On the Cost-QoE Trade-off for Cloud Media Streaming under Amazon EC2 Pricing Models

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1 On the Cost-QoE Trade-off for Cloud Media Streaming under Amazon EC2 Pricing Models Jian He, Yonggang Wen, Jianwei Huang,DiWu Department of Computer Science, Sun Yat-Sen University, China School of Computer Engineering, Nanyang Technological University, Singapore Department of Information Engineering, Chinese University of Hong Kong, Hong Kong Abstract Exponential growth of video traffic challenges the current paradigm to stream large amounts of video contents to end users. Cloud computing with elastic resource allocation supported enables cost-effective video streaming with desired QoE requirements. We abstract a new theoretical model from real systems for elastic media streaming by introducing a virtual content service provider that rents cloud resources from cloud service providers with multiple purchase pricing options and provides streaming service to end users. The major objective of the virtual content service provider is to reduce monetary cost with good user QoE. The responsibilities of this role are to resolve two problems under real cloud environments: resource provisioning and acquisition. In this new model, more comprehensive formulation of virtual machine provisioning problem is considered by incorporating with dynamic resource provisioning and resource acquiring with real monetary cost under multiple pricing models. We formulate the virtual machine provisioning problem into a constrained stochastic optimization problem, and design an online algorithm which can obtain approximately optimal solution with explicitly provable performance upper bounds through applying Lyapunov optimization framework. Results from extensive trace-driven simulation experiments demonstrate that our proposed OPT-ORS algorithm can well balance the monetary cost and user QoE. We also find that reserved VM instances are utilized fully to satisfy baseline user demand, ondemand instances are always rent only when flash-crowd user demand happens, and spot instances are rent more frequently than on-demand instances to serve user demand over the baseline due to low prices. I. INTRODUCTION Lately Internet traffic has witnessed an exponential growth, mainly driven by video contents. It has been reported [] that the video traffic will grow with annual rate of 34%, and contribute to 55 percent of all consumer Internet traffic by 26. Such an explosive growth of video traffic has started to and would continue to stress the global Internet, possibly resulting in poor quality of service (QoS) or quality of experience (QoE) for users. Specifically, this tussle demands new paradigm to distribute and stream video contents over Internet in the most cost effective manner, while maintaining required QoE for users. Existing solutions, mainly based on content delivery network (CDN) (e.g., Akamai[2] and ChinaCache[3]), are inefficient in resolving the aforementioned fundamental tussle. In a CDN-based architecture, video contents are pushed to the network edge, closer to the users. It serves well as a solution to improve QoE and reduce economical cost, compared to the traditional client-server architecture[4]. However, highly dynamic video traffic would result in low resource utilization due to semi-static resource allocation in CDNs. It has been reported that the utilization of most CDNs today can be as low as 5%-% [5]. Such a low utilization would translate directly into high cost. The situation would be made worse when dealing with a flash-crowd situation[6], in which a lot of users are interested in the same content simultaneously. In this case, system resources will be undersubscribed, resulting in deteriorated user experience. Therefore, a more dynamic resource provisioning paradigm should be in order. The emerging cloud computing paradigm, owing to its elastic resource allocation from a shared pool, offers a natural solution for cost-effective video streaming with desired QoE requirements. Specifically, system resources can dynamically scale up and down, matching the application demand. Adopting this design principle, researchers have started to investigate elastic media streaming services over cloud infrastructure. One example is the cloud-centric media network(ccmn)[7], which proposed a system architecture of media services over cloud infrastructure with preinary performance verification. Another family of works focus on how to reduce resource oversubscription[8], [9], [] with ensured QoE, without considering the monetary cost of provisioning cloud media streaming service under multiple pricing models. In this paper, we propose a new theoretical model which is abstracted from real systems (e.g., the system employed by Netflix [] which outsources its video streaming services to CDNs) for elastic media streaming service, in which a Virtual Content Service Provider (VCSP) rents cloud resources from Cloud Service Provider (CSP) to provide video streaming services to the end consumers. In this arrangement, the VCSP aims to minimize its operating cost, while providing a good QoE for end users. Compared to previous investigations, the VCSP not only needs to minimize its resource consumption, but also acquire resources from CSP in the presence of price volatility. An example of price variety in cloud resource is the Amazon EC2[2] model, which provides three different price schemes (reserved price model, on-demand price model, and spot price model). This price difference makes it possible for VCSP to further reduce its operating cost, with ensured user QoE. By combining all three price models, one would expect to reach a lower monetary cost, compared to the case with

2 only on-demand price model[8], [9], []. In this new model, the major challenges come from three aspects: dynamic user demand, price diversities of virtual machines and mismatched timescales of user required playback duration time, VCSP decision period and virtual machine instance charging period. Mathematically, we formulate the operating practice for the VCSP as a joint optimization of resource provisioning and acquisition, in the presence of price variety and dynamic user demand. In this formulation, the objective is to minimize the time average of weighted sum of total monetary cost and QoE. We then propose an approximate online algorithm, called OPT-ORS, with explicitly provable performance upper bound by using Lyapunov optimization framework. The benefit of this proposed approach is to decrease the complexity of the problem resulted from stochastic user demand evolution and mismatched timescales of user required playback duration time, VCSP decision period and virtual machine charging period significantly. Finally, through extensive trace-driven simulation experiments, we verify the effectiveness of OPT- ORS in practical settings. In summary, our contributions in this work are three-fold, including: We introduce a new theoretical model in providing elastic video streaming service via