorithm, which may be of independent interest. Our ap-proach can easily be combined with interfaces which trans-late high-level customer goals into virtual cluster require-ments and compute resource combinations, such as [5].We find that the proposed specification-dependent pric-ing can increase the social welfare, leading to savings of upto 25% compared to
DRP . In fact
DSP enables customerto have guaranteed application performance while they onlyneed to pay for the resources they use, including a smallextra fee. Moreover, we find that
Tetris distributes vir-tual clusters with skewed resource requirements over severalhosts and therefore embeds 5% more virtual resources than
Oktopus .In our future research, we want to extend the
DSP schemeby a spot market to deal with more volatile traffic patterns.
7. REFERENCES [1] B. Hindman et al. Mesos: a platform for fine-grainedresource sharing in the data center. In
NSDI , 2011.[2] H. Ballani, P. Costa, T. Karagiannis, and A. Rowstron.The price is right: towards location-independent costsin datacenters. In
HotNets , 2011.[3] H. Ballani et al. Towards predictable datacenternetworks. In
SIGCOMM , 2011.[4] J. C. Mogul and L. Popa. What we talk about when wetalk about cloud network performance.
CCR , 2012.[5] V. Jalaparti et al. Bridging the Tenant-Provider Gap inCloud Services. In
SoCC , 2012.[6] D. Xie, N. Ding, Y. C. Hu, and R. Kompella. The only con-stant is change: incorporating time-varying network reser-vations in data centers.