Optimal Resource Allocation for Multimedia Cloud Based on Queuing Model

Transcription

1 Optimal Resource Allocation for Multimedia Cloud Based on Queuing Model Xiaoming Nan, Yifeng He, Ling Guan Department of Electrical and Computer Engineering Ryerson University, Toronto, Ontario, Canada Abstract Multimedia cloud, as a specific cloud paradigm, addresses how cloud can effectively process multimedia services and provide QoS provisioning for multimedia applications. There are two major challenges in multimedia cloud. The first challenge is the service response time in multimedia cloud, and the second challenge is the cost of cloud resources. In this paper, we optimize resource allocation for multimedia cloud based on queuing model. Specifically, we optimize the resource allocation in both singleclass service and multiple-class service. In each, we formulate and solve the response time minimization problem and resource cost minimization problem, respectively. Simulation results demonstrate that the proposed optimal allocation scheme can optimally utilize the cloud resources to achieve a minimal mean response time or a minimal resource cost. I. INTRODUCTION Cloud computing is an emerging computing paradigm that can provide computation, storage, and communications resources as services in a scalable and virtualized manner. Among various cloud-based applications, multimedia applications strongly need cloud assistance. Multimedia processing, such as image/video retrieval, typically requires intensive computation, which is difficult to be performed on powerconstrained mobile devices. Multimedia Cloud (MC) [1] focuses on how cloud can provide Quality of Service (QoS) provisioning for multimedia applications and services. In MC, cloud service providers deploy cloud resources as utilities to process multimedia requests and then deliver computing results or media data to users. By using multimedia cloud service, users do not need to pay for costly computing devices. Instead, they can process multimedia applications on powerful cloud servers and pay for the utilized resources by the time. There are two major concerns for MC service providers. The first concern is the Quality of Experience (QoE) of customers. The service response time in the data center is defined as the period from the time when the service request arrives at the data center to the time when the service result departures the data center. Service response time is a significant QoE factor to measure the performance of multimedia cloud service. A lower service response time will lead to a higher QoE. Thus, it is important for cloud service providers to meet customer s requirements on service response time. The second concern is the cost of the allocated cloud resources. The cloud service can generally be divided into three consecutive phases: schedule, computation and transmission. Inappropriate resource allocation among the three phases will result in resource waste and QoE degradation. For example, with much resource allocated on computation phase while little resource on transmission phase, customers requests will be processed fast, but the service results cannot be transmitted in time due to the limited transmission capacity. Therefore, it is challenging for cloud service providers to optimally allocate resources to minimize cost and satisfy customers QoE requirements at the same time. In this paper, we employ the queuing model to investigate resource allocation problems in both single-class service and multiple-class service. Furthermore, we optimize the resource allocation to minimize the mean response time or minimize the resource cost in each. Our contributions in this paper are presented as follows. We model the service process at multimedia cloud data center as three concatenated queuing systems, which are schedule queue, computation queue and transmission queue. Moreover, we theoretically analyze the relationship between the service response time and the allocated resources in each queuing system. Based on the queuing model, we study cloud resource optimization problems in single-class service and multiple-class service, respectively. In each, we formulate and solve resource allocation optimization problems to minimize the mean response time and minimize the resource cost, respectively. The remainder of this paper is organized as follows. Section II discuses the related work. Section III introduces system models. In Section IV, we optimize the cloud resources in single-class service and multiple-class service, respectively. The simulation results are provided in Section V and the conclusions are drawn in Section VI. II. RELATED WORK Cloud computing, as a promising computing paradigm, has broadly attracted significant attentions of researchers from both industry [2], [3], [4] and academia [5-18]. Surveys on cloud computing service can be found from [5], [6]. Several approaches have been proposed on critical research issues in cloud computing, including cloud security [7], [8], [9], privacy [10], [11], energy efficiency [12], and resource management [13], [14], [15]. Multimedia cloud, as a specific cloud, majorly addresses how cloud can process multimedia applications and provide QoS provisioning for multimedia services. Authors in [1]