a virtual content service provider. This model decouples media service operations from infrastructure service providers, thus offering more flexibility in reducing the cost of video streaming, and incorporating with resource provisioning and resource acquisition for virtual machine provisioning problem. We formulate the operations of VCSP as an joint optimization problem of resource provisioning and acquisition, manifested through constrained stochastic optimization problem, and apply the Lyapunov optimization framework to solve this optimization problem. Approximate online algorithm with provably explicit performance bound is designed, with low complexity due to the structural properties of the optimal solution. We characterize the fundamental trade-off between the QoE and the monetary cost, via extensive trace-based simulation experiments, and our numerical results suggest that reserved instances are utilized fully to satisfy baseline user demand without any information about user demand fluctuation statistics in future, spot instances are rent more frequently than on-demand instances to serve user demand over the baseline due to their low prices, and ondemand instances are always rent only when flash-crowd user demand happens. The rest of the paper is organized as follows. Section II reviews related work. The theoretical model is described in Section III. We formulate the objective problem in Section IV. In Section V, we describe the design of online strategy. Tracedriven simulation evaluation is given in Section VI. Section VII concludes the paper and discusses future works. II. RELATED WORK Cloud computing paradigm has been a dominant approach for recent large-scale content distribution infrastructures due to its elasticity for dynamic resource management, pioneered by Netflix[]. Highly dynamic traffic demand drives researchers to investigate how to migrate various applications to clouds[3], [], [9], [8], [4] to reduce probabilities of resource oversubscription which will incur unnecessary operation cost for service providers. However, two major problems need to be resolved for the employment of applications in cloud: resource provisioning and resource acquisition. Resource provisioning is responsible for reducing resource oversubscription. In [8], [9], [], resource provisioning strategy has been investigated intensively. Through optimal resource provisioning strategies, content service providers can scale up and down resources provisioned in clouds according to the dynamic demand evolution. However, resource acquisition, which is in charge of acquiring resources from the resource pool of cloud with real resource prices, has not yet been investigated. Cloud resources are rented in the unit of virtual machine. Price variety, which can possibly reduce monetary cost for content service providers, exists in recent cloud services, such as Amazon EC2[2]. Three different price models are provided by EC2, including: on-demand price model, spot price model, and reserved price model. Only on-demand price model has been analyzed for cloud-assisted VoD services[], [3]. Stochastic evolution of spot prices are characterized in [5], [6], [7]. Monetary cost reduction for computation-intensive service is analyzed in [8], [9], [2]. The major difference between our work and previous works is that we jointly consider resource provisioning and resource acquisition under multiple pricing models by introducing a virtual content service provider for the implementation of cloud media streaming services. III. SYSTEM MODEL AND ARCHITECTURE A. Elastic Media Streaming In this paper, media streaming capacity is rented elastically from CSP, such as Amazon EC2. Specifically, new streaming virtual machines are requested dynamically and configured by a VCSP, in response to the changing user requests. Fig. gives an abstract architecture of elastic media streaming system, in which a general elastic streaming system consists of three major parts: users, VCSP and CSP. To serve user requests, a CSP maintains a VM instance pool, and a VCSP rents VM instances from one or more CSPs in a dynamic manner. The interactions between different components of elastic streaming system are also illustrated in Fig.. We will use Amazon EC2 as a typical example of CSPs in the following description. All VM instances of EC2 are classified into three groups based on their corresponding price models: on-demand instances, reserved instances and spot instances. In each instance group, there are K different types of instances with different configurations. User requests are classified into W groups according to their specified required playback rate. After renting VM instances from EC2, each user s request can be served by any provisioned instances. In this paper, we do not consider specific VM instance and request relationship because we can consider these provisioned VM instances as an

3 integrated instance. However, we consider resource allocation strategy among different user request group. Note that, the number of available instances in each VM group that can be rented is variant at different time. Fig.. Serve User group User group 2 User group W Reserved VM Instances On-Demand VM Instances Spot VM Instances Type-2 Type- VM VM Type-K VM Type-2 Type- VM VM Rent Type-K VM Serve Type-2 Type- VM VM Virtual Content Service Provider Type- KVM Cloud Service Provider Abstract architecture of elastic media streaming system Amazon offers four types of standard instances each of which has specific configurations, including small, medium, large and extra-large instances. Each type of instance is capable of serving requests with a fixed streaming capacity, depending on the specific VM configurations (e.g., CPU, memory and I/O capacity). Note that we assume the streaming capacity of VM instances is the only bottleneck to support cloud media streaming service. Price models for these instances will be elaborated in the next subsection. In elastic media streaming, the design objective is two-fold. First, the VCSP aims to provide good user experience with an desired QoE. Second, the VCSP should also reduce its monetary cost to rent virtual machines. However, these two goals are in conflict with each other. To enhance the QoE, the VCSP might need to over-provision virtual machines, which in turns increase the monetary cost. It follows that, the VCSP should first understand the trade-off between the QoE metrics and the monetary cost, and then identify an optimal operating point on the trade-off curve. B. User Request and QoE Model Denote ω, r ω, and ω as required playback rate, downloading rate and serving playback rate respectively. Before stepping into details of the models, it is necessary to clarify the definition of three different rates: required playback rate, downloading rate, and serving playback rate. Fig. 2 illustrates where each rate appears during the transmission of video content. Note that, we consider the chunk-based streaming application, in which the whole video will be divided into multiple chunks. A user