Author’s Accepted Manuscript

Cloud Based Video-on-Demand Service ModelEnsuring Quality of Service and Scalability

Carlos Barba-Jimenez, Raul Ramirez-Velarde,Andrei Tchernykh, Ramón Rodríguez-Dagnino,Juan Nolazco-Flores, Raul Perez-Cazares

PII: S1084-8045(16)30086-8DOI: http://dx.doi.org/10.1016/j.jnca.2016.05.007Reference: YJNCA1649

To appear in: Journal of Network and Computer Applications

Received date: 7 September 2015Revised date: 29 February 2016Accepted date: 10 May 2016

Cite this article as: Carlos Barba-Jimenez, Raul Ramirez-Velarde, AndreiTchernykh, Ramón Rodríguez-Dagnino, Juan Nolazco-Flores and Raul Perez-Cazares, Cloud Based Video-on-Demand Service Model Ensuring Quality ofService and Scalability, Journal of Network and Computer Applications,http://dx.doi.org/10.1016/j.jnca.2016.05.007

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Cloud Based Video-on-Demand Service Model Ensuring Quality of Service andScalability

Carlos Barba-Jimeneza, Raul Ramirez-Velardea,∗, Andrei Tchernykhb, Ramon Rodrıguez-Dagninoa, JuanNolazco-Floresa, Raul Perez-Cazaresa

aTecnologico de Monterrey, Campus Monterrey, Ave. Eugenio Garza Sada 2501, Monterrey, N.L., Mexico, 64849bCICESE Research Center, Carretera Ensenada-Tijuana 3918, Ensenada, B.C., Mexico, 22860

Abstract

Increasing availability and popularity of cloud Storage as a Service (STaaS) offers alternatives to traditional on-linevideo entertainment models, which rely on expensive Content Delivery Networks (CDNs). In this paper, we present anelastic analytic solution model to ensure Quality of Service (QoS) when providing Video-on-Demand (VoD) using severalthird party elastic cloud storage services. First, we individually gather cloud storage start-up delays, and characterizethem to show that they are heavy-tailed. Then, we perform a meta-characterization of these delays using PrincipalComponent Analysis (PCA) to create a characteristic cloud delay trace. By using different estimation techniques ofthe Hurst Parameter, we demonstrate that this new trace (also heavy-tailed) exhibits self-similarity, a property notsufficiently studied in cloud storage environments. Finally, we pursue stochastic modeling using different heavy-tailedprobability distributions to derive prediction models and elasticity parameters from the cloud VoD system. We obtaina stochastic self-similar model and compare it with trace based simulation results by testing different heavy-tailedprobability distributions, meta-cloud elasticity values and Hurst parameters. Since our approach optimizes QoS, weguarantee a specific video start-up delay for a number of arriving clients. This is a strong commitment for a VoD service,because traditional cloud approaches often focus on a best-effort paradigm optimizing performance, cost, and bandwidth,among other parameters.

Keywords: Video-on-Demand, Cloud computing, Elasticity, Heavy-tails, PCA, Self-similarity.

1. Introduction

Nowadays, the cloud paradigm has become increasinglypopular, offering new services and products every year.The concept has reached areas beyond traditional IT envi-ronments, research, software development, and even entire5

business models. Providers such as Amazon offer elasticcomputing and cloud Storage as a Service (STaaS) com-mercially. These services have increased interoperability,usability and reduced cost of application hosting, contentstorage and delivery (Buyya et al., 2010). These condi-10

tions open the door for creating new services that can sat-isfy existing and future user demands. This is especiallyimportant if one considers the trends of IP traffic reportedin Cisco (2013), where it is shown that Video-on-Demand(VoD) traffic will be tripled in 2017 with rising mobile15

content consumption (Passarella, 2012).VoD and online video content services are generally

supported by a centralized delivery architecture based onprivate or rented servers with fixed costs and little flex-ibility (Buyya et al., 2009). Such a model poses a chal-20

lenge, since predicting the user demand erroneously could

∗Corresponding authorEmail address: rramirez@itesm.mx (Raul Ramirez-Velarde)

cause performance bottlenecks with an under-estimation,and high costs with an over-estimation. The model has tobe adapted to include a Content Delivery Network (CDN),usually operated by a third party in multiple external sites25

(Buyya et al., 2009). CDNs have a central entity that canenforce Quality of Service (QoS) levels, but this comes ata non-negligible financial cost (Passarella, 2012).

There are Peer-to-Peer (P2P) alternatives, but rarelyprovide guaranteed services (Passarella, 2012). They are30

used primarily in live streaming, where they help withflash crowds that need to access certain content at thesame time (Mansy and Ammar, 2011). This is not alwaysthe case in a VoD service. Now, the CDN model is stillthe most prevalent, with services like Akamai. The recent35

P2P propositions in Thomas et al. (2015) have included ahybrid cloud component to facilitate video streaming bytaking advantage of characteristics from both technologies,but only focus on a best-effort approach to QoS.

There are third party services (e.g. YouTube, Vimeo,40

etc.) for delivering video content. However, even withlarge infrastructures behind, they only offer best-effortQoS. It makes them not suitable for all businesses andentertainment conditions.

STaaS can be used as an alternative, with some com-45

mercially available services that use characteristics and ad-

Preprint submitted to Journal of Network and Computer Applications May 11, 2016

vantages of the cloud, in a similar manner as proposedunder the MetaCDN project (Broberg et al., 2009). Theauthors describe characteristics of the model, but left outdetails of the algorithms. The described statistical analy-50

sis is also limited for accurate predictive models. Our workhas a similar motivation.

We extend the preliminary work presented in Barba-Jimenez et al. (2014) by widening the scope of our studyand the problem definition. We include new parameters55

and characteristics to the proposed end-to-end VoD ser-vice. Furthermore, in this paper, we consider the deriva-tion of the different stochastic models for predicting usercapacity under certain QoS level and start-up delay takinginto account the self-similarity property of the Character-60

istic Cloud Delay Trace (CCDT), and elasticity character-istics of the cloud. Additionally, we compare and evalu-ate the model and uncertainties of its parameters againstsimulation results. These aspects were not fully elucidatedneither in Broberg et al. (2009) nor in Barba-Jimenez et al.65

(2014).In this paper, we use third party cloud services to cre-

ate a meta-VoD service (similar to MetaCDN) using agateway as suggested in Islam and Gregoire (2012). Thisgateway creates a CDN like functionality sitting in a layer70

above the clouds. It takes into account some of the mainchallenges of VoD content delivery, namely, response time,and start-up delay.

