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TSINGHUA SCIENCE AND TECHNOLOGY ISSNll1007-0214ll09/11llpp298-307 Volume 18, Number 3, June 2013

Performance Evaluation and Dynamic Optimization of Speed Scaling on Web Servers in Cloud Computing Yuan Tian, Chuang Lin, Zhen Chen , Jianxiong Wan, and Xuehai Peng Abstract: The energy consumption in large-scale data centers is attracting more and more attention today with the increasing data center energy costs making the enhanced performance very expensive. This is becoming a bottleneck to further developments in terms of both scale and performance of cloud computing. Thus, the reduction of the energy consumption by data centers is becoming a key research topic in green IT and green computing. The web servers providing cloud service computing run at various speeds for different scenarios. By shifting among these states using speed scaling, the energy consumption is proportional to the workload, which is termed energyproportionality. This study uses stochastic service decision nets to investigate energy-efficient speed scaling on web servers. This model combines stochastic Petri nets with Markov decision process models. This enables the model to dynamically optimize the speed scaling strategy and make performance evaluations. The model is graphical and intuitive enough to characterize complicated system behavior and decisions. The model is serviceoriented using the typical service patterns to reduce the complex model to a simple model with a smaller state space. Performance and reward equivalent analyse substantially reduces the system behavior sub-net. The model gives the optimal strategy and evaluates performance and energy metrics more concisely. Key words: cloud computing; green IT; energy consumption; data centers; stochastic Petri nets; performance evaluation; dynamic optimization; service computing

1  Yuan Tian and Chuang Lin are with the Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China. E-mail: ftianyuan, [email protected].  Jianxiong Wan is with the College of Information Engineering, Inner Mongolia University of Technology, Jinchuan Development Area, Hohhot, Inner Mongolia 010080, China. E-mail: [email protected].  Zhen Chen is with the Research Institute of Information Technology, and Tsinghua National Laboratory for Information Science and Technology (TNList), Tsinghua University, Beijing 100084, China. E-mail: [email protected].  Xuehai Peng is with the Beijing Municipal Commission of Economy and Information, Beijing 100029, China. E-mail: [email protected].  To whom correspondence should be addressed. E-mail: [email protected].. Manuscript received: 2013-04-02; revised: 2013-05-05; accepted: 2013-05-06

Introduction

Data centers are an important infrastructure component in cloud computing that are expanding rapidly in both quantity and scale[1] . The high energy consumption in data centers is known as “the grey field in the Internet”. Estimates for the year 2010 are that data centers in the USA consumed 760 billion kWh, 2% of the total energy consumption in the USA[2] . If the energy consumption continues to grow, it will bring more economic and environmental problems[3, 4] . For data center owners, the energy consumption increases the operating costs, with large electricity demands becoming a barrier to further development[1, 5, 6] . As a result, both the performance and the price of performance must be considered in cloud computing. Furthermore, related carbon emissions will also increase environmental pollution

Yuan Tian et al.: Performance Evaluation and Dynamic Optimization of Speed Scaling on Web Servers in   