2 present the framework of multimedia cloud computing and elaborate it from multimedia-aware cloud and cloud-aware multimedia perspectives. Several cloud-based multimedia applications have also been proposed in the recent years [16], [17], [18]. A cloud-based video sensing system [16] is presented to perform scalable and adaptive online monitoring. An efficient video-based mobile location search application is implemented in cloud environment in [17]. Lau et al. [18] develop an architectural framework to employ the on-demand cloud resources on IPTV, which enables subscribers to receive television programs and video streams from anywhere. Various resource management techniques have been proposed for cloud resource management [13], [14], [15]. Lin et al. [13] develop a self-organizing model to manage cloud resources in the absence of centralized management control. Authors in [15] focus on the maximization of the steady-state throughput by deploying resources for the independent equalsized tasks in the cloud. Teng et al. present a resource pricing and equilibrium allocation policy based on the consideration of cloud users competition for limited resources [14]. Compared to the work in [13], [14], [15], our work demonstrates the following novelties: 1) we study the relationship between QoS and cloud resource allocation in different phase based on queuing model; 2) we analyze the cloud resource allocation in both single-class and multiple-class service s, and provide optimal resource allocation respectively to meet response time requirements or to meet budget constraints. III. SYSTEM MODELS In this section, we present our system models, including data center architecture model, queuing model and cost model. A. Data Center Architecture Most of clouds are built in the form of data centers [1]. The data center architecture in this paper consists of a master server and a bunch of computing servers. The master server receives all coming requests, and then schedules the requests to computing servers. Computing servers act as the real processors, which receive tasks from the master server and then process customer s requests using their own resources and associated media data. The master server and all computing servers form a node-weighted tree-like graph with the master server as root connecting to all computing servers with highspeed communications links. We assume the latency of internal communications between the master server and the computing servers is negligible. The weight of the node represents the corresponding processing rate. The weight of the master server represents requests schedule rate, while the weight of the computing server represents task computation rate. The computation capacity indicates an integrated performance in terms of processor frequency, memory size, I/O rate and etc. We assume that each task is indecomposable and independent with each other. After processing, all the service results will be transmitted back to customers by a transmission server. B. Queuing Model Fig. 1. Queuing Model The queuing model of the data center is shown in Fig. 1. The model consists of three concatenated queuing systems, which are schedule queue, computation queue and transmission queue. The master server maintains the schedule queue to receive all requests from customers. Since the two consecutive arriving requests may be sent from two different customers, the inter-arrival time is a random variable, which can be modeled as an exponential random variable in cloud computing [19]. Therefore, the arrivals of the requests follow a Poisson Process with arrival rate λ. Requests in the schedule queue are distributed to different computing servers and the scheduling rate depends on the master server capacity. Suppose there are N computing servers, denoted as C 1,...,C N, in the data center. In this paper, we employ possibility random generation method as scheduling scheme, which means the possibility p i of task requests sent to computing server i is randomly generated. Thus, the arrival rate of scheduling requests to computing server i is p i λ. According to the decomposition property of Poisson Process, the arrivals of task requests at computing server i follow a Poisson Process with arrival rate p i λ. For each computing server, it has its own computation queue to store task requests waiting for processing. After computation phase, all results are sent to the transmission server and a transmission queue is used to store coming results. Since the whole system is a close system, the arrivals of results at transmission queue follow the Poisson Process with arrival rate λ. The service rate of the transmission queue is determined by the bandwidth capacity of the data centre. C. Cost Model The resource cost in data center is charged according to the utilized resources by the time. The allocated resources in our system include the resources at the master server, the computing servers, and the transmission server. In this paper, we employ a linear function to model the relationship between the cost and the allocated resources. The total cost is formulated as N Cost = (αs +β C i +γb)t, (1) where t is the time period which is set to 1 hour in this paper, S is the schedule rate of master server, C i is the computation rate of computing server i, B is the transmission rate of the transmission server, α, β and γ are costs of scheduling, computing and transmitting one request, respectively. The linear cost model is justified by numerical analysis in [2], [3].