can view each video chunk independently, that is, a video chunk can be viewed immediately after being downloaded. The playback duration time of one video chunk lasts for a few seconds (e.g., 2-5 seconds). Furthermore, for one video, multiple video copies encoded with different playback rate are stored in streaming servers. In this figure, the dashed lines represent the control information exchange between the streaming server and the user, while the solid line stands for video data transmission from streaming server to user. The downloading rate r ω indicates how fast video data can be transmitted from streaming server to user. A user request specifies a required playback rate ω, which indicates that this user desires to download the video copy with playback rate ω. Based on the downloading rate r ω, the streaming server will respond a video copy with a playback rate ω, which is closest to the downloading rate r ω, to this user. The serving playback rate ω represents the playback rate of the video copy responded by the streaming server. We consider a time-slotted system in which each slot lasts for T p, and assume that the arrival of user requests follows a Poisson process with mean rate λ(t) in slot t. Each user request is associated with a required playback rate, denoted as ω>. The number of total user request arrivals in slot t is denoted as μ(t). Without loss of generality, we assume that ω takes values from a finite and discrete set Ω with Ω = W, and ω is a random variable with a pmf of f(ω) for ω>. The number of total user request arrivals with required playback rate ω in time slot t is μ(ω, t). The mean arrival rate of user requests with required playback rate ω in time slot t is λ(ω, t) =f(ω)λ(t). User (3)Transmit video chunks with rate r (2)Respond a video copy with playback rate ()Request a video with playback rate Streaming Server Fig. 2. Differences among required playback rate, downloading rate, and serving playback rate For a user with a downloading rate of r ω and a required playback rate of ω, we define a function g(r ω ) to map the downloading rate r ω to the serving playback rate ω, that is, g(r ω )=arg ω min r ω ω,ω Ω. Note that, the function g(r ω ) should satisfy that g(r ω ) ω because the surplus serving playback rate over the required playback rate ω will not provide any QoE benefits. The QoE of this user is defined by a function Q(ω, ω )=Q(ω, g(r ω )), which falls in the range of [, 5]. Note that, the interval [, 5] is obtained through curve fitting based on the dataset in [2], [22]. Moreover, we assume that the QoE measurement exhibits the following properties over the interval [,ω]: Q(ω, ω ) is a continuous differentiable, and an increasing function of the playback rate ω over [,ω]. If ω >ω, we assume Q(ω, ω ) will keep at the maximum value Q (i.e., equals to 5). We adopt the logarithmic form definition of QoE function from [2], [23]. That is, a ln a2ω Q(ω, ω ω ω ω )= Q ω >ω a 2 ω <ω, where a and a 2 are two positive constant parameters, and a ln a 2 = Q = 5. Note that, the streaming server tends to transmit a video copy with a serving playback rate lower than the required playback rate ω since the surplus serving

4 playback rate over the required playback rate will incur cost without providing any QoE benefits. C. EC2 Price Model Amazon EC2 offers three alternative purchase pricing options, including On-Demand Instances: On-Demand Instances let users pay for streaming capacity by the hour with no long-term commitments or upfront payments. A user can increase or decrease streaming capacity depending on the demands of the application and only pay the specified hourly rate for used instances. Amazon EC2 always strives to have enough On-Demand capacity available to meet user demands, but during periods with very high demand, it is possible that the user might not be able to launch specific On-Demand instance types for short periods of time. Reservation Instances: Reserved Instances let users make a low, one-time, upfront payment for a long-term reservation of an instance (e.g., or 3 years) and pay a significantly low hourly rate for running that instance. For applications that have steady state needs, Reserved Instances can provide nearly 5% savings compared to using On-Demand Instances. Functionally, Reserved Instances and On-Demand Instances perform identically. Spot Instances: Spot Instances provide the ability for customers to purchase streaming capacity with no upfront commitment and at hourly rates usually lower than the On-Demand rate. Spot Instances allow customers to specify the maximum hourly price that they are willing to pay to run a particular instance type. Amazon EC2 sets a Spot Price for each instance type dynamically, which is the price all customers will pay to run a Spot Instance for that given period. The Spot Price fluctuates based on supply and demand for instances, but customers will never pay more than the maximum price they have specified. If the Spot Price moves higher than a customers maximum price, the instance will be shut down by Amazon EC2. Other than those differences, Spot Instances perform exactly the same as On-Demand or Reserved Instances. For a given VM instance, it is specified by a vector (s, p), where s is the streaming capacity, and p is the unit price per unit time (e.g., one hour). Note that, the unit price varies under different pricing options. To simplify the model, we assume the streaming capacity s of a VM instance only takes K values from {s,s 2,,s K }. Therefore, VM instances are classified into K types by streaming capacity. To capture these purchasing options, we adopt the following price models for any specific instance (s, p), On-Demand Price Model: the price to provision a type-k on-demand instance is p k per unit time. The total cost for using t units of time is calculated as p k t. Reserved Price Model: the price to provision a type-k reserved instance consists two parts, including: () a onetime fee of q k and (2) a usage-based fee of ˆp k. If reserved, the total cost of using a reserved instance for t units of time is q k +ˆp k t. Spot Price Model: the price to provision a type-k spot instance depends on the latest spot price of p k (t) at time t and the bidding price. The VCSP can use the instance only if the bidding price exceeds p k (t). IV. PROBLEM FORMULATION To capture realistic system dynamics, we assume three different time scales < T p < T c, where stands for the playback duration time of a whole video which is several minutes mentioned in [][24], T p represents the duration time of one decision period of VCSP to re-adjust the resource acquisition which can be tens of minutes, and T c is the duration time of one charging period which is on the order of hours (such as, one hour in EC2 pricing models). Assume T c = mt p,m. The VCSP determines the number of VM instances of each type under different price models to be provisioned in each time slot with the objective of reducing monetary cost and ensuring QoE. We define users, who have not completed downloading the required