As a metric for the meta-VoD service quality, we usestart-up delay. We take into account the abandonment75

rate described in Krishnan and Sitaraman (2012), wherethe authors found that VoD clients start leaving the serviceafter a start-up delay of 2000ms (milliseconds), losing 5.8%of users for each additional second. This delay time TDincludes all network times, server times, and additional80

overheads.We propose a methodology to model and analyze stor-

age cloud delays, considering their statistical characteris-tics, and elasticity. Then we develop a meta-VoD elas-tic model that estimates the number of users that can be85

served for a given QoS and start-up delay time. This modelalso uses self-similarity and heavy-tail properties, followingRamirez-Velarde et al. (2013) and Ramirez-Velarde andRodrıguez-Dagnino (2010).

We provide background of our work and introduce an90

elasticity concept in Section 2. We discuss related work inSection 3. Then, in Section 4, we present the basic solu-tion model. Section 5 includes a detailed statistical analy-sis regarding real cloud data delay traces. It includes thedetermination of heavy-tails. We characterize real cloud95

data using statistical analysis, determine the heaviness ofeach individual cloud delay time tails and then reduce di-mensionality of these data sets using Principal ComponentAnalysis (PCA). We provide a meta-characterization ofthe individual clouds with the CCDT. The objective is to100

simplify the model for the delay time TD, which enables usto make predictions of the probability of successful serviceunder a certain threshold of abandonment rate. Section 6

introduces the concept of self-similarity and different esti-mations using the CCDT. Additionally, the self-similarity105

and elasticity are included to derive delay stochastic mod-els using sub-exponential probability distributions. Sec-tion 7 validates the models by experimentation. Sections8 and 9 describe the results and conclusions.

2. Background110

2.1. Cloud Computing

The cloud is defined as a model for enabling ubiquitous,convenient, on-demand network access to a shared pool ofconfigurable computing resources (e.g., networks, servers,storage, applications, services) that can be rapidly provi-115

sioned and released with minimal management effort andservice provider interaction. Cloud computing has threeservice models: Software as a Service (SaaS), Platform asa Service (PaaS), and Infrastructure as a Service (IaaS)(Mell and Grance, 2009).120

Cloud providers offer service level agreements (SLAs),which guarantee a level of QoS. Resource usage is moni-tored, controlled and reported, providing transparency forboth the provider and consumer (Espadas et al., 2013).This makes the idea of using the existing third party cloud125

services for content distribution very attractive. Payingonly for storage and computing, instead of having a po-tentially expensive contract with one CDN or an under-provisioned private server.

2.2. Cloud Elasticity130

One of the main characteristics of cloud computing isthe pay-per-use model. In order to provide metered ser-vices and resources under SLAs, the cloud providers mustbe able to match the resource demand with the resourceoffer as close as possible. Elasticity can be defined as the135

degree to which a system is able to adapt to workloadchanges by provisioning and de-provisioning resources inan autonomic manner, such that at each point in time theavailable resources match the current demand as closelyas possible (Herbst et al., 2013).140

In real scenarios, clouds are not perfectly elastic (Breb-ner, 2012). The infrastructure cannot respond instantly tosudden, significant increases in demand. There is a delaybetween the time when resources are requested, and whenthe application starts running.145

Elasticity has been studied in several works, includingAlmeida et al. (2013), Costa et al. (2013), Herbst et al.(2013) and Kaur and Chana (2014), for frameworks con-sidering costs, QoS, under/over provisioning and task ex-ecution. Ideally, there would be an external way of mea-150

suring or polling a measure of elasticity at any given time.However, obtaining these values from outside the cloudblack-box is not easy.

We denote this elasticity metric as ξ, where 0 < ξ ≤ 1.In this definition, 1 describes a 100% elastic cloud system,155

where the resources always match the demand in every

2

Cloud 1Cloud 1

GATEWAY

User n-1

QoS Aware Redirector

Asynchronous Resource Discovery

Asynchronous Resource

Monitoring

Redirection Logic

Provider Statistics

Probing Messages

Monitoring Messages

Content Requests

Content Address

User 1

User n

.

.

.

.

.

.

Video Content

Video Content

Internet

Cloud mCloud mVideo

Content

Video Content

Figure 1: VoD System using Third Party Clouds

instant in time. The proposed ξ metric is similar to theprecision of scaling up described in Herbst et al. (2013).

3. Related Works

We address the video CDN based on the cloud. In160

Broberg et al. (2009), the authors present the price com-parison of delivering content through a CDN versus dif-ferent cloud providers. The traditional CDN model is themost expensive in TB data/month, while cloud and cloudCDN options come as the cheaper alternatives. The au-165

thors presented interesting points related to QoS provi-sions. However their proposal is vague for a proper math-ematical setting.

In a recent work, the use of cloud CDN-like function-ality has also been reported (Guan and Choi, 2014). How-170

ever, it is aimed at minimizing bandwidth and cost inthe content placement problem (from a provider point ofview). In contrast, we consider the latency and QoS asuser centric criteria.

Additionally, on the topic of CDN modeling, in Pathan175

and Buyya (2009), the authors explore resource discoveryand request redirection in a multi provider content deliverynetwork environment. They show that CDNs evolve as asolution for Internet service degradations and bottlenecksdue to large user demands to certain web services. They180

address some of the internal problems that CDN providersface, like the break down of system locations, increase ofutilization rates, over-provisioning and external resourceharnessing to satisfy a certain SLA. The proposal is tointerconnect a constellation of CDNs that collaborate for185

short or long periods of time to handle the different work-load situations. This constellation uses a load distributionscheme with a request redirection and a mediator or coor-dinator agent that redirects load according to the workloadof the different CDNs.190

In Qi et al. (2012), the authors describe a QoS awarecomposition method supporting cross-platform service in-vocation in cloud environments, which explores a web ser-vice composition attaining a QoS optimal solution.

