Multi-objective Optimization of Servers used in Online Games using Response Surface Methodology and...

Multi-objective Optimization of Servers used in Online Games using Response Surface Methodology and Reliability Function

Ali Ghorbanian * Department of Industrial Engineering, Faculty of Engineering, Tarbiat Modares University, Iran. Ali Salmasnia Department of Industrial Engineering, Faculty of Engineering and Technology, University of Qom, Iran. Mohamad Vardi Department of Industrial Engineering, Faculty of Engineering, Tarbiat Modares University, Iran.

*Corresponding author: [email protected]

Keywords Abstract Online games Reliability function approach Design of experiments Multi-objective optimization

Today internet based technologies effect on all aspects of our life rapidly. Undoubtedly, our hobbies get changed by technology like online games. Because of online games servers are expensive, determining optimal number of them in all around the world is became critical for game companies. On the other hand decreasing costs by reducing game servers result to servers overload therefore new users have to wait until free capacity will be available. It is worth noting that waiting users have extra costs like lost users for companies. In this paper we will provide a methodology in five following phases: mathematical modeling, collecting data and simulation, experimental design with reliability function approached in order to find out optimal answer of this problem.

1. Introduction Experimental design is the sequence of tests, so that using it we can make meaningful changes in the input variables of a process or system and distinguish the reasons for the changes that occur in response variables. In this study we have used the reliability function that has 7 steps, to obtain the optimal solution. Due to the significant increase in the development of computer games as well as their use by millions of users, one of the challenges of designers of these games is to minimize the users returned by the system, however, with regard to minimizing costs of the servers. Projections show that in 2009 over 230 million people using the network game. [12] 5 steps to resolve the above issue is expected including 1. Mathematical Modeling 2. Design of experiments 3. mathematical modeling and simulation 4. 4. reliability function Approach and 5. Optimization. In the first phase, for example, we have 4 servers on four continents examined. In this phase some information gathered about the distribution of logins to servers and the time spent in the system by users. Then, in the second step the mathematical model of the problem is stated, and also network simulation is performed using Arena simulation software. In the second step, also high and low levels of each control variable are specified as well as required answers of each test with regard to the design of experiments and the model of simulation. The final step is to optimize the problem using two approaches: Reliability function and the Simple weighting function. One of the concepts of the design of experiments is response surface method. This method is a set of mathematical and statistical techniques to model and analyze the issues in which a response variable influenced by multiple variables. The method’s purpose is to optimize the response variable. In some cases, the final evolution of process must be done in a manner that several output characteristics be considered simultaneously, thus, a multi-level response process arises. A simultaneous evaluation of multiple answers includes at first, creating an appropriate response surface model for each response variable, and then trying to find a set of operating conditions that optimizes all response variables, or at least keeps them at an optimal range [10]. One of the most widely used methods of optimization with multiple response level is Dual Response method, which includes two objective functions. One of these functions keeps response variable at the optimum level, and the other one minimizes the deviation of the response variable. When there is curvature in the system, a quadratic regression model is used. Let X i be I the factor’s level, and Y be answer’s level, then the quadratic regression model is expressed as equation (1).