amount of video content, as active users. For each required playback rate ω, we define a queue H ω for each user group, and use H ω (t) to represent the number of active users with required playback rate ω in current time slot t. Denote Γ ω (t) as the total downloading rate allocated to the group of active users with required playback rate ω. Given Ω={ω,ω 2,,ω W } and ω <ω 2 < <ω W, we assume a demand-proportional resource allocation strategy which is determined by the total required playback rate of users in each group and is possible to ensure users to experience the same QoE. The total downloading rate allocated to each user group satisfies the following relationship Γ ω (t) :Γ ω2 (t) ::Γ ωw (t) = ω H ω (t) :ω 2 H ω2 (t) :: ω W H ωw (t). The downloading rate of an active user in slot t with required playback rate ω is denoted by r ω (t). We assume even resource allocation within a group, that is, r ω (t) = Γ ω(t), ω Ω. H ω (t) Under such a resource allocation strategy, we can see that the downloading rate of any two users in two different user groups, with required playback rate ω i and ω j respectively, satisfy r ωi (t) :r ωj (t) =ω i : ω j due to r ωi : r ωj = Γω i (t) H ωi (t) : Γ ωj (t) H ωj (t) = ω i : ω j. Therefore, we can have g(r ωi ) g(r ωj ) a ln a 2 a ln a 2 = ω i ω j a ln g(r ω i )ω j = a ln r ω i ω j =, if g(r ω i ) g(r ωj )ω i r ωj ω i g(r ωj ) = ω i. ω j Thus, under this demand proportional resource allocation strategy, any two users in two different user groups can experience the same QoE. Due to even resource allocation within a user group, users within one group will certainly experience the same QoE. Thus, if one user in one group

5 receives a QoE of 5, then each user in other user groups can also receive a QoE of 5. Note that, any other resource allocation strategies which can achieve some kind of fairness among users can be applied to this model directly as long as it can tell us the amount of downloading rate allocated to each user group. Denote the total downloading rate from all provisioned VM instances in time slot t as R(t). Given the demand-proportional resource allocation strategy, we have Γ ω (t) = R(t), ωh ω (t) Γ ω (t) = R(t). ωh ω(t) We assume that the required playback rate will not change during the downloading of the whole video, while the serving playback rate will change dynamically according to the downloading rate. Then, the total QoE from all active users are Q(t) = Q(ω, g(r ω )) H ω (t) = = a ln a 2 min(g(r ω ),ω) ω a ln a 2 min(ω,ω) ω H ω(t) H ω(t). It is assumed that the required playback duration time τ of each user follows a uniform distribution within the interval [, ]. The required playback duration time is reflected by the playback duration time of video content having downloaded from streaming server. A user will leave the system if the playback duration time of downloaded video content has exceeded τ. For example, if the required playback duration time is 6 seconds and each video chunk lasts for 5 seconds, then the user will leave the system after having downloaded 2 video chunks. For one user with required playback rate ω, the downloading rate during time slot t is Γω(t), then the H ω(t) amount of video content can be downloaded during time slot t is Γω(t) H T ω(t) p when the user arrives the system at the beginning of the slot. If the user arrives at the middle of the time slot, then the amount of video content is less than Γω(t) H T ω(t) p. Given the serving playback rate g(r(ω)), the playback duration time of the video content downloaded during time slot t is no longer than Hω (t) Tp g(r(ω)). Thus, the probability that a user will leave the system is no more than Pr(τ Hω (t) Tp g(r(ω)) Hω (t) Tp g(r(ω)) Hω (t) Tp g(r(ω)) )= min{, }. Note that, if, the user arriving at the beginning of the time slot will leave the system with a probability of. The update of each queue H ω (t) can be expressed as follows H ω (t +) max[h ω (t) min{ Γ ω(t) H ω(t) T p g(r ω ), }H ω (t), ] + μ(ω, t) () =max[h ω (t) Γ ω(t)t p, ] + μ(ω, t) (2) g(r ω ) max[h ω (t) Γ ω(t)t p, ] + μ(ω, t), (3) ω where μ(ω, t) represents the number of arrivals during time Hω (t) slot t. In inequality (), min{ Tp, }H ω (t) is the average number of users in queue H ω who will leave the Hω (t) system given that min{ Tp, } represents the maximum probability that a user will leave the system. For equality (2), if <, then max[h ω (t) min{ Hω (t) Tp, }H ω (t), ] = max[h ω (t) otherwise, max[h ω (t) min{ Hω (t) Tp Hω (t) Tp Hω (t) Tp H ω (t), ]; Hω (t) Tp, }H ω (t), ] = max[h ω (t) H ω (t), ] =. The inequality (3) is obtained from g(r ω ) ω. Denote P (t) as the total monetary cost to provision VM instances in time slot t, which will be specified in the next section. Denote P on (t), P re (t) and P sp (t) as the monetary cost associated with provisioning on-demand instances, reserved instances and spot instances respectively in time slot t, then P (t) =P on (t)+p re (t) +P sp (t). The objective problem is defined as the following constrained stochastic optimization problem T P. : min T T ( Q(t)+α P (t)) s.t. t= sup T T ζ(t) χ(t), T H ω (t), t= where the first constraint is to ensure the stability of all user queues. α is a tunable parameter which represents the tradeoff between monetary cost and QoE. We denote A k (t) (B k (t), N k (t)) as the maximum number of type-k on-demand (reserved, spot) VM instances that can be rented from cloud service provider in time slot t. A feasible provisioning strategy is one strategy which does not violate these upper bounds A k (t), B k (t) and N k (t) in each time slot t. ζ(t) denotes the provisioning strategy in slot t which tells how many VM instances of each type to be rented under each price model, and χ(t) stands for the set all feasible provisioning strategies at slot t. If we know the mean arrival rate of user requests in time slot t beforehand, then the Problem P. can be transformed into the following problem P.2 :min s.t. T T T Q(t)+α P (t) t= Γ ω (t)t p λ(ω, t), t ω ζ(t) χ(t), t,