In Calheiros et al. (2012), a coordinator for scaling elas-195

tic applications across multiple clouds is used. The mainfocus is in elastic web applications, where the applicationcharacteristics and usage in the cloud are better known(although provisioning is still a challenge). The authorsdo not address content delivery, like a VoD service, since200

the application characteristics of a web application andcontent storage in the cloud have different behavior. How-ever, it does give some ideas to take into consideration forour work. We also take into consideration previous workrelated to VoD specific topics like the specification of an205

integrated QoS model for VoD applications (Sujatha et al.,2007).

4. Cloud Based VoD Service Solution Model andProblem Defintion

In this paper, we address a cloud based CDN-like VoD210

service. Our solution model uses the concept of peeringCDNs, where several content delivery networks cooperateto fulfill various requests. In our case, the cooperatingCDNs are the different clouds without the concepts of au-thoritative rights. Our model works with STaaS and uses215

IaaS for required computing. The solution model consistsof the following main components:

1. Asynchronous Resource Discovery: Since each cloudprovider operates individually, this module keeps trackof available resources.220

2. Asynchronous Resource Monitoring: This moduletakes care of probing the different providers.

3

3. QoS Aware Resource Redirector: This module is incharge of analyzing the information available fromthe clouds and redirecting the load to the best re-225

source location and provider.

Figure 1 shows the basic components of the solutionmodel, with details of the gateway and data connectionsflows. User requests go through the gateway, which hasthe redirection and resource monitoring logic. The gate-230

way gives back an address of redirection for the content toone of the cloud providers. Here, the various cloud storageproviders are working in a similar manner as the ContentDistribution Inter networking model, in which the gate-way considers the clouds and their networks as black-boxes235

(Pathan and Buyya, 2009).It differs from the main model because cloud providers

usually do not have mechanisms that will allow peering,and there is no central entity or supervisor with access tointra cloud information. One of the main challenges is to240

work without knowing the request and response loads ofeach inter cloud networks in real time, which is essentialfor the peering CDN scheme and algorithms (Pathan andBuyya, 2009). In order to overcome these limitations, wemake conclusions based on the response or start-up delay.245

We use the total delay times, since they can be monitoredand discovered from outside of the black-boxes. Addition-ally, our assumptions are based on the published requestsper second statistics from some cloud providers like Ama-zon (Barr, 2012).250

To determine how many users the service can handleunder a maximum delay time, we have to take into consid-eration the abandonment rate times (Krishnan and Sitara-man, 2012). Once we make predictions about users andsystem scalability, the problem of the redirector is to min-255

imize the delay time that the end user has when connectingto the final cloud provider, taking into consideration theredirection time caused by the decision making time in thegateway. In addition, the downtime status and QoS levelsof each provider are aggregated to the model parameters.260

The delay time TDij of the user i to access the contentof a certain provider j is determined by:

TDij = Trij + Tnij + TOg, (1)

where Trij is the response time from the cloud storage, TOgis the delay time in the gateway caused by the redirectionoverhead, and Tnij is the network time the request takes to265

travel from client i to cloud j. We follow a simple schemeto minimize the redirection time and cost by using thefollowing objective function (similar to Pathan and Buyya(2009)):

minn∑i=1

m∑j=0

Rc(i, j)SijCjQj . (2)

Rc = TDij if the cloud provider does not reject re-270

quests, otherwise Rc = ∞. Sij takes a value from theclosed interval [0,1] according to how geographically close

they are located. Cj is the completion rate of the providerj and can take a value in [0,1], and finally Qj is the qualityof service that provider j has. It can take a value in [0,1]275

as well.The solution model from Eq. (2) does not consider the

stochastic nature of the response and network times or itsprobability distribution. Considering the probabilistic na-ture of TDij , taking into account viewer behavior (Krish-280

nan and Sitaraman, 2012), and the 2000ms abandonmentstart time θ as a measure of a successfully redirected re-quest, we create a new model for a client i connected tocloud j using the following premise:

P (TDij > θ) < ϕ, (3)

where ϕ is the probability that the delay time is over the285

θ limit (2000ms in our case). Using Eq. (3) as a base, andassuming that TDij is heavy-tailed, we can model it usingPareto, Lognormal or Weibull distributions. However, wefirst provide a statistical analysis of different real life clouddelay times to use the best fitted probability distribution.290

5. Cloud Data Analysis

We use real cloud delay times to have a good estima-tion of the extreme values and distribution. These delaytimes are obtained using the PRTG Network Monitor fromPaessler (Paessler, 2014). The measurements are taken295

from an Amazon EC2 instance (small) located in N. Vir-ginia, acting as a client, which is connected to differentcloud providers to gather the total delay time (consistingof disk access times, memory access times, and networktimes) required to retrieve a 65 Kilobyte file (represent-300

ing a worst case video frame size). These measurementshave been taken every 60s over a period of 40 days for 6cloud storage providers. In Table 1, we see their descrip-tive statistics.

Table 1: Cloud Providers Statistics

ProviderMeanDelay(ms)

MaxDelay(ms)

Std De-viation(ms)

Kurtosis

Google 65.74 3425 97.8 170GoGrid 22.88 11768 175.1 959.6Rackspace 118.17 8790 101.2 1168CloudFront 37.26 3001 86.6 152.4S3 USA 188.24 27059 284.6 2725.9S3 EU 652.48 22653 411.4 386.66

In Figure 2, we see an example of a time series (which305

we call trace) for the Cloudfront delay times.The bursty behavior of the delay times is clearly ob-

served. However, to make a conclusion, we have to lookat the distribution of the values. Figures 3 , 4 and 5 showthe histograms for each of the clouds. They reveal de-310

lay times that are several orders of magnitude above themean. In addition, the high kurtosis values presented in

4

0 1 2 3 4 5

x 104

0

500

1000

1500

2000

2500

3000

3500

Sample

De

lay T

ime

(m

s)

Time Series for CloudFront Cloud delay times in ms

Figure 2: Time Series for CloudFront Delay Times

Table 1 could indicate heavy-tailed distributed data (De-Carlo, 1997). To confirm it, more tests are conducted.