and global warming[7] . Thus, greening of data centers is now an urgent issue. The traditional cloud computing seeks to provide good performance. Thus, over-design and redundancy have lead to many idle or under-utilized servers to deal with the large work loads that rarely happen. Barroso and Holzel[8] reported that only 20%-30% of the total servers capacity is utilized in a typical data center and the idle servers consume as much as 60% of the peak energy even when they are not processing any task. The energy wasted in servers is a challenge for the greening of data centers, with energy-efficiency methods needed in data centers to provide cloud services[9] . The management of system resources seeks to reduce energy costs in cloud computing by managing multiple power states to tradeoff energy against performance[10, 11] . The traffic through the typical cloud computing platform used in the security center of the Collaborative Network Security Management System (CNSMS)[12, 13] varies daily and weekly[14] . When the load is light, the servers can be in a lowpower state to eliminate energy waste. Then as the load increases, the servers can transfer to a highpower state for high performance computes. This state management can be designed to adapt to the work load characteristics. The Advanced Configuration and Power Interface (ACPI)[15] provides hardware support for different power states in servers. The ACPI Cstates reduce energy use by powering down processors or sub-components to different levels, while the ACPI P-states enable Dynamic Voltage and Frequency Scaling (DVFS)[16-18] . The DVFS mechanism is used throughout industry today, such as Intel’s Speed-Step technology[19] and AMD’s Cool’n’Quiet technology[20] . Speed scaling[21-25] adapts the server speed to the workload. Unlike shutting down or sleeping idle servers, speed scaling runs the server at different factors of the peak service rate. Speed scaling designs are classified into static speed scaling and dynamic speed scaling. Static speed scaling is the simplest where the server runs at a specified static speed. Dynamic speed scaling adapts the server speed based on the current server state, using a more sophisticated algorithm. This paper analyzes speed scaling strategies from a serviceoriented point of view to gain insights into issues of (1) How does the service perform with speed scaling, which is termed performance evaluations. (2) How to design an optimal speed scaling strategy, which is termed dynamic optimization. These two problems are addressed by a Stochastic

299

Service Decision Net (SSDN) model[26] , which is an extension of Stochastic Petri Nets (SPN)[27] . The model is used to analyze strategy implementation and model reduction using various service patterns, to significantly reduce the time to obtain the optimal strategy.

2

2.1

Stochastic Service Preliminaries

Decision

Nets

Definition

Definition 1 A stochastic service decision net is defined as an 8-tuple ˙ D .P; T; A; ; ; R t ; Rm ; F /, where (1) P D fp1 ; p2 ;    ; pk g is a finite set of places; (2) T D ft1 ; t2 ;    ; tm g is a finite set of transitions; P \ T D ∅; (3) A  I [O is a set of arcs, in which I  P T and O  T P , such that P [T D ∅. The pre-set and post-set of x are defined as x D fyj.y; x/ 2 Ag and x D fyj.x; y/ 2 Ag; (4)  is a decision policy which determines the transition t 2 Td for the decision maker in a given marking; (5)  D f t g t 2T is the set of firing rates for transition set T ; (6) R t W T ! R is a reward function when a transition t 2 T fires and Rm W M ! R is a reward function when a marking is reached; (7) F is the objective function for the decision maker. The SSDN model is a service-oriented modeling tool. Since net structures can describe the service process[28] , this SSDN model can capture the major characteristics of various service patterns, especially in cloud service scenarios. The model combines SPN and the Markov Decision Process (MDP)[29] . SSDN models have the same abilities as SPN as a formal, graphical, executable method to describe complicated system behaviors. SPN is particularly well-suited for modeling and analyzing parallel and synchronous actions in parallel and distributed systems. The SSDN has two basic structures[26] with a system behavior sub-net and a decision maker sub-net. The two sub-nets are connected by transitions or places with places used here. Transition firing in the preset of these two places means finishing the related actions in the current round with only one transition firing at a time. 2.2

SSDN strategies implementation

The sophisticated service patterns in cloud computing are the product of system behaviors interacting with the

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decision maker. The decision maker makes decisions according to the system states and the system must react to these decisions with system behavior. The dynamic nature of service patterns results in variations of the relations between the transitions and places. These variation can be implemented in the SPN model by control of the transition firing rate or the arc weights. This type of control can be realized by state dependent functions. These functions can be categorized into four groups as Arch Weight Functions (AWF), Firing Weight Functions (FWF), Firing Rate Functions (FRF), and Guard Functions (GF). These functions extend the ability to characterize dynamic systems beyond the basic model structure. The FRF determines the firing rate for the time transition, while the FWF determines the probability of firing when multiple instant transitions are enabled. The GF returns boolean values with 1 denoting firing enabled and 0 denoting firing disabled. The AWF controls the number of tokens consumed or generated by a transition. Thus, these can be used to characterize service rate variations and the condition of transitions among various states.