)1( 푌 = 훽 + 훽 푥 + 훽 푥 + 훽 푥 푥 + 휀

Where ε represents is the observation error in the answer’s value, after obtaining the model, response surface analysis is performed on the model. To do so, factors affecting response and the effect of each encountered, the interaction of factors are determined and then, the optimal points which meet the conditions of problem are set. In [13] a study of the application of response surface methodology in the present and future is done, which in recent years has been focused on the design of stability parameters of response surface methodology for variance reduction and process improvement. Until now several techniques have been proposed for response level optimization problems. In [5] a reliability function to convert a variable number of responses to a single response variable is defined. In reference [7] an algorithm is available for optimizing multiple response functions that depend on the same set of control variables and appropriately expressed by a polynomial regression model. First, a distance function is defined by considering the ideal solution, and then optimal conditions are determined by minimizing this function. In reference [4] a GRG method is used for nonlinear programming based on Dual Response Method. The proposed method is simpler than the Dual Response methods and in some cases obtains a more optimized solution. In [9] the use of nonparametric variance estimation process is studied, then response function is weighted using a semi-parametric method in least squares framework and nonparametric regression is performed to variance and the response variable . Reference [8] proposes the general framework of multi-level problems with some existing works related to some kind of decision making, which attempts to aggregate all details in one approach. In reference 11, the reliability function is used to combine models. The reliability function method is conceptually simple and provides flexibility for individual weighted responses. In reference [6] Vikor method is used for optimization problems with multi-level response. In the proposed method, both mean and quality losses’ variance associated with response variables are considered, and it also seeks a low variance between response variables and low average of overall quality loss . Issues of placement have been discussed by some people, among them we can refer to Cong Duc Nguyen, Farzad Safaei, Paul Boustead in 2006 and Kang-Won Lee, Bong-Jun Ko, Seraphin Calo in 2005

World appl. programming, Vol(5), No (10), October, 2015. pp. 140-148

TI Journals

World Applied Programmingwww.tijournals.com

ISSN:

2222-2510

Copyright © 2015. All rights reserved for TI Journals.

2. The approach This step describes the method used to solve the problem, which has seven steps as forward:

2.1 Mathematical modeling In this step, we prepare mathematical model of the problem and show that using these models we cannot determine optimized answer.

2.2 Data gathering and model simulating In fact, to obtain response variable for each run of the experiments, a simulation model is developed by Arena software which obtains response variables for each of the factor levels. In this phase a regression model is specified, with regard to results obtained, and for each of the objective functions. Note that in this phase a regression model is also introduced for the variance of each objective function, and indeed, in addition to objective functions, we will also minimum their variance.

2.3 Design of experiments Test design involves more than one response variable. A test is designed with multiple levels of response, which relates to a process involving more than one repeatable response variables. This is illustrated in Table 1.

Table 1. Design pattern of tests

Responses Factor Levels Run 푌 푌 푋 푋 푦 .... 푦 푥 .... 푥 1 ..... ... ..... ... ... 푦 .... 푦 푥 .... 푥 n

2.4 Calculation of reliability function In reference [16] reliability function to optimize the multi-response is introduced. For this we use equation (2) for the reliability function in the case of minimization, and equation (3) to maximization.

)2( 푑 (푦 ) =

1,푦 < 푙푦 − 푢푙 − 푢 , 푙 ≤ 푦 ≤ 푢

0,푦 > 푢

)3( 푑 (푦 ) =

⎩⎨

⎧1,푦 < 푙

푦 − 푙푢 − 푙

, 푙 ≤ 푦 ≤ 푢

0,푦 > 푢

In equation (2), 푙 is the minimum acceptable value of 푦 and 푢 is the maximum acceptable value of 푦 . From a practical standpoint, we can imagine that any amount more than 푢 leads to an unacceptable answer in general case. Also 푙 specifies some values for 푦 , which lower values of those have the same benefits as 푙 . The following explains how to calculate these limits. One of the most popular ways of dealing with multi-objective problems is a reliability function approach. This approach was first presented in 1965 by Harrington (Joseph E. Harrington, 1965). This method systematically converts estimated value of 푌 (푋), to a unit less value of 푑 (푥) so called “reliability”, which changes in [0, 1] domain. In order to bring together the individual reliability functions, Harrington defines overall reliability function (D) as equation (4), which is the geometric mean of 푑 (푥):

)4( 퐷 = (푑 (푥) × 푑 (푥) × … × 푑 (푥))

In this study, we also use this approach to obtain overall reliability of each of the function, and to calculate variance of each.

2.5 Optimization On this point, the total reliability function is resolved using the Lingo software, optimal answers for the problem are obtained, and also these answers are compared using a simple weighted method.

3. Case study Today, due to significant growth in the computer games, an optimum level of server in different location is one of the biggest concerns of these games, in order to reduce the cost of these servers and also to minimize the number of returned users from system. As is clear from the nature of the problem, these two goals are in conflict with each other. We have tried to solve this problem using the methodology presented below.