Taking a look at the definition of heavy-tails (Cooke315

and Nieboer, 2011; Crovella et al., 1998; Willinger et al.,1998), let X be a random variable with cumulative distri-bution function (CDF) F (x) = P [X ≤ x] and its comple-ment F (x) = 1−F (x) = P [X > x]. F (x) is heavy-tailed ifF (x) ∼ cx−α, where c is a positive constant and α is gen-320

erally 0 < α < 2. By extending the range to 0 < α < ∞,we obtain the sub-exponential distributions class, which isalso considered as having heavy-tail distributions (Crov-ella, 2001).

An estimation of the tail index is usually provided by325

parametric methods, where a cut off point x0 value is de-termined. The tail index is then calculated using Log-LogComplementary Functions (Cirillo, 2013; Crovella, 2001),or Hills Estimators (Adler et al., 1998; Borak et al., 2005;Resnick and Rootzen, 2000; Resnick, 1998, 1997; Willinger330

et al., 1998). However, Crovella and Taqqu (1999) pro-pose a method based on scaling estimation, which is non-parametric. It produces a single α estimate and has beenproved to be effective even if the empirical data does notexactly follow a Pareto or power law in all curve sections335

of its distribution. We present the results of the tail indexα estimations for the cloud data sets in Table 2

Table 2: Cloud Delay Times Distribution Tail Index Estimations

Cloud α EstimateCloudFront 1.445Rackspace 1.472GoGrid 0.697Google 1.265S3usa 1.138S3eur 1.758

All cloud traces exhibit heavy-tailed behavior accord-ing to their tail index calculations. Additionally, if we take

0 500 1000 1500 2000 2500 3000 35000

1

2

3

4x 10

4 Google Cloud Histogram

Delay Time (ms)

Fre

qu

en

cy

0 1000 2000 3000 4000 5000 6000 7000 8000 90000

1

2

3x 10

4 RackSpace Cloud Histogram

Delay Time (ms)

Fre

qu

en

cy

Figure 3: Cloud Delay Histograms I

0 500 1000 1500 2000 2500 3000 35000

1

2

3x 10

4 CloudFront Cloud Histogram

Delay Time (ms)

Fre

qu

en

cy

0 2000 4000 6000 8000 10000 120000

2

4

6x 10

4 GoGrid Cloud Histogram

Delay Time (ms)

Fre

qu

en

cy

Figure 4: Cloud Delay Histograms II

into consideration that their histograms are not symmet-340

rical, and the high variability, we conclude that the datacannot be modeled by a symmetric probability distribution(such as a Gaussian) or a short-term memory process likea Markov one (Ramirez-Velarde and Rodrıguez-Dagnino,2010).345

Now, in order to generate a single model of the VoDsystem, we have to select a cloud with the most represen-tative behavior. The various clouds have similar statisticsand histograms, but have different kurtosis, means, etc.We deal with the existence of several cloud data sets as a350

problem of multidimensionality. We consider each cloudas a dimension for the total delay time. Therefore, weuse Principal Component Analysis (PCA) to determine aCharacteristic Cloud Delay Trace (CCDT), as in Ramirez-Velarde et al. (2013), to capture as much of the variability355

of all clouds as possible. The goal is to reduce dimension-ality to at most 2 components, from our available 6, to

5

0 0.5 1 1.5 2 2.5 3

x 104

0

1

2

3

4x 10

4 S3 USA Cloud Histogram

Delay Time (ms)

Fre

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en

cy

0 0.5 1 1.5 2 2.5

x 104

0

2000

4000

6000

8000

10000S3 EUR Cloud Histogram

Delay Time (ms)

Fre

qu

en

cy

Figure 5: Cloud Delay Histograms III

Figure 6: Scores vs Components vs Observations Plot from the PCAprocedure

generate a single trace that can be analyzed and used formodeling.

To find the Principal Components (PCs), we build a360

correlation matrix using the delay traces for each cloud.Traces are used as columns to indicate the dimensions with∼50k different observations. We subtract the overall meanµ from each element. We use the mean of all values, not ona per cloud basis (180.83 ms). Then we use Pearsons cor-365

relation coefficient, since all observations are in the samems units.

Figure 6 shows a 3D representation of the scores againstobservations and components from the PCA procedure.The resultant PCs, eigenvalues and variability are shown370

in Table 3.We select m components that will keep most of the

variability present in p variables, with m� p for a dimen-sionality reduction. From Table 3, we see that selecting 1

PC will give us ∼ 50% of the original data variability, but375

if we select 2 PCs we have ∼ 81%. After that, the percent-age of added variability of each extra PC is < 10%. Underthese conditions, choosing 2 PCs give us significantly moreinformation than the other 4, so the CCDT is generatedby using PC1 and PC2.380

Using these PCs, we reconstruct a single trace that hasthe same variance that the whole set of cloud delay timetraces σ2

original = 98894.582. The reconstruction also hasto take into account the subtracted overall mean µ whiledoing the PCA procedure. To reconstruct it, we start with385

the following:

E[PC1] = 0 E[PC2] = 0 (4)

Var[PC1] = λ1 Var[PC2] = λ2, (5)

where E is the expected value, Var is the variance, and λiis the eigenvalue for the corresponding PCi. We proposeto create a new variable C :

C = PC1 + PC2. (6)

The variable C has the following expected value, vari-390

ance, and standard deviation:

E[C] = E[PC1] + E[PC2] = 0 (7)

Var[C] = Var[PC1] + Var[PC2] = λ1 + λ2 (8)

σc =√λ1 + λ2. (9)

Then, to create the final reconstructed trace X, whichmust have a σ2

X = σ2original = 98894.582, we use the fol-

lowing transformation (taking into account µ):

X = µ+σoriginal ∗ C√

λ1 + λ2. (10)

Obtaining the expected value and variance for X, we395

get:

E[X] = E[µ] +σoriginal√λ1 + λ2

E[C] = µ (11)

Var[X] = Var[µ] +σ2original

λ1 + λ2Var[C] = σ2

original. (12)