3

System Modeling with Speed Scaling

Consider a data center service model. When a user submits jobs, the incoming jobs first arrive at a frontend proxy server and are then distributed among the web servers with load balancing. Some jobs containing static content can be served only by the web servers,

Fig. 1

such as accessing the index pages. The dynamic content usually need to be handled by the back-end data storage servers, which store persistent data on disks in form of databases. The computation resources in the web servers must wait until the data is fetched. Therefore, this access process significantly slows the response time and user experience. Caches are widely used to improve performance by caching the most popular data. Caches significantly reduce the number of back-end data storage server accesses with only a fraction of the requests that are not in the cache significant degrading performance due to the accessing of data on the hard disk. The web servers dynamically adapt their processing capacity to the work load. When the load is light, the service rate is scaled down to reduce power consumption with little performance degradation. To simplify the analysis, multiple effective service rates will be abstracted into just two macro states, a high state and a low state. The decision maker determines which macro state the server should be in and when to trigger the transition to another state. The analysis assumes that all the service times, such as for computing, cache access, and disk accessing, are exponentially distributed random variables. The SSDN model is used to characterize the decision maker and system behaviour as shown in Fig. 1. The token in place Decision start indicates that the decision maker has completed its final decision while the token in place Decision end indicates that the system has completed its operations in the current round.

SSDN model.

Yuan Tian et al.: Performance Evaluation and Dynamic Optimization of Speed Scaling on Web Servers in   

In the decision maker sub-net, places PHIGH and PLOW denote that the server is either in the high service rate state HIGH or the low service rate state LOW . In the high service rate, the server provides good performance, but with high power cost. Inversely, in high service rate, the server will suffer a performance degradation, but with lower power cost. The two stateindicated places enable the system behavior subnet to detect the decisions by the decision maker. Each state has two actions to maintain its current state and to transfer to the alternative state. The SSDN model uses a selective structure to denote each action. For state #PHIGH D 1, the action space is fDH2H ; DH2L g, while for state #PLOW D 1, the action space is fDL2L ; DL2H g. Transferring to the alternative state incurs an extra cost denoted by the time transitions TH2L and TL2H . The system behavior sub-net assumes that job arrivals conform to a Poisson distribution with average rate arrival , which is denoted by the transition Tarrival . Jobs in the front-end proxy server will be routed to the waiting queue (denoted by place Buffer) of the selected web server. Once the job is ready to be executed, the token in place Buffer will fire into the data access unit (place Data) and into the execution waiting unit (place Waiting) in parallel. The token in place Waiting cannot be fired until the data access process is finished. The cache hit probability is assumed to be Prhit and the miss probability is Prmiss . Thus, the firing probabilities for instant transitions Thit and Tmiss are Prhit and Prmiss and Prhit C Prmiss D 1. Furthermore, the firing probability can also be set as a function of the cache performance dynamics. If a miss event occurs, more than one backend data storage server will be accessed in parallel, denoted by transitions Taccess 1 ;    ; Taccess n . These data access processes may be repeated due to timeout events. When the requested data is ready, the server will process this job with detected service rate HIGH or LOW , which means that the transition firing rate of Tprocess is marking-dependent. Finally, the job will successfully return its results to the end users.

4

Performance and Reward Equivalent Analysis

This section introduces structural performance and reward equivalent methods[30] to reduce the complexity of the SSDN model and cut down the number of states. The four basic routing patterns shown in Fig. 2 are parallel routing, selective routing, iterative routing,

Fig. 2

301

Four service patterns.

and sequential routing. 4.1

Parallel routing

Parallel routing means that more than one job can be processed in parallel. The parallel routing model is shown in Fig. 2. One token is forked into n tokens and these tokens fire transition ti in parallel. The n parallel branches then gather together in the end. Theorem 1 Assume a parallel routing SSDN subnet with n time transitions t1 ;    ; tn and a firing delay of ti is an exponentially distributed random 1 , where i is the variable with expected value i expected value of the firing rate. The reward of each transition ti is ri . The performance and reward equivalent transition t with expected firing rate  and reward value r satisfies n n 1 X n X 1 X 1 1 D C  i i C j i D1

i D1 j Di C1

n 2 X n 1 X

n X

i D1 j Di C1 kDj C1

. 1/n

1

1 C C i C j C k

1 n X

(1)

i

i D1

r D r ts C r te C

n X

ri

(2)

i D1

The parallel routing structure in Fig. 1 is shown in detail in Fig. 3. The transitions Taccess 1 ;    ; Taccess n are reduced into a single transition T1 in Fig. 4, with the firing rate and reward satisfying Eq. (1) and Eq. (2). 4.2