6 where λ(ω, t) =E[μ(ω, t)] are the mean arrival rate of the Poisson process associated with users with required playback rate ω. Due to mismatched timescales of decision period and charging period, the feasible region ζ(t) is dependent on the solution in previous slots. However, if we consider that the rental of virtual machines only happens in time slots t satisfying t mod m =. That is, the number of provisioned instances in other slots is zero. Then, the problem P.2 can be decomposed into one-shot problems: P.3 : min Q(t )+αp (t ) s.t. Γ ω (t )mt p ω ζ(t ) χ(t ), t. t +(m )T p t=t λ(ω, t), t Note that, we consider all user request arrivals during each one charging period in Problem P.3, and ζ(t ) is independent of solutions in previous slots. What s more, we can know that any online algorithm can not do better than the optimal algorithm solving Problem P.3 from [25]. Define a cost function c t (ζ(t)) = Q(t) +α P (t). Denote c t (ɛ) as the optimal results of Problem P.3 with λ(ω, t) being replaced by λ(ω, t) +ɛ, and the c t is the optimal value when ɛ =. c (ɛ) is the time average cost under the optimal provision strategy, and c (ɛ) = T T t= c t (ɛ). V. ONLINE STRATEGY DESIGN In this section, we introduce how to design an approximate online algorithm solving the objective problem P.. What s more, we also try to decrease computation complexity of the online algorithm by characterizing structural properties of the optimal solution. The online algorithm can only achieve an approximately optimal solution to the objective Problem P. while the computation complexity is low and the approximation can be as close as possible. A. Characteristics of Different VM Instances Before designing online algorithms, we should characterize specific properties of VM instances under different price models. The charging time point of one VM instance is defined by the one after a time period of T c from the time point of renting this instance. Across all price models, we define active VM instances as instances whose charging time point do not exceed the current time slot. ) On-Demand Instances: Denote a k (t) as the number of type-k on-demand VM instances provisioned in time slot t. Then m i= a k(t it p ) is the number of active ondemand VM instances provisioned in previous slots before slot t. Therefore, the number of active on-demand type-k VM instances in slot t is a k (t) + m i= a k(t it p ). Note that, a k (t it p )=if t it p <. The monetary cost in time slot t incurred by provisioning on-demand instances is defined by P on (t) = K k= a k(t)p k. 2) Reserved Instances: We assume that the reservation time of a VM instance is much longer than the interval of interest. For example, the reservation time of EC2 instances can be one or three years. Denote the one time fee of a type-k VM instance is q k, and the usage-based fee is ˆp k. Due to the onetime fee, reserved VM instances should ensure their utilization ratio after being reserved. However, utilization ratio can not be guaranteed if we do not know the user demand in future slots. For example, if the mean arrival rate of user requests is high due to a flash crowd during the first several slots while the arrival rate drops significantly after this flash crowd, we tend to reserve large number of VM instances to serve high user demands during the flash crowd. This will result in low utilization ratio of reserved VM instances since the user demand is low after the initial flash crowd. Therefore, the provisioning of reserved instances is largely determined by stable user demand. However, if we can find the infimum of mean arrival rate λ min (ω), then from [25], we can know that any online optimal provisioning strategy should ensure the following property To guarantee queue stabilities of queues H ω, the optimal online provisioning strategy should ensure that Γ ω(t)t p ω λ min(ω), t. Define λ min (ω) as the baseline demand from the user group in which each user has a required playback rate of ω. Without demand prediction, we only utilize reserved instances to satisfy baseline user demand. Denote b k as the number of type-k reserved instances, then b k is determined by the following optimization problem K P 2. :min b k q k b k s.t. k= K s k b k T p k= b k B k. λ min (ω) ω, Denote â k (t) as the number of reserved type-k VM instances provisioned in time slot t. The number of active type-k reserved instances in time slot t is â k (t)+ m i= âk(t it p ). Note that, â k (t it p )=if t it p <. After the remove of one-time fee which does not affect the results of online algorithm, the usage based monetary cost of reserved instances at time slot t is defined by P re (t) = K k= âk(t)ˆp k, where K is the number of VM instance types. 3) Spot Instances: The price of a spot VM instance p k (t) can be modelled by a stochastic process. Due to the low spot price, renting spot instances may further reduce monetary cost compared with the other two price models. Without assuming specific stochastic process for spot price model, we only assume that it is feasible to obtain the following information: The expected spot price E[ p k (t)] of a type-k spot instance. We adopt the calculating methodology in [8] to obtain the expected spot price by constructing semi- Markov process for spot price evolution. E[ p k (t)] is attained from the stochastic kernel of the semi-markov

7 process, which is constructed by a Maximum Likelihood Estimator based on observed spot price history. The reliability insurance ρ, which indicates the probability that the bid price can exceed the actual spot price of a VM instance after declaring the bid price. We do not specify bidding strategy but assume that it is possible to ensure reliability ρ. Reliability is investigated in [5]. Intuitively, the reliability is a function of the declared bid price as a fraction of on-demand price. For example, the reliability is.8 if the declared bid price as a fraction of on-demand price is.44 for an instance us-west.linux.m.xlarge. Denote the number of type-k spot instances provisioned in time slot t as n k (t), then the number of active type-k spot instances at slot t is n k (t) + m i= n k(t it p ). Note that, n k (t it p )=if t it p <. The expected monetary cost of spot instances in time slot t is defined by P sp (t) = K k= n k(t)e[ p k (t)]ρ. B. Lyapunov Optimization Techniques Lyapunov optimization techniques [25] transform the original stochastic optimization problem into an optimization problem of minimizing Lyapunov drift-plus penalty. Denote the queue vector by H(t) =(H ω (t),,h ωw (t)), and define a quadratic Lyapunov function L(H(t)) = H2 ω(t) to measure the size of the queue vector. Lyapunov drift Δ(H(t)) is defined as the expected change in the Lyapunov function over one time slot. Then the solution to the original stochastic optimization problem can be approximately obtained by solving the problem of minimizing drift-pluspenalty Δ(H(t))+VE{ Q(t)+αP (t) H(t)} in each time slot, with explicit approximation upper bound. The drift-pluspenalty can be considered as the weighted sum of queue size and objective value. Note that, V is a tunable parameter which affects the performance of the online algorithm. What s more, the online algorithm only needs to observe the state of the system, such as the size of queues, to make decisions in each time slot without any knowledge of user demand statistics in future slots. C. Design Approximate Online Algorithm By integrating three price models together, we can transform the objective problem P. into the following optimization problem P 3. : s.t. min â k (t),a k (t),n k (t) T T sup T T T ( Q(t)+α P (t)) t= T H ω (t) t= K s k y(t) =R(t), t [,T] k= (a) m â k (t)+ â k (t it p ) b k, i= t [,T],k [,K] (b) ωh ω (t) Γ ω = R(t), ωh ω(t) ω Ω,t [,T] (c) a k (t) A k (t), t [,T],k [,K] (d) n k (t) N k (t), t [,T],k [,K]. Note that, n k (t) ρ is the expected number of type-k spot VM instances that can be bid successfully, and y(t) =(â k (t)+ m i= âk(t it p ))+(a k (t)+ m i= a k(t it p ))+((n k (t)+ m i= n k(t it p )) ρ) is the number of active instances in time slot t. The total