The variance is the same in our new reconstructed traceX as in the σ2

original, evidenced by Eq. (12) and numeri-cally tested. This transformation and properties hold formore than 2 PCs, they have to be added to Eq. (6) and400

their respective eigenvalues to Eq. (10). We apply thetransformation to each row of the PC1 + PC2 to obtainthe Characteristic Cloud Delay Trace (CCDT). We see theresult in Figure 7. The CCDTs behavior is similar to the

6

Table 3: PCA ResultsVariables PC1 PC2 PC3 PC4 PC5 PC6Eigenvalue 169231.8 80962.5 30646.5 10249.8 9555.8 7490.3Variability(%) 54.92 26.27 9.94 3.32 3.10 2.43Cumulative (%) 54.92 81.2 91.14 94.47 97.57 100

0 1 2 3 4 5

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10000

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De

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(m

s)

Reconstructed Charcateristic Cloud Delay Times (CCDT) trace

Figure 7: CCDT Trace

0 3000 6000 9000 12000 15000 180000

1000

2000

3000

4000

5000

6000

7000

8000

9000Reconstructed Characteristic Cloud Delay Times (CCDT) Histogram

Delay Time (ms)

Fre

qu

en

cy

Figure 8: CCDT Histogram

delay times presented in Figure 2. Figure 8 shows the405

histogram for the new reconstructed CCDT.Calculating the tail index α, as in Crovella and Taqqu

(1999), we obtain α ∼ 1.7. This means that the CCDTdata has a heavy-tailed distribution, which is not symmet-ric. Following Ramirez-Velarde and Rodrıguez-Dagnino410

(2010), we assume that the data cannot be modeled usingtraditional symmetric probability distributions and Markovprocesses, as with the individual clouds.

6. Self-Similarity

To characterize the cloud delay times, we have to take415

into account its probability distributions and statisticalproperties. From Park and Willinger (2000) and Lelandet al. (1994), we know that to analyze network perfor-mance and video traffic, we should consider the self-similarityof the data. Self-similarity in this context is a property420

that denotes that the data is bursty over a range of timescales. It contradicts the notion made in most traffic andservice models where exponential models are used, andburst modeling only holds for very limited range of timescales (Willinger et al., 1998).425

There are several, not equivalent, definitions for self-similarity. The most common one for data traffic flows innetworks establishes that a continuous-time stochastic pro-cess Y = Y (t), t ≥ 0 is self-similar, with a self-similarity orHurst parameter H, if it satisfies the following conditions430

(Willinger and Paxson, 1998).

Y (t)d= a−HY (t),∀ t ≥ 0,∀ a > 0,

and 0.5 < H < 1. (13)

The equality means that the expressions have an equiv-alent probability distribution. A process satisfying Eq.(13) can never be stationary, but it is assumed to have sta-tionary increments. The Hurst parameter is further stud-435

ied by Lobo et al. (2013), Kirichenko et al. (2011), Clegg(2006) and Abry and Veitch (1998). They present sim-ilar conclusions about values that indicate self-similarity(0.5 < H < 1).

6.1. Self-Similar nature of the CCDT440

The Hurst parameter H estimation is defined mathe-matically, however, it is not easy to measure it using realdata traces. Several Hurst parameter estimators, ratherthan just one should be used to avoid false conclusions(Clegg, 2006). It must be said that all estimators are vul-445

nerable when the data has a trend or a periodic component(Clegg, 2006; Kirichenko et al., 2011).

In this paper, we use the data filtering techniques de-scribed in Clegg (2006) (Linear de-trend and Poly de-trend) and nine methods to estimate the Hurst parame-450

ter: the R/S (Rescaled/Range), aggregate variance, peri-odogram, boxed periodogram, Abry-Veitch method (Abryand Veitch, 1998), Whittle’s estimator, absolute moments,Higuchi’s Method, and Peng’s variance of residuals. Moreinformation on each individual estimator can be found in455

Clegg (2004). Table 4 summarizes the results.

7

Table 4: Hurst Parameter EstimationsEstimator H(Raw) H(LDet) H(PolyDet)R/S 0.78 0.78 0.79Absolute Moments 0.80 0.79 0.78Aggregated Variance 0.79 0.79 0.77Box Periodogram 0.68 0.68 0.68Higuchi 1.00 0.80 0.78Peng’s Var Residuals 0.79 0.79 0.79Periodogram 0.67 0.67 0.67Whittle 0.80 0.80 0.79Abry-Veitch 0.82 0.82 0.82

We can conclude that (for the CCDT) 0.67 < H <0.82. This is a definite indication of self-similarity.

6.2. Self-Similar Client Delay Model

Now, when the self-similar nature of the data has been460

established, we present a model to determine the numberof clients n for a given a maximum delay time θ. Theseclients have to be handled concurrently by a VoD serviceresiding on a cloud represented by the CCDT. Since weare simplifying the multivariate nature of multiple clients465

connecting to multiple clouds to one single cloud, we re-define the TDij delay time that the user i needs to accessthe content in a provider j as TDi.

We characterize TDi in the following manner. Let Yi(i = 1, · · · , n) be a discrete-time random process repre-470

senting the total cumulative delay for client i connectingto a video in a cloud. Let Xi = Yi − Yi−1 be the strictlypositive increment process. We find the client load n suchthat:

P [TDi > θ] = P [X1 +X2 +X3 + · · ·+Xn > θ] = ϕ. (14)

However, this model does not take into account the475

elastic nature of clouds (see Section 2.2), when they dy-namically scale capacity and available resources accordingto the demand from n clients. This paper introduces theelasticity ξ into the model under the assumption that thecloud is not perfectly elastic, this means a non-linear re-480

lationship between cloud resources and n clients or ξ < 1.Taking this into account for the right side of the inequality,we propose:

P [X1 +X2 +X3 + · · ·+Xn > θnξ] = ϕ. (15)

Now, let Yt = Zt be the delay time process for clientt. Let Zt be a self-similar process with E[Z0] = 0 and485

E[Z2t ] = σ2t2H . The accumulation process is then:

n∑i=1

Xi = Yn − Yn−1 + · · ·+ Y1 − Y0. (16)

Following Park and Willinger (2000), we know that thisprocess can be expressed as:

n∑i=1

Xid= nHZ1. (17)

Substituting the accumulation process from Eq. (17)into the model from Eq. (15), we obtain:490

P [X1 + · · ·+Xn > θnξ] = P [nHZ1 > θnξ] = ϕ. (18)

If we define a = θnH−ξ , we get

P [X1 + · · ·+Xn > θnξ] = P [Z1 > a] = ϕ. (19)

Zt can have different probability density functions (PDFs),such as Pareto (Type I), Lognormal or Weibull. Next sub-sections, deal with each one of them.