Selective routing

Selective routing means that more than one transitions can fire, but only one transition can fire at one time. The selective routing model is shown in Fig. 4. One place

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Fig. 3

Fig. 4

Fig. 5

Parallel routing.

Selective routing.

forks into n branches and the token in the start place has some probability to fire into any branch. Theorem 2 Assume a selective routing SSDN subnet with n time transitions t1 ;    ; tn , and a firing delay of ti as an exponentially distributed random 1 variable with expected value where i is the i expected value of the firing rate. The reward value for each transition ti is ri . Then, the performance and reward equivalent transition t with expected firing rate  and reward value r satisfies 1 n D n X  (3) i i D1 n X

rD

i ri

i D1 n X

(4) i

i D1

The selective routing structure in Fig. 1 is shown in Fig. 4. The transitions Taccess m and T1 are reduced into a single transition T2 in Fig. 5, with the firing rate and reward satisfying Eq. (3) and Eq. (4). 4.3

Iterative routing.

Theorem 3 An iterative routing SSDN subnet contains three transitions, T1 , T2 , and T3 . The firing delay of ti is exponential distributed random variable 1 with expected value , where i is expected value i of the firing rate. The reward value of each transition ti is ri . Then, the performance and reward equivalent transition t with expected firing rate  and reward value r satisfies 1 1 C 2 C 3 (5) D C 3  1 3 2 rD .r1 C r2 / C .r1 C r3 / (6) 3 The parallel routing structure in Fig. 1 is shown in Fig. 5. The transitions Ttrans , T2 , and Ttimeout are reduced into a single transition T3 in Fig. 6 and the firing rate and reward satisfy Eq. (5) and Eq. (6). 4.4

Sequential routing

Sequential routing handles jobs one by one. The model of sequence routing is shown in Fig. 6. Theorem 4 Assume a sequential routing SSDN subnet has n time transitions t1 ;    ; tn , and the firing delay of ti is exponential distributed random variable 1 , where i is expected value with expected value i of the firing rate. The reward value of each transition ti is ri . Then the performance and reward equivalent transition t with expected firing rate  and reward value r satisfies n X 1 1 D (7)  i i D1

Iterative routing

Iterative routing means that a particular action executes repeatedly. The iterative routing model is shown in Fig. 5.

Fig. 6

Sequential routing.

Yuan Tian et al.: Performance Evaluation and Dynamic Optimization of Speed Scaling on Web Servers in   

rD

n X

ri

(8)

i D1

The parallel routing structure in Fig. 1 is shown in Fig. 6. The transitions Tarrival , Ttrans , T3 , Tprocess , and Tsucceed are reduced into a single transition T4 . The firing rate and reward satisfy Eq. (7) and Eq. (8).

5

Model Analysis Optimization

and

Strategy

will incur a cost, C.a/, which is caused by the power consumption of serving at the service rate costs .a/ or the pulse transition power consumption cost t .a/. Furthermore, each job completion event will generate a reward R, for the reward function in Eq. (10) Policy: The optimization objective is finding an optimal policy  to maximize the accumulated reward function with respect to an infinite horizon. 1 X max Ef R.t /g (9) a