cost incurred in time slot t is P (t) = P on (t)+p re (t)+p sp (t). Through Lyapunov optimization techniques [25], we can design an online algorithm which can achieve the approximately optimal solution to the Problem P3.. And the online algorithm can achieve the optimal solution to the following optimization problem P 3.2 : min W H ωj (t) Γω j (t)t p + a k (t),â k (t),n k (t) ω j j= (e) W V [ Q(ω j,g( Γ ω j(t) H j= ωj (t) )) H ω j (t)] + V α P (t) s.t. (a)(b)(c)(d)(e). Denote the algorithm which can achieve the optimal solution to Problem P3.2 as OPT-ORS (which is short for approximate OPTimal provisioning strategy with On-demand, Reserved and Spot instances). We can have the following theorem Theorem 5.: The online algorithm OPT-ORS can stabilize the system with upper bounded average queue length and time average cost. What s more, for a given parameter V > and any non-negative value ɛ, we have T T T t= T T E[H ω (t)] B 2ɛ + V c (ɛ) 2ɛ T E[c t (ζ t )] c + B V, t= where B = ( K k= (A k+b k +N k )s k ) 2 T 2 p 2 + ω2 μ2 max(ω), μ max (ω) is upper bound of the number of request arrivals μ(ω, t) during one slot, and A k = max{a k (t), t},n k = max{n k (t), t}. Proof: See details of proof in appendix. From the structure of Problem P3.2, we can know that the optimal results obtained by OPT-ORS have the following properties Theorem 5.2: Denote â k (t), a k (t) and n k (t) as the solution to Problem P3.2, then we have

8 () Given ˆp k p k, k, we have the following relationship (a) (b) (c) If E[ p k (t)] ˆp k, then (i)n k (t) <N k(t) â k (t) =,a k (t) =; m (ii)n k(t) =N k (t), â k(t)+ â k(t it p ) <b k i= a k (t) =; If ˆp k <E[ p k (t)] p k, then m (i)â k(t)+ â k(t it p ) <b k i= n k (t) =, a k (t) =; m (ii)â k (t)+ â k (t it p)=b k,n k (t) <N k(t) i= a k(t) =; If ˆp k <p k <E[ p k (t)], then m (i)â k(t)+ â k(t it p ) <b k i= a k (t) =,n k (t) =; m (ii)â k (t)+ â k (t it p)=b k,a k (t) <A k(t) i= n k(t) =. K (2) If k= s k(â k (t) + a k (t) + n k (t)) W j= H ω j (t)ω j (which indicates that total downloading rate is larger than total required playback rate), then we have W Hω 2 s j (t)tp 2 k ωh + Vαp k a k = A k (t), ω(t) j= s k W s k j= W j= H 2 ω j (t)t 2 p ωh ω(t) + Vαˆp k â k = b k, H 2 ω j (t)t 2 p ωh ω(t) + VαρE[ p k (t)] n k (t) =N k(t). Proof: ()We prove the part (i) of (a) at first. (i) If n k (t) <Nt k and â k > (or a k (t) > ), we can achieve smaller objective value by decreasing â k (t)(or a k (t)) and increasing n k (t), this is contradictory to the optimality of n k (t) and â k (t)(or a k (t)). For other parts in (), similar method can be applied. (2)From the definition of QoE function, we know that if the total downloading rate exceeds the total required playback rate the total QoE will keep constant even increasing provisioned resource. Therefore, if K k= s k(â k (t)+a k (t)+ n k (t)) > W j= H ω j (t)ω j, the total QoE will not change with the increase of a ˆ k (t), a k (t) or n k (t). What s more, if W Hω 2 s j (t)tp 2 k j= ωhω(t) T +Vαp k, then the minimal value of the objective of Problem P3.2 will decrease if increasing the value of a k (t). Thus, the optimal value a k (t) will equal to A t k. The same reason for the optimal value â k (t) =b k and n k (t) =N k t. Intuitively, given a VM instance type k, renting type-k instances under the price model providing lower price has higher priority. For example, from the property ()(a) in Theorem 5.2, the expected price of the type-k spot VM instance E[ p k (t)] is the lowest among the three pricing models. If the optimal number of provisioned type-k spot instances has not reached the upper bound, that is n k (t) < N k(t), then no type-k on-demand instances and reserved instances will be rented in the optimal solution. Thus, for each instance type, the rentals from each pricing model is prioritized by the price under each pricing model. The priorities may be variant across different VM instance types. The variant prices of spot instances also affects the priorities. Furthermore, since the surplus total downloading rate over the total required playback rate will result in excess monetary cost without providing any QoE benefits, the total downloading rate provided by all active instances in slot t is upper bounded by the total required playback rate from all active users in slot t. From the property (2) in Theorem 5.2, though surplus downloading rate can not provide QoE benefits, the leaving rate of users can be improved by surplus downloading rate. Thus, to ensure queue stability, surplus downloading rate will exist when the queue size is large enough. From Theorem 5.2, we can know that it is able to further decrease the computation complexity of algorithm OPT- ORS. The property (2) in Theorem 5.2 indicates that we can decrease the size of feasible region into a smaller set K k= s k(â k (t) +a k (t) +n k (t)) = W j= H ω j (t)ω j, then determining the optimal solution by applying property (2). From property () in Theorem 5.2, we can know that further decrease of computation complexity can be achieved by dδ(h(t))+v ( Q(t)+αP (t)) determining the derivative of dr(t).for example, given ˆp k <E[ p k (t)] p k, k, then only reserved instances will be provisioned if the derivative is larger than at point R(t) = K k= s kb k. VI. SIMULATION EXPERIMENTS A. Dataset Description and Experiment Settings The dataset consists of video traffic logs of Youku, which is the largest video streaming service provider in China, between March 24, 22 and March 3, 22. Each traffic log includes user ID, user arrival time, requested video ID, and the data size of the requested video. Divide the one week time into -min slots, we calculate the number of user request arrivals in each time slot, which is illustrated in Fig. 3. Define Ω = {2kbps, 4kbps, 8kbps}, the playback duration time of a whole video is = 3s, and the length of one slot is T p = 6s. There are 4 types of VM instances, and their corresponding streaming capacity is {Mbps,2Mbps,4Mbps,8Mbps}. The number of each

9 Number of User Arrivals ,2 Fig. 5. instances. Transition probabilities among spot price states of small VM Price of Small VM Instance Price of Large VM Instance Fig Number of user request arrivals in each time slot Spot Price On Demand Price Reserved Price Spot Price On Demand Price Reserved Price Fig. 4. Price of Medium VM Instance Price of Extra Large VM Instance Spot Price On Demand Price Reserved Price Spot Price On Demand Price Reserved Price Prices of VM instances type of VM instances follows a uniform distribution U(, 3). α = 8,V =, ρ =.8 and b k =, k =, 2, 3. The prices of each kind of VM instances within the same time range as video traffic are obtained directly from the EC2 pricing website[2]. There are four types of VM instances: small, medium, large and extra large. Fig. 4 shows the prices (in the unit of US dollars) in each time slot. The price of on-demand instances are much higher than reserved and spot VM instances. The price of spot instances change dynamically, and can be lower than the price of reserved instances. Fig. 5 illustrates the transition