6.3. Pareto Distribution

Let us assume that Zt has a Pareto (Type I) PDF495

denoted by:

f(a) =α(A)α

aα+1, (20)

where A is the scale parameter (the lower bound at whichthe distribution starts), and α is the shape parameter,where 0 < A ≤ a and α > 0. The probability that Zt > a,also called the survival function or tail function, can be500

expressed in terms of its complementary CDF:

F = 1− F = P [Zt > a] =

(A

a

)α= ϕ. (21)

Substituting Eq. (19) and a into Eq. (21)

P [Z1 > a] =

(AnH−ξ

θ

)α= ϕ. (22)

Solving it for n, we get the number of clients using thePareto I distribution.

n =

(θϕ

1α

A

) 1H−ξ

. (23)

6.4. Lognormal Distribution505

Now assume that Zt has a Lognormal PDF denoted by

f(a) =1

aσ√

2πe−

(ln a−µ)2

2σ2 , (24)

where the two parameters µ and σ are the mean and stan-dard deviation, respectively. The survival function for alognormal random variable is

P [Zt > a] = 1− 1

2erfc

(− ln a− µ

σ√

2

)= ϕ. (25)

8

0 200 400 600 800 1000 1200 1400 1600 1800 20000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Delay Time (ms)

Cum

ulat

ive

prob

abili

ty (

p)

CCDT Empirical CDFLognormal FitWeibull FitPareto Fit

Figure 9: Lognormal, Pareto, and Weibull fit cdf’s against data trace cdf

The term erfc refers to the complementary error func-510

tion. Working with that survival function is difficult, espe-cially if we want to analytically solve the inequality for aparticular term. To help with that, we use the asymptoticupper bound presented in Liu et al. (1999)

lima→∞

sup1

ln a2lnP [Zt > a] ≤ − 1

2σ2. (26)

Solving for P [Zt > a] and substituting Eq. (19) into515

Eq. (26), we obtain

lnP [Z1 > a] = lnϕ ≤ − ln a2

2σ2. (27)

Now, substitute a into Eq. (27)

lnθ

nH−ξ≤ (−2σ2 lnϕ)

12 . (28)

Solving it for n, we get the number of clients using theLognormal distribution.

n ≤(e−(−2σ

2 lnϕ)12 +ln θ

) 1H−ξ

. (29)

Other option to manage the erfc in Eq. (25) is to520

use the tight and simple approximations for the erfc andinverse erfc found in Chiani et al. (2003), and denoted by:

erfc(x) ≤ 1

6e−x

2

+1

2e−

43x

2

(30)

inverfc(y) ≤√−ln(y). (31)

A final option is to apply a numerical approximationof the erfc for a specific ϕ and then solving for n.

6.5. Weibull Distribution525

Finally, assume that Zt has a Weibull PDF with a sur-vival function denoted by

P [Zt > a] = e(−aλ )k

= ϕ, (32)

where k > 0 is the shape parameter, and λ > 0 is the scaleparameter of the distribution. Substituting a and Eq. (19)into Eq. (32)530

θ

nH−ξ= λ(− lnϕ)

1k . (33)

Solving for n, we can get the number of clients usingthe Weibull distribution.

n =

(θ

λ(− lnϕ)1k

) 1H−ξ

. (34)

6.6. Heavy-Tail Fits

After defining the PDFs used for modeling, we need toget the distribution parameters by fitting the CCDT data.535

Figure 9 shows obtained CDFs versus empirical CDF fromthe CCDT. The fit for all three probability distributions isobtained using the maximum likelihood estimation (MLE)method. Table 5 shows the obtained fit parameter valuesfor each PDF using the MLE estimates.540

Table 5: PDF MLE fit parameters

Pareto I Lognormal Weibull

A = 459 ms µ = 5.51 λ = 313.71α = 3.388 σ = .81963 k = .99

7. Description of Experiments

The main objective of the experiments is to validatethe stochastic self-similar models defined in the previousSection. It requires a simulation of the arrival of n clientvideo requests to a cloud represented by the CCDT. The545

simulation determines the probability ϕ of exceeding thetolerance time θ for a number of clients n. These proba-bilities are then used to evaluate the proposed self-similarmodels.

Another objective is to empirically determine the elas-550

ticity parameter ξ described in Section 2.2 and the best fitfor the models.

9

The arrival of clients with heavy-tailed delays has tobe Poisson, so the aggregation process can be self-similar(Park and Willinger, 2000). Therefore, the simulation uses555

a Poisson process for the clients arrival over a 1s totalperiod, and delay times taken directly from the CCDTinstead of being simulated by a Markov process as in aclassic M/M/1 system. The λ is changed as the amountof n clients increases for each simulation.560

The simulation is fed with the client Poisson arrivalsand delay times. Output is the probability of exceedingthe maximum delay after sampling 500 random 1s periodsfrom the total simulation. The resulting ϕ’s and corre-sponding values for n are then fed into the analytical mod-565

els to make several evaluations. Additionally, 95% confi-dence intervals (CI) are calculated for the ϕ’s obtainedfrom the different n clients simulations.

For the Lognormal model, the erfc approximations de-scribed in Eq. (26), Eq. (30) and Eq. (31) are not as570

tight as expected and give preliminary results at least oneorder of magnitude larger than with simulation and otheranalytical models. So, we use a numerical approximationfor the erfc.

The obtained ϕ values used for evaluating the model575

are in the common range for SLAs, as seen in Google(2015).