3 The service process is described as follows. When customers use a cloud based application, the task requests are sent to data center and stored in the schedule queue in the master server. According to randomly generated possibility, the task requests are scheduled to a corresponding computing server. If the computing server is idle at that time, the task can be processed immediately; otherwise, it has to wait in the computation queue. After processing, the service results are transferred into the transmission queue to be sent back to customers. IV. OPTIMAL ALLOCATION OF CLOUD RESOURCES In Section III, we present our system models to represent the relationship among the allocated resource, the service response time and the resource cost. In this section, we use the proposed models to study the resource allocation problems in singleclass service and multiple-class service, respectively. In each, we optimize the resource to minimize the service response time or minimize the resource cost, respectively. A. Single-Class Service Case In this subsection, we study the optimal cloud resource allocation in single-class service, in which there is only one kind of application service provided in the data center. Thus, all cloud customers request for the same kind of service which has the same processing procedure. As presented in Section III, the arrivals of customer requests at the data center follow a Poisson Process with arrival rate λ. All requests enter into the schedule queue first. The service time of the schedule queue is assumed to be exponentially distributed with mean service time S 1, where S captures schedule capacity of the master server. Thus, the schedule queue is modeled as an M/M/1 queuing system. In order to maintain a stable queue, λ < S is required. The response time of the schedule queue is given by T schedule = 1/S 1 λ/s. The master server distributes requests to different computing servers according to the randomly generated possibility. Suppose that there are N computing servers in the data center and their computation rates are represented by C 1,...,C N, respectively.p i is the possibility that a task is assigned to computing server i. According to the decomposition property of Poisson Process, the arrivals of scheduled tasks at computing serverialso follow a Poisson Process with arrival ratep i λ. The service time of computing server i is exponentially distributed with mean service time C 1 i. To maintain a stable queue, the constraint p i λ < C i should be satisfied. The response time in computing server i is given by Tcompute i = 1/Ci 1 p iλ/c i, and the mean response time of all N computation queues can be formulated as T compute = N p itcompute i = N p i/c i 1 p iλ/c i. After processing, all service results are sent to the transmission queue. Since there is no customer loss in the previous systems, the arrivals of service results at the transmission queue also follow the Poisson Process with mean arrival rate λ. The service time of the transmission queue is assumed to be exponentially distributed with mean service time B 1, where B represents the transmission capacity of the data center. The transmission queue is modeled as an M/M/1 queue. To maintain a stable queue, λ < B is required. The mean response time of the transmission queue is given by T transmit = 1/B 1 λ/b. The total service response time for single-class service is the summation of response times of the three queues, which can be formulated as T single = T schedule +T compute +T transmit = 1/S N 1 λ/s + p i /C i + 1/B 1 p i λ/c i 1 λ/b. (2) 1) Response Time Minimization Problem: We optimize the resource allocation to provide services with minimal response time to customers. The response time minimization problem can be stated as: to minimize the total service response time in the data center by optimizing the capacities of the master server, the computing servers, and the transmission server, subject to the queuing stability constraint in each queuing system and the resource cost constraint. Mathematically, the problem can be formulated as minimize subject to 1/S 1 λ/s + N p i/c i 1 p iλ/c i + 1/B 1 λ/b λ < S, p i λ < C i, i = 1,...,N, λ < B, (αs +β N C i +γb)t M. where M is the upper bound of the resource cost. The Lagrange multiplier method [20] is applied to solve the optimization problem (3). The optimal analytical solution to the response time minimization problem is given as follows, S = C i = B = M (α+β +γ)λ α( α+ β N pi + γ) +λ, (3) pi (M (α+β +γ)λ) β( α+ β N pi + γ) +p iλ, i = 1,...,N, M (α+β +γ)λ N γ( α+ β pi + γ) +λ. (4) 2) Resource Cost Minimization Problem: We optimize the resource cost minimization problem to provide services at minimal resource cost. The resource cost minimization problem can be stated as: to minimize the total resource cost in the data center by optimizing the capacities of the master server, the computing servers, and the transmission server, subject to the queuing stability constraint in each queuing system and the constraint on the service response time. Mathematically, the problem can be formulated as minimize (αs +β N C i +γb)t subject to λ < S, p i λ < C i, i = 1,...,N, λ < B, 1/S 1 λ/s + N p i/c i 1 p iλ/c i + 1/B 1 λ/b τ, (5)