5.1

Model analysis

The reduced performance and reward equivalent SSDN model is discrete event-driven and the decision epoch is on job arrival or job completion. Action space: The two unique action spaces for each state are #PHIGH D 1 and #PLOW . For state #PHIGH D 1, the action space is fDH2H ; DH2L g, where action DH2H denotes maintaining the current high service rate state and action DH2L denotes transferring to the low service rate state. For state #PLOW D 1, the action space is fDL2L ; DL2H g, where action DL2L denotes maintaining the current low service rate state and action DL2H denotes transferring to the high service rate state. Cost function: Each system behavior for action a 8 ˆ R costs .a/ cost t .a/; ˆ ˆ < R cost .a/; s R.s.t /; a; s.t C 1// D ˆ cost .a/; t ˆ ˆ : 0; 8 arrival ; ˆ CHIGH ˆ ˆ arrival HIGH < ; arrival CHIGH Pr.s.t C 1/js.t/; a/ D arrival ˆ ; ˆ CLOW ˆ arrival : LOW ; arrival CHIGH Dynamic programming is used to solve the MDP problem. The optimization criterion is set to maximize Formula. (9), which is the sum of the current reward (task reward minus energy cost). Thus, Bellmans equation[32] can be obtained as: X V .s/ D maxa.i/ fR.s; a.i // C ı pij .a/  V .j /g

5.2

t D0

MDP model

The method developed by Beccuti et al.[31] is used to obtain the isomorphic MDP for the MDP model shown in Fig. 7. In Fig. 7, the cycles denote the system states while the blocks denote actions related to the states joined by the arches, which means that the actions are dependent on the system states. The MDP model is a Continuous-Time Markov Chain (CTMC), that is embedded in a Discrete-Time Chain (DTMC). Pr.s.t C 1/js.t /; a/ is defined as the transition probability from state s.t / in time t to state s.t C 1/ in time .t C 1/ for action a. The state transition probability has the form given in Eq. (11). if s.t C 1/ D s.t / C 1 ^ a 2 DL2H [ DH2L I if s.t C 1/ D s.t / C 1 ^ a 2 DH2H [ DL2L I if s.t C 1/ D s.t / 1 ^ a 2 DL2H [ DH2L I otherwise if s.t if s.t if s.t if s.t

C 1/ D s.t / 1; w D H I C 1/ D s.t / C 1; w D H I C 1/ D s.t / 1; w D LI C 1/ D s.t / C 1; w D L

(10)

(11)

satisfies, Vn C

˛ 1

˛

ˇn e 6 V  6 Vn C

˛ 1

˛

˛n e

(13)

where e is the unit vector and ˛ and ˇ are defined as, ˛n D maxfŒV n s

ŒV n

ˇn D minfŒV n s

ŒV n

s2X

s2X

j 2X

(12) where R.s; a.i// is the reward of action a in the current state, pij is the transition probability from state i to j , X is the state space and ı is the discounted factor. The value iteration algorithm is used to solve the unconstrained MDP problem. In each iteration, the bound of the optimal solution, the optimal value V  ,

303

5.3

1 s g; 1 s g

(14)

Metric formulation

The optimal policy is obtained by solving the MDP, which is then put into the SSDN to get the performance and energy metrics. The metrics are the response time and the saved energy. The SPN is solved to formulate these two metrics. The response time can be obtain

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Fig. 8

Fig. 7 MDP model. Each state in this model is denoted by a 2-tuple as fs(t), L/Hg, s(t) is the buffer size of place BUFFER and the L/H denote whether in the low or high service rate state.

according to the Little formula as EfBufferg (15) PrfEfDecision endg > 0g  T arrival  arrival where EfBufferg is the average queue length, PrfDecision endg is the probability of the number of tokens in the queue being larger than 0, T arrival is the firing probability of transition Tarrival and arrival is the average arrival rate. The saved energy is defined as the probability of being in the low service rate plus the energy gap between the high service rate and the low service rate, (16) PrfEfPLOW g > 0g  .EHIGH ELOW / where PrfEfPLOW g > 0gg is the probability of the number of tokens in place LOW being greater than 0 and EHIGH and ELOW are the average energy consumption rates for the high and low service rates.