8. Results

As previously discussed, an elasticity metric (ξ) is notpublicly available or easily measured for the commercial580

third party clouds used to create the CCDT. This promptedus to use several scenarios to mitigate the uncertaintyin our analytic model. Another parameter with uncer-tainty is the Hurst parameter that was set in a range0.67 < H < 0.82. Evaluations must be performed in order585

to determine the best approximation for each one.

8.1. The Elasticity Uncertainty

First, we have to analyze the impact of the uncertaintyon the elasticity ξ. Figure 10 shows results of simulationand modeling with four values of ξ (0.5. 0.6, 0.7, 0.8) and590

H = 0.82. It is clear that assuming a ξ = 0.5 flattens themodeling results, not approaching the simulation results.While ξ = 0.8 makes the models to over-estimate the num-ber of clients. The elasticity values ξ ∼ 0.7 perform better.The models obtain results closer to the simulation line.595

Figure 11 presents more detailed analysis. It showsthat elasticity values in the range of 0.65-0.68 approxi-mate results without significant under-estimating or over-estimating n.

8.2. The Hurst Parameter Uncertainty600

To understand the uncertainty of the Hurst Parameter,let us consider two scenarios with ξ = 0.68. We set H =0.71 and H = 0.74 (low and mid range values for H) toestimate n. Figure 12, in Log scale for better visualization,

shows results of simulation and modeling. These values do605

not approximate simulation results with good accuracy. Inour models, we set H = 0.82 (at the top range of possibleH values).

8.3. Evaluation and Discussion

From the results obtained in all scenarios, we can see610

that the Pareto model gives a very pessimistic predictionwith a clear lower bound. It gets far from the simulationresults with a ϕ > 0.01. This can be a result of the Paretofit not being adequate for the whole distribution of val-ues. It can also be a problem with the number of samples615

being < 106, which could limit extreme values empiricallygathered and described by this tail distribution.

The Lognormal model prediction is the second mostpessimistic. However, it does follow the simulation results,and can over-estimate if the model assumes a very elastic620

cloud. As seen in Figure 11, it establishes a lower boundprediction to the simulation throughout the different ex-cess probabilities (ϕ’s). This is a desired outcome sinceit allows to generate conservative modeling predictions,where no under-provisioning occurs in the video service625

with promises of serving more clients than it can.A similar assessment can be obtained from the Weibull

model results presented in Figure 11. The prediction comesvery close to the simulation results, with tighter results incomparison to the Lognormal model. However, it can give630

as over-estimation for different values of ξ, for ϕ < 0.007and ϕ > 0.017. This turns the Lognormal model with(H = 0.82 and ξ = 0.68) to be the closest one, it canbe used as a lower bound with respect to the simulationresults.635

However, the model does not follow the simulationtrends or even be within the CI. To obtain a better approx-imation, we take into account three principal components(PCs) for the CCDT instead of two.

The analysis and methodology are valid with more640

PCs. The Hurst parameter is still 0.67 < H < 0.82, andthe elasticity value is 0.6 < ξ < 0.7. Figure 13 shows themain results. The Lognormal model with µ = 5.51 andσ = .81963 (similar to the parameters with 2 PCs) followsthe simulation curve more closely, falling within the 95%645

CI.With this fully parametrized model, we make predic-

tions with less restrictive values of ϕ, and process moreclients per second for the VoD cloud service. Some ofthese predictions can be seen in Table 6. To get those pre-650

dictions in context of real cloud data and give them somevalidity, one can look at the public data from cloud storageservices like Amazon S3 as an example (Barr, 2013, 2012).It indicates that, in peak conditions, they were serving650,000 requests per second in 2012 and 1.1 million re-655

quests per second in 2013. So, the prediction model, witha little relaxation in the probability of not exceeding a de-lay threshold is close to the real data of a single massivecloud storage provider. However, their quality assurances

10

0.005 0.01 0.015 0.02 0.0250

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Probability of Exceeding max delay time (p)

Nu

mb

er

of

Clie

nts

(n

)

Simulation/Models Results H=0.82 Elasticity = 0.5

Simulation

Weibull Self−Similar Model

Pareto Self−Similar Model

Lognormal Self−Similar Model

95% CI For Simulation

(a) Simulation vs Models with ξ = 0.5

0.005 0.01 0.015 0.02 0.0250

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Probability of Exceeding max delay time (p)

Nu

mb

er

of

Clie

nts

(n

)

Simulation/Models Results H=0.82 Elasticity = 0.6

Simulation

Weibull Self−Similar Model

Pareto Self−Similar Model

Lognormal Self−Similar Model

95% CI For Simulation

(b) Simulation vs Models with ξ = 0.6

0.005 0.01 0.015 0.02 0.0250

1000

2000

3000

4000

5000

6000

7000

8000

9000

Probability of Exceeding max delay time (p)

Nu

mb

er

of

Clie

nts

(n

)

Simulation/Models Results H=0.82 Elasticity = 0.7

Simulation

Weibull Self−Similar Model

Pareto Self−Similar Model

Lognormal Self−Similar Model

95% CI For Simulation

(c) Simulation vs Models with ξ = 0.7

0.005 0.01 0.015 0.02 0.0250

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2x 10

4

Probability of Exceeding max delay time (p)

Nu

mb

er

of

Clie

nts

(n

)Simulation/Models Results H=0.82 Elasticity = 0.8

Simulation

Weibull Self−Similar Model

Pareto Self−Similar Model

Lognormal Self−Similar Model

95% CI For Simulation

(d) Simulation vs Models with ξ = 0.8

Figure 10: Simulation vs Models Scenarios with H = 0.82

are in uptime, while all other services are provided in a660

best-effort manner. Our cloud based VoD service modelcan give QoS assurances for start-up delay time.

9. Conclusions and Future Work

Using cloud computing storage services for efficient im-plementation of VoD and online video content demand is a665

new approach. The main idea is to use the CDN paradigmand adapt it to the challenges and advantages of cloudcomputing and storage.