3.1 The mathematical model As is clear from the nature of the problem, we have two conflicting aims: first, minimizing the total cost which includes fixed and variable costs, and second, minimizing the percentage of users who cannot login. First, we introduce the problem variables (table 2) and then, we describe the mathematical model.

141 Multi-objective Optimization of Servers used in Online Games using Response Surface Methodology and Reliability Function

World Applied Programming Vol(5), No (10), October, 2015.

Table 2. Problem variables

푓(퐶) Total cost 푓(퐶 ) Fixed costs total volume purchased 푓(퐶 ) The cost of moving people between different servers 푓(푅) Percent of those who have returned 푟 Percent return from the server Asia 푟 Percent return from the server Europe 푟 Percent return from the server, Australia 푟 Percent return from the server America 푥 Volume purchased from the server Asia 푥 Volume purchased from the server Europe 푥 Volume purchased from the Australian server 푥 Volume purchased from the America server 푇푟 All persons who have been placed on different servers 푐 Cost per person on different servers handling 푐 Cost per KB bought the server i

3.1.1 Total cost The total cost consists of two parts: the first one includes the costs of purchased server and second, the costs of relocating users on different servers. Equation (5) represents the mathematical model for this problem.

)5(

푓(퐶 ) = 푥 푐 + 푥 푐 + 푥 푐 + 푥 푐 푓(퐶 ) = 푇푟 ∗ 푐 푓(퐶) = 푓(퐶 ) + 푓(퐶 )

3.2 Data collection and simulation First, due to a large number if users we have chosen 4 continents for testing: Asia, Europe, Australia and America. To obtain the number of people from each of these continents are connected to the server, a number of countries that rank highest number of internet users has been selected. Due to past experiences and elite opinion, we assume that 1% of internet users from these countries want to use the game. Table 3 shows the statistics

Table 2. Number use the game

Country Number use the internet Number use the game China 511,963,000 511,963

America 242,614,880 242,615 Indian 119,749,712 119,750 Japan 101,376,528 101,377 Brazil 88,917,974 88,918

Germany 67,621,622 67,622 France 51,962,632 51,963 Korea 40,856,403 40,856 Italy 34,657,545 34,658 Spain 31,606,234 31,606

Canada 28,245,389 28,245 Argentina 19,925,830 19,926 Australia 17,195,702 17,196

Iran 16,357,156 16,357 Britain 51,412,657 51,413 Mexico 41,111,308 41,111

New Zealand 3,689,698 3,690 These statistics actually show that each year nearly one and a half million users use the game, which of course is very small compared to real games. Each user is logged according to a Poisson function, which is different for each country and is a Poisson function with parameter λ. The interval between each two login follows an exponential function with parameter λ, which table 4 represents it.

Table 3. Distribution function of user login DFC Intelligence, The Online Game Market

Country Type of function Average time between Member Login

China Exponential 1.03 America Exponential 2.17 Indian Exponential 4.39 Japan Exponential 5.18 Brazil Exponential 5.91

Germany Exponential 7.73 France Exponential 10.11 Korea Exponential 12.86 Italy Exponential 15.17

Spain Exponential 16.63 Canada Exponential 18.61

Argentina Exponential 26.38 Australia Exponential 30.57

Iran Exponential 32.13 Britain Exponential 10.22 Mexico Exponential 12.78

New Zealand Exponential 142.45

142 Ali Ghorbanian *, Ali Salmasnia, Mohamad Vardi


3.2.1 Time of usage Each user’s play time duration is determined with a time distribution, and it varies from one country to another. According to information obtained and previous evidence, the function is a normal distribution function and its mean and variance for each country will be a certain amount. This is itself is a function of various factors such as the age of the users, the social and cultural conditions, and other factors which are described in Table (5).