6

Numerical Results

A small scale parametrization is used as a example. The firing rates of the time transitions in Fig. 1 are given in Table 1. The high service rate is assumed to be 10, low service rate is assumed to be 5, the arrival rate is from 35, and the ratio between the task reward and the energy cost varies from 0 to 100. Figure 8 shows the model reduction results as the number of states in the original SSDN model and with Table 1 Name TH2L Tarrival Taccess i Tprocess

Number of states.

reduced SSDN model with respect to queue length. The performance and reward equivalent reduction techniques effectively simplify the complicated service model. For queue lengths of 30 and 60, the state space of the reduced SSDN is significantly less than that of the original model. Furthermore, as the queue length grows, both models grow linearly, but the absolute increase in the reduced model is much smaller than in the original model. Figure 9 shows the optimal policy for solving the SSDN is a threshold-based policy, with the threshold varying with different scenarios. In Fig. 9, the values on the x-axis denote the transition threshold from the low to high service rates, which the values in the y-axis denote the relative task reward to energy cost. For the same task arrival rate, as the task reward becomes larger, the transition threshold from the low to high service rates decreases. This trend means that the server will spend more time in the high service rate to get more task rewards. For threshold from 0-40, the server never changes into the high service rate because of the low task reward. This case is used to set the threshold about 0. Furthermore, for the same task reward, the threshold will decrease with increasing arrival rate because the faster arrivals increase the service rate requirement, which leads to earlier transitions from the low to high

Main parameter values.

Value 2.0 3.0/4.0/5.0 2.5 5.0/10.0

Name TL2H Taccess m Ttimeout Tsucceed

Value 10.0 3.5 5.0 10.0

Fig. 9

Variation of threshold.

Yuan Tian et al.: Performance Evaluation and Dynamic Optimization of Speed Scaling on Web Servers in   

service rates. Figure 10 shows that a larger task reward improves performance, e.g., a reduced response time. For threshold to be of 0-40, the response time remains high while for states larger than 40, the response time decreases. This is due to the varying of the threshold seen in Fig. 9. The server will not transition into the high service rate for task rewards from 0 to 40. Thus, the response time is constant for the same arrival rate. As the task reward becomes larger, the server will transition into the high service rate with a larger probability and the performance will improve. The increase of the task reward reduces saved energy as seen in Fig. 11 due to the threshold variation in Fig. 9. The saved energy is proportional to the probability of being in the low service rate, which will decrease with increasing task reward.

7

Conclusions

305

and MDP to dynamically optimize the speed scaling strategy and provide performance evaluations. The definition and structure of the SSDN are given with state dependent functions to implement the strategies. The model is graphical and intuitive enough to characterize the complicated system behavior and decisions action. The SSDN model is service-oriented, so a typical service pattern can be used to reduce the complex model to a simple model with a smaller state space. A performance and reward equivalent analysis is used to reduce the system behavior sub-net to one transition. The MDP model is more easily constructed so the MDP methodology is used to optimize the strategy. This analysis uses two system states, the high service rate and the low service rate, but this model can be scaled to more states. Future study will investigate larger scale states and how to solve state space explosion problem. Acknowledgements

This study uses the SSDN model to investigate speed scaling in cloud computing. This model combines SPN

This work was supported by the National Key Basic Research and Development (973) Program (Nos. 2012CB315801, 2011CB302805, 2010CB328105, and 2009CB320504), the National Natural Science Foundation of China (Nos. 60932003, 61020106002, and 61161140320), and the Intel Research Council with the title of “Security Vulnerability Analysis based on Cloud Platform with Intel IA Architecture”.

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[2] Fig. 10

Response time under different arrival rates.

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[8] Fig. 11

Energy consumption under different arrival rates.

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Yuan Tian received his BEng degree in computer science and technology from Tsinghua University, China, in 2007. Currently, he is working toward his PhD degree in the Computer Science and Technology Department, Tsinghua University, China. His current research interests include green network and performance evaluations.