probabilities of spot price states of a small VM instance, which has five different spot prices. For comparison, we select the algorithm which achieves optimal results of problem P.3 as a baseline, and denote it as optimal algorithm. Note that, the optimal algorithm needs to know all video traffic statistics a priori, which is impossible in practical system. B. Simulation Results At first, we analyze the total monetary cost on all VM instances. The total one-time fee for reserved instances is 35 US dollars. Fig. 6(a) illustrates cumulative total monetary cost on all VM instances. The algorithm OPT-ORS provisions more instances than the optimal algorithm, while OPT-ORS can ensure higher time average QoE, which is illustrated in Fig. 6(b). High demand will incur more monetary cost, which is consistent with the property (2) in Theorem 5.2. That is, large queue size leads to provision more instances to ensure stability of queues, which will result in larger monetary cost increasing rate. From Fig. 6(a), we can see that the increasing rate of monetary cost between slot and 2 is much smaller than that between slot 3 and 4. From Fig. 3, we can see user demand between slot and 2 is much smaller than that between slot 3 and 4. Fig. 6(b) illustrates the time average QoE per user. The algorithm OPT-ORS provides higher expected QoE for each user by provisioning more VM instances. Because we calculate the time average expected QoE, the fluctuation of QoE during the early slots will result in significant change of the time average value. Cumulative Total Monetary Cost on VM Instances OPT ORS Optimal ,2 (a) Total monetary cost on all VM instances Fig. 6. Time Average QoE per User Optimal OPT ORS ,2 (b) Time Average QoE per User Monetary cost and QoE Fig. 7(a) illustrates the percentage of monetary cost on each kind of VM instances. Note that, we do not include one-time fee of reserved instances since both OPT-ORS and optimal algorithm incur the same one-time fee. In this figure, we can see that the percentage of monetary cost on reserved instances keeps stable because we only utilize reserved instances to satisfy baseline demand. Flash-crowd user demand will lead to more monetary cost on on-demand instances. For example, the increase of monetary cost on on-demand instances in time slot around 5, 2 and 95. Flash-crowd user demand results in large queue sizes which further require more rentals of on-

10 demand instances to ensure queue stability. Note that, the high price of on-demand VM instances also leads to high increasing rate of monetary cost on on-demand instances. Spot instances are rent more frequently than on-demand instances to satisfy user demand over the baseline demand due to their low prices. Because of high prices of on-demand instances, the percentage of monetary cost on spot instances will decrease significantly in slot 5, 2 and 95. Percentage of Monetary Cost on each kind of VM Instances On Demand VM Instances Reserved VM Instances Spot VM Instances ,2 (a) Percentage of monetary cost on each kind of VM instances Fig. 7. Time Average Weighted Sum of Total Monetary Cost and QoE OPT ORS Optimal ,2 (b) Time average weighted Sum of total monetary cost and QoE Monetary cost distribution and time average of objective value Fig. 7(b) illustrates the time average weighted sum of total monetary cost and QoE. In this figure, we can see that the difference between OPT-ORS and optimal algorithm which is around is smaller than the upper bound proved in theorem 5.2 which is larger than 3. Fig. 8(a) shows the amount of bandwidth allocated to each user group. Fig. 8(b) illustrates the evolution of queue sizes. Queue H, H 2 and H 3 are correspondent to user group with required playback rate 2Kbps, 4Kbps, and 8Kbps respectively. From the two figures, we can see that the amount of allocated bandwidth is almost consistent with the evolution of queue sizes. The number of provisioned VM instances are highly correlated between two continuous time slots due mismatched timescales of decision period and charging period, while user arrivals and leaves between two continuous time slots are independent. Therefore, we analyze the correlation between bandwidth and queue size in the time unit of one charging period. From the figures, we can see that large queue sizes require large bandwidth to be allocated. Large bandwidth will lead to high user leaving rate, then the queue size will decrease fast. The correlation between the amount of allocated bandwidth and queue size are.79,.86 and.8 respectively. User Group User Group 2 User Gruop 3 Bandwidth Allocated to Each User Group(Mbps) , , ,2 (a) Bandwidth allocated to each user group Fig. 8. Size of Queue H Size of Queue H 2 Size of Queue H 3 2 x , , ,2 (b) Size of each queue at each time slot Bandwidth allocation and queue size evolution Fig. 9 illustrates the time average monetary cost and QoE with varying α. We take 5 different values in the interval [, 25]. Note that, we do not include the one-time fee in the monetary cost since the one-time fee has no effect on the results of OPT-ORS. In this figure, we can see that monetary cost and QoE represent concave relationship. Therefore, the objective problem is convex. What s more, when α is large (i.e., larger than 2), the QoE will decrease fast and there is no significant reduction of monetary cost. If α is small (i.e., close to ), the QoE can hardly increase because it has approached to the maximum value. Note that, α = 8 is a sweet spot for real system configurations. Time Average QoE per User α=8 α= α= Time Average Monetary Cost Fig. 9. Tradeoff between time average monetary cost and QoE with varying α [, 25]. VII. CONCLUSION AND FUTURE WORK In this paper, we propose a new theoretical model for cloud media streaming service by introducing a virtual content service provider which is responsible for the two parts of operations in virtual machine provisioning strategy: resource provisioning and acquisition. By formulating the virtual machine provisioning problem as a constrained stochastic optimization problem, online algorithm which can achieve approximately optimal solution with provably explicit performance upper bounds is designed through Lyapunov optimization techniques. We further characterize the structural properties of online algorithm to reduce computation complexity of the proposed online algorithm. Through extensive trace-driven simulation experiments, we evaluate the effectiveness of the proposed online algorithm. The online algorithm can result in an optimal tradeoff between monetary cost and QoE efficiently. Furthermore, simulation results suggest that reserved instances are utilized fully to service baseline demand, on-demand instances are provisioned only when flash-crowd user demand happens, and spot instances are rent more frequently than on-demand instances to absorb user demand over the baseline. In the future, we will continue to investigate the problem under the case in which the playback rate of each video chunk can be changed dynamically during one time slot.