4 where τ is the upper bound of the service response time. Similarly, we employ the Lagrange multiplier method to solve the optimization problem (5), and get the optimal analytical solution as follows, N α+ β pi + γ S = +λ, ατ N α+ β pi + γ C i = +p i λ, i = 1,...,N, βτ/ pi B = N α+ β pi + γ +λ. γτ B. Multiple-Class Service Case In this subsection, we study the resource allocation problem in multiple-class service, in which multiple kinds of application services are provided by the data centre. Each kind of service has a different processing procedure at the computing server, a different size of the service result, a different transmission time, and a different requirement on the service response time. Different kinds of requests arrive at the schedule queue first. They will then be assigned to corresponding computing servers for processing. Suppose there are K classes of services and the arrivals of each class requests follow a Poisson Process with mean arrival rate λ 1,λ 2,...,λ K respectively. According to composition property, the total arrivals of the requests follow a Poisson Process with a rate λ = K λ i. Since each class service requires a different processing procedure, we assign the computing server i to specifically serve the requests of class-i service. The number of computing servers is K, which is identical to the number of service classes. In such a way, the scheduling scheme in the master server is deterministic. Moreover, the scheduling rates for different classes requests are assumed to be the same, since the master server doesn t involve any specific processing procedure. The service time in master server is assumed to be exponentially distributed with mean service time S 1 where S represents the scheduling capacity of the master server. Therefore, the average response time in the master server is given by T schedule = 1/S 1 λ/s. The requests arriving at computing server i are all for classi service, which follows a Poisson Process with mean arrival rate λ i. Different computing servers have different computation resources. Furthermore, the service time is assumed to be exponentially distributed and the mean service time for computing serveri is denoted asc 1 i. Thus, the response time at computing server i is given by Tcompute i = 1/Ci 1 λ i/c i. The average response time in the computation phase is formulated as T compute = K λi λ Ti compute = K λ i/c i λ(1 λ. i/c i) After processing, the service results are sent to the transmission queue. Since the system is a close system, the arrival rate of results at the transmission queue is λ. Each class of service has a different size of service result. The average size of result for class-i service is denoted by D i. The transmission time for the class-i service result is exponentially distributed with (6) mean service time B 1 i = D i /B, where B is the transmission capacity of the transmission server. Therefore, the transmission queue can be viewed as a queuing system in which customers are grouped into a single arrival stream and the service distribution is a mixture of K exponential distributions. In fact, the service time follows hyper-exponential distribution [19]. The transmission queue is actually an M/H K /1 queuing system, where H K represents a Hyperexponential-K distribution. And the response time of the M/H K /1 queuing system can be deduced from M/G/1 queuing system [19]. Therefore the response time of transmission queue is given by K K T transmit = λid2 i λidi. To ensure a stable queue, K B 2 B K + λidi λ i B i < 1 is required. Based on the above analysis, we can get the total service response time for multiple-class service in the data center, which can be formulated as T multi = T schedule +T compute +T transmit. (7) Furthermore, the mean service response time for class-i service in the data center is formulated as T i multi = T schedule +T i compute +T transmit. (8) 1) Response Time Minimization Problem: We optimize the resource allocation in multiple-class service to provide the services with minimal response time. The response time minimization problem can be stated as: to minimize the total service response time in data center by optimizing the capacities of the master server, the computing servers, and the transmission server, subject to the queuing stability constraint in each queuing system and the resource cost constraint. Mathematically, the problem can be formulated as λb minimize T schedule +T compute +T transmit subject to λ < S, λ i < C i, i = 1,...,N, K λi B i < 1, (αs +β K C i +γb)t M. The response time minimization problem is a convex optimization problem. Efficient solution methods for convex optimization problems are well developed. In this paper, we use the primal-dual interior-point methods [20] to solve the convex optimization problem. 2) Resource Cost Minimization Problem: We next optimize the resource allocation in multiple-class service to provide services at minimal resource cost. The resource cost minimization problem can be stated as: to minimize total resource cost in the data center by optimizing the capacities of the master server, the computing servers, and the transmission server, subject to the queuing stability constraint in each queuing system and the constraint on the service response time for each class of service. Mathematically, the problem can be (9)