We present an analytical model and describe the ele-ments necessary to create a CDN-like service in a logical670

layer above different third party public storage clouds. Weconclude that it can be based on a gateway redirector thataccepts requests from incoming clients and provides theoptimal cloud redirection based on a set of available met-rics.675

We propose to use video start-up delay to optimize theVoD cloud service and reduce the loss of customers. Thisallows us to treat each cloud as a black-box, with very littlevisibility. In order to make a proper redirection scheme,we propose a performance and scalability model based on680

real life cloud start-up delay data.Facing with overwhelming multidimensional informa-

tion, we perform a PCA of the multiple cloud data, andgenerate a Characteristic Cloud Delay Time Trace. Thistrace acts as a proxy. We show that it retains the same685

variance as the original cloud traces, and contains up to80% of the variability from all the data with 2 PCs. To-gether with simplification of the statistical analysis, it al-lows to model clouds as a single one maintaining importantstatistical characteristics. Under this PCA conditions, the690

Lognormal assumption provides a lower bound, but nottight to the simulation trends. We found that with 3 PCs,

11

0.005 0.01 0.015 0.02 0.0250

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Probability of Exceeding max delay time (p)

Nu

mb

er

of

Clie

nts

(n

)

Simulation/Models Results H=0.82 Elasticity = 0.65

Simulation

Weibull Self−Similar Model

Pareto Self−Similar Model

Lognormal Self−Similar Model

95% CI For Simulation

(a) Simulation vs Models with ξ = 0.65

0.005 0.01 0.015 0.02 0.0250

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Probability of Exceeding max delay time (p)

Nu

mb

er

of

Clie

nts

(n

)

Simulation/Models Results H=0.82 Elasticity = 0.66

Simulation

Weibull Self−Similar Model

Pareto Self−Similar Model

Lognormal Self−Similar Model

95% CI For Simulation

(b) Simulation vs Models with ξ = 0.66

0.005 0.01 0.015 0.02 0.0250

1000

2000

3000

4000

5000

6000

Probability of Exceeding max delay time (p)

Nu

mb

er

of

Clie

nts

(n

)

Simulation/Models Results H=0.82 Elasticity = 0.67

Simulation

Weibull Self−Similar Model

Pareto Self−Similar Model

Lognormal Self−Similar Model

95% CI For Simulation

(c) Simulation vs Models with ξ = 0.67

0.005 0.01 0.015 0.02 0.0250

1000

2000

3000

4000

5000

6000

7000

Probability of Exceeding max delay time (p)

Nu

mb

er

of

Clie

nts

(n

)

Simulation/Models Results H=0.82 Elasticity = 0.68

Simulation

Weibull Self−Similar Model

Pareto Self−Similar Model

Lognormal Self−Similar Model

95% CI For Simulation

(d) Simulation vs Models with ξ = 0.68

Figure 11: Detailed Simulation vs Models Scenarios with H = 0.82

12

0.005 0.01 0.015 0.02 0.02510

−4

10−2

100

102

104

106

108

Probability of Exceeding max delay time (p)

Nu

mb

er

of

Clie

nts

(n

)

Simulation/Models Results H=0.71 Elasticity = 0.68

Simulation

Weibull Self−Similar Model

Pareto Self−Similar Model

Lognormal Self−Similar Model

95% CI For Simulation

(a) Simulation vs Models with H = 0.71

0.005 0.01 0.015 0.02 0.02510

0

101

102

103

104

105

Probability of Exceeding max delay time (p)

Nu

mb

er

of

Clie

nts

(n

)

Simulation/Models Results H=0.74 Elasticity = 0.68

Simulation

Weibull Self−Similar Model

Pareto Self−Similar Model

Lognormal Self−Similar Model

95% CI For Simulation

(b) Simulation vs Models with H = 0.74

Figure 12: Simulation vs Models Scenarios with ξ = 0.68

0.01 0.015 0.02 0.0250

1000

2000

3000

4000

5000

6000

7000

Probability of Exceeding max delay time (p)

Nu

mb

er

of

Clie

nts

(n

)

Simulation/Models Results H=0.82 Elasticity = 0.65

Simulation

Weibull Self−Similar Model

Pareto Self−Similar Model

Lognormal Self−Similar Model

95% CI For Simulation

Figure 13: Simulation vs Models with CCDT using 3 PCs

the Lognormal model matches simulation results withinthe 95% CI.

We found that the cloud delay times can be modeled695

using heavy-tailed probability distributions, and they ex-hibit self-similarity. We reached this last conclusion bytaking advantage of different Hurst parameter estimatorsand data filtering techniques.

Self-similarity is a well established property of tradi-700

tional network communications, web traffic and video. Butthe role of self-similarity in cloud computing and modelingVoD cloud services has not yet been adequately addressedin the scientific literature. We propose a methodology thatallows us to obtain consistent values for the degree of self-705

similarity in clouds for video start-up delays. We expectthat it could be applied in other areas. However, furtherstudy is needed to analyze more cloud metrics that help

Table 6: Client (n/s) Predictions

Probability (TDi > θ = ϕ) ∼ Clients (n)0.05 19,7920.06 30,0750.07 43,7780.08 60,8730.09 82,7920.1 109,6290.11 141,9420.12 182,4650.13 230,2510.14 284,4440.15 350,4270.20 899,123

us to better understand QoS.We propose and evaluate a novel cloud scalability model710

(using three different heavy-tailed distributions) that takesthe self-similar and elastic nature of the cloud into accountto determine the amount of clients that can be served,maintaining a maximum delay time. The main result isthe prediction model for n clients using the Lognormal715

self-similar model that closely matches simulation results.Another contribution is an empirical measurement of theelasticity ξ of the cloud using different uncertainty scenar-ios.

We validate the assumptions and derivations through720

an evaluation of the best found model predictions againstthe known data of clients per second of real storage cloudproviders. These results help us to understand its elasticproperty for consumer entertainment applications. Thiscould improve under/over estimation of the number of725

clients and serve as a tool for providing SLA restrictionsother than uptime or best-effort.

13

However, further study is required for better under-standing the role of PCA and variability for the improve-ment of the CCDT and the model.730

Another direction for future work is to apply these con-cepts and stochastic self-similar models to improve the ef-ficiency of the user demand allocation in the VoD cloudbroker (gateway) taking into account the elasticity of theclouds, self-similarity and the tail data characteristics.735

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