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us/products/technologies/cool-n-quiet/Pages/cool-n-quiet. aspx, 2007. N. Bansal, K. Pruhs, and C. Stein, Speed scaling for weighted flow time, in Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms, Astor Crowne Plaza & New Orleans, Louisiana, 2007, pp. 805-813. T.W. Lam, L.K. Lee, I. To, and P. Wong, Speed scaling functions for flow time scheduling based on active job count, in Algorithms-ESA 2008, Karlsruhe, Germany, 2008, pp. 647-659. A. Wierman, L. L. Andrew, and A. Tang, Power-aware speed scaling in processor sharing systems, in the 28th IEEE Conference on Computer Communications, Rio de Janeiro, Brazil, 2009, pp. 2007-2015. L. L. Andrew, M. Lin, and A. Wierman, Optimality, fairness, and robustness in speed scaling designs, ACM SIGMETRICS Performance Evaluation Review, vol. 38, no. 1, pp. 37-48, 2010. C. Gunaratne, K. Christensen, and B. Nordman, Managing energy consumption costs in desktop pcs and lan switches with proxying, split tcp connections, and scaling of link speed, International Journal of Network Management, vol. 15, no. 5, pp. 297-310, 2005. X. D. Xiang, C. Lin, J. X. Wan, and Y. Tian, Stochastic service decision nets: Modeling, dynamic optimization, and performance evaluation for service computing systems, Technical report, 2013. M. K. Molloy, Performance analysis using stochastic petri nets, IEEE Transactions on Computers, vol. 100, no. 9, pp. 913-917, 1982. J. Q. Li, Y. S. Fan, and M. C. Zhou, Performance modeling and analysis of workflow, IEEE Transactions on Systems, Man and Cybernetics, vol. 34, no. 2, pp. 229-242, 2004. M. Puterman, Markov Decision Processes, Wiley, 1994. C. Lin, Q. Yang, F. Y. Ren, and M. Dan, Performance equivalent analysis of workflow systems based on stochastic petri net models, Engineering and Deployment of Cooperative Information Systems, Beijing, China, 2002, pp. 64-79. M. Beccuti, G. Franceschinis, and S. Haddad, Markov decision petri net and markov decision well-formed net formalisms, Petri Nets and Other Models of Concurrency, Siedlce, Poland, 2007, pp. 43-62. Bellman equation, http:// en.wikipedia.org/wiki/ Bellmanequation/, 2013.

Chuang Lin received his PhD degree in computer science from Tsinghua University in 1994. Currently, he is working as a professor in the Department of Computer Science and Technology, Tsinghua University, Beijing, China. His current research interests include computer networks, performance evaluation, network security analysis, and Petri net theory and its

Yuan Tian et al.: Performance Evaluation and Dynamic Optimization of Speed Scaling on Web Servers in    applications. He has published more than 300 papers in research journals and IEEE conference proceedings in these areas and has published three books. He serves as the Technical Program vice chair, the 10th IEEE Workshop on Future Trends of Distributed Computing Systems (FTDCS 2004); the General Chair, ACM SIGCOMM Asia workshop 2005; the associate editor, IEEE Transactions on Vehicular Technology; the area editor, Journal of Computer Networks; and the area editor, Journal of Parallel and Distributed Computing. He is a member of the ACM Council, a senior member of IEEE, and the Chinese Delegate in TC6 of IFIP.

Zhen Chen is an associate professor in the Research Institute of Information Technology at Tsinghua University. He received his BEng and PhD degrees from Xidian University in 1998 and 2004. He worked as a postdoctoral research associate in the Network Institute of Department of the Computer Science in Tsinghua University during 2004 to 2006. He was also a visiting scholar in UC Berkeley ICSI in 2006. His research interests include overlay networking architectures, Internet security, P2P systems, and Trusted Computing. He has published around 80 academic

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papers. Jianxiong Wan received his BS degree in computer science from Shanxi Normal University, received his master degree in management science from Beijing Information Technology Institute, he is now working towards his PhD in computer science from University of Science and Technology Beijing. His research interests include optimal control and performance evaluation of computer systems. Xuehai Peng received his PhD degree in communication and information systems from Beijing Jiaotong University in 2004. He finished a postdoctor at the Department of Computer Science and Technology, Tsinghua University in 2006. His current research interests include e-government, network routing and switching, trustworthy networks, and the mobile wireless Internet.

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