5 formulated as minimize (αs +β K C i +γb)t subject to λ < S, λ i < C i, i = 1,...,N, K λ i B i < 1, T schedule +Tcompute i +T transmit τ i (10) where τ i is the upper bound of the service response time for class-i service. Similar to the response time minimization problem, the resource cost minimization problem is also a convex optimization problem, which can be solved efficiently using the primal-dual interior-point methods [20]. V. SIMULATIONS A. Simulations for Single-Class Service Case 1) Simulation Settings: We perform simulations to evaluate the proposed methods in the single-class service. Windows Azure [3] is a cloud platform developed by Microsoft, which provides on-demand compute, storage, and networking resources for services through Microsoft data centers. We employ the pricing rate and device configuration of Microsoft Azure in our simulation. One medium instance server is employed as master server and four large instance servers are employed as computing servers to process customer requests. The scheduling probabilities for four computing servers are set as p = {0.1,0.2,0.3,0.4}. The resource of the master server, the computing server, and the transmission server are charged by α =0.12$/request, β=0.48$/request, and γ=0.20$/request, respectively. The mean arrival rate of customer s requests is set in the range between 500 and 600 requests/hour. 2) Simulation Results: We first compare the performance between the proposed optimal allocation scheme, in which the resources for schedule, computation, and transmission are allocated optimally by solving the optimization problem (3) or (5), and the equal allocation scheme, in which the resources for schedule, computation, and transmission are allocated equally. Comparison of the mean response time between the proposed optimal allocation scheme and the equal allocation scheme is shown in Fig. 2. The resource cost constraint is set to 1000$. From Fig. 2, we can see that the proposed optimal allocation scheme achieves much lower response time compared to the equal allocation scheme under the same budget constraint. Fig. 3 shows the detailed information of the allocated resource for two schemes when λ is set to 600 requests/h. As shown in Fig. 3, the equal allocation scheme allocates a smaller portion of resource in the computing servers, thus leading to a higher response time. We next evaluate the resource cost between the proposed optimal allocation scheme and the equal allocation scheme in the data center. We set the service time constraint τ = 0.01 hour, which means the mean service response time should not exceed this time requirement. From Fig. 4, we can see that the proposed optimal allocation scheme achieves a much lower resource cost compared to the equal allocation scheme under same service time constraint. We can get the reason from the allocated resource shown in Mean response time (h) Fig. 2. Comparison of the mean Fig. 3. Comparison of the allocated response time in single-class service resources in single-class service Resource cost ($) Fig. 4. Comparison of the resource Fig. 5. Comparison of the allocated cost in single-class service resources in single-class service Fig. 5. In equal allocation scheme, a small part of resource is allocated to the master server and the transmission server. Thus customer s requests cannot be scheduled or transmitted in time, which degrades the system performance. B. Simulations for Multiple-Class Service Case 1) Simulation Settings: In this subsection, we perform simulations to evaluate our proposed resource allocation methods in the multiple-class service. We set 4 classes of services provided in the data center. Each kind of service has a different arrival rate, a different size of result, and a different requirement on service response time. Table I shows the settings of arrival rate, results size and service time limit for each class. The pricing rates and total arrival rate range of requests are the same as those configured in Section V-A. TABLE I PARAMETER SETTINGS FOR MULTIPLE-CLASS SERVICE CASE Service Class Class 1 Class 2 Class 3 Class 4 Proportion of 10% 20% 30% 40% arrival rate Size of result (MB) Upper bound of service time (h) 2) Simulation Results: We first compare the performance between the proposed optimal allocation scheme, in which the resources for schedule, computation, and transmission are allocated optimally by solving the optimization problem (9) or (10), and the equal allocation scheme, in which the resources for schedule, computation, and transmission are allocated equally.

6 Mean response time (h) Comparison of the mean re- Fig. 7. Fig. 6. sponse time in multiple-class service Resource cost ($) Comparison of the allocated resources in multiple-class service Fig. 8. Comparison of the resource Fig. 9. Comparison of the allocated cost in multiple-class service resources in multiple-class service Fig. 6 shows the comparison of service response time. The resource cost constraint is set as 1000$. From Fig. 6, we can see that the proposed optimal allocation scheme takes less response time than the equal allocation scheme under same budget constraint. Fig. 7 shows detailed resource allocation when arrival rate is 600 requests/hour. The master server is allocated too much resource in the equal allocation scheme, which results in the less resource allocated in the computing servers and the transmission server. The comparison of resource cost in the multiple-class service is shown in Fig. 8, from which we can see that the proposed optimal allocation scheme achieves a much lower resource cost than the equal allocation scheme. The detailed resource allocation is shown in Fig. 9. Compared with the proposed scheme, the equal allocation scheme assigns less resource on schedule and transmission phases and more resource on computation phase, which causes resource unbalance and degrades the system performance. VI. CONCLUSIONS In this paper, we have studied the resource optimization problem in multimedia cloud to provide services with minimal response time or minimal resource cost. We model the data center infrastructure as a node-weighted tree-like graph, and then use the queuing model to capture the relationship between the service response time and the allocated resources. We also study the resource allocation problem in single-class service and multiple-class service, respectively. 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