11 VIII. APPENDIX Proof: Denote H(T ) = (H ω,h ω2,,h ωw ), and Lyapunov function as L( H(t)) = H2 ω (t). Define oneslot Lyapunov drift as follows: Δ( H(t)) = E{L( H(t +) L( H(t))) H(t)} Then, we have Hω(t 2 +) Hω 2 Γ2 ω (t)t p 2 ω 2 2 T + μ2 (ω, t)+ Thus, we have d 2H ω (t) (μ(ω, t) Γ ω(t)t p T ) ω T t= Thus, we have Δ( H(t)) E[ Γ 2 ω (t)t p 2 ω 2 2 T H(t)] + E[ μ 2 (ω, t) H(t)] + Furthermore, we can get d 2 E[ H ω (t) (μ(ω, t) Γ ω(t)t p ) H(t)] ω T T d T T t= ( K k= A ks k ) 2 Tp μ 2 ω2 max (ω) 2 E[ H ω (t) Γω(t)T p H(t)] ω T + d 2 E[ H ω (t) μ(ω, t) H(t)] = B 2 E[ H ω (t) Γω(t)T p H(t)] ω T + d 2 E[ H ω (t) μ(ω, t) H(t)] Consider the drift-plus-cost as follows: Δ( H(t)) + V E[c t (A t ) H(t)] B + 2 H ω (t) μ(ω, t) 2E[ Γ ω H ω (t)t p H(t)] ω T + d V E[c t (A t ) H(t)] B +2 H ω (t) μ(ω, t)+v c t (ɛ) 2 E[ H ω (t) (μ(ω, t)+ɛ) H ω (t)] = B 2ɛ H ω (t)+v c t (ɛ) Therefore, we have Δ( H(t)) B 2ɛ H ω (t)+ By taking expectation, we have V c t (ɛ) V E[ct (ζ t ) H(t)] E[L( H(t + ))] E[L( H(t))] B 2ɛ H ω (t)+v c t (ɛ) V E[c t(ζ t )] Summing over time slots, E[L( H(T ))] E[L( H())] T TB 2ɛ H ω (t)+ V t= As to the resulted cost, we have T E[c t (ζ t )] T T T Thus, t= T T t= T T c t (ɛ) V E[c t (ζ t )] t= E[H ω (t)] B 2ɛ + V T t= c t (ɛ) + 2Tɛ E[L( H())] 2Tɛ E[H ω (t)] B 2ɛ + V T t= c t (ɛ) 2Tɛ t= B 2ɛ + V c (ɛ) 2ɛ c t (ɛ)+b V + E[L( H())] TV T E[c t (ζ t )] c (ɛ)+ B V t= Since T T T t= E[ct (ζ t )] is independent of ɛ,wehave T E[c t (ζ t )] c + B T T V t= REFERENCES [] Cisco visual networking index: Forecast and methodology, [2] Akamai, [3] ChinaCache, [4] C. Huang, J. Li, and K. Ross, Can internet video-on-demand be profitable? SIGCOMM, 27. [5] F. Lo Presti, C. Petrioli, and C. Vicari, Distributed dynamic replica placement and request redirection in content delivery networks, in MASCOTS. IEEE, 27. [6] B. Li, G. Keung, S. Xie, F. Liu, Y. Sun, and H. Yin, An empirical study of flash crowd dynamics in a P2P-based live video streaming system, in Globecom. IEEE, 28. [7] Y. Jin, Y. Wen, G. Shi, G. Wang, and A. Vasilakos, CoDaaS: An experimental cloud-centric content delivery platform for user-generated contents, in ICNC. IEEE, 22. [8] X. Qiu, H. Li, C. Wu, Z. Li, and F. Lau, Dynamic scaling of VoD services into hybrid clouds with cost minimization and QoS guarantee, in PV. IEEE, 22. [9] F. Wang, J. Liu, and M. Chen, CALMS: Cloud-assisted live media streaming for globalized demands with time/region diversities, in IN- FOCOM. IEEE, 22. [] Y. Wu, C. Wu, B. Li, X. Qiu, and F. Lau, Cloudmedia: When cloud on demand meets video on demand, in ICDCS. IEEE, 2. [] Netflix, [2] Amazon EC2 pricing,

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