Table 4. Game-time distribution function for users

DFC Intelligence, The Online Game Market

Country Type of function Average(min) Deviation

China Normal 70 7 America Normal 80 20 Indian Normal 70 7 Japan Normal 70 7 Brazil Normal 80 20

Germany Normal 60 8 France Normal 60 8 Korea Normal 70 7 Italy Normal 60 8 Spain Normal 60 8

Canada Normal 80 20 Argentina Normal 80 20 Australia Normal 85 15

Iran Normal 70 7 Britain Normal 60 8 Mexico Normal 80 20

New Zealand Normal 85 15

Basically, the connections between two computers or a computer and a server have 4 different states, that figure (1) shows them [2].

Figure 1. Types of users’ connection in a game

The model used in this study, is model of C. In this type users are connected to multiple servers, and each of the users with respect to the costs, connects to the nearest server. The servers are also connected to each other. In the model, indeed first, user connects to a considered server. If the server due to lack of capacity does not have the ability to respond to user, the user will automatically be transferred to the next server and so all servers will be reviewed. Finally, if there would be no empty server, the user is logged out. Simulating this model, we have used the simulation software Arena 14 which is shown by figure (2).

3.3 Design of experiments The above model is to determine the optimal level of four servers from Asia, Europe, Australia and America. For this purpose we first obtained up and down level for each of them. To obtain down level, it is assumed that the servers have no connection with each other, and indeed, each server has its own user. We’ve chosen server size such that at least 80% of users could use it. In fact, the maximum rate of return for each server is equal to 15%. The same methodology is used to obtain up level and for each server you have selected the amount of volume that all users can login. In fact, in this point return rate is zero and the results are shown in Table (6).



Figure 2. Simulated network using software

Table 6. Up and down limits of factors

Up level Down level Server name 47000 28000 Asia 16000 8000 Europe 3800 1500 Australia

30500 17500 America Since each factor has two levels, the number of tests is 16 and we tested each of them four times. The results are shown in Table (7). Each of the experiments is coded using equations 6 to 9.

)6( 푥 (푐표푑푒푑) =푥 − 37500

23500 − 14000

)7( 푥 (푐표푑푒푑) =푥 − 12000

8000 − 4000

)8( 푥 (푐표푑푒푑) =푥 − 2650

1900 − 750

(9) 푥 (푐표푑푒푑) =푥 − 24000

15250 − 8750

Fractions’ denominators are obtained from and the numerators are derived from 푋 − .

Table 5. Cost function test results

Asia Europe Australian America Total cost Deviation -1 -1 -1 -1 117,736 117,659 17,661 117,929 127 1 -1 -1 -1 104,514 104,528 104,483 104,527 21 -1 1 -1 -1 98,958 99,001 98,976 98,974 18 1 1 -1 -1 113,689 113,744 113,648 113,687 40 -1 -1 1 -1 94,076 94,026 93,990 94,002 38 1 -1 1 -1 107,256 107,231 107,177 107,209 34 -1 1 1 -1 100,494 100,531 100,332 100,440 87 1 1 1 -1 116,346 116,406 116,308 116,348 40 -1 -1 -1 1 104,824 104,848 104,719 104,771 57 1 -1 -1 1 119,852 119,867 119,843 119,852 10 -1 1 -1 1 112,397 112,506 112,406 112,423 50 1 1 -1 1 129,806 129,799 129,796 129,797 4 -1 -1 1 1 107,455 107,393 107,307 107,370 61 1 -1 1 1 122,686 122,708 122,687 122,694 122,686 -1 1 1 1 115,167 115,164 115,060 115,237 73 1 1 1 1 132,640 132,640 132,640 132,640 0



Table 6. Results of return percentage experiments

Asia Europe Australian America Percent return Deviation Asia Europe Australian -1 -1 -1 -1 0.107400000 0.107400000 -1 -1 -1 1 -1 -1 -1 0.000069760 0.000010980 1 -1 -1 -1 1 -1 -1 0.022690000 0.023190000 -1 1 -1 1 1 -1 -1 0.000000000 0.000000000 1 1 -1 -1 -1 1 -1 0.076650000 0.076730000 -1 -1 1 1 -1 1 -1 0.000012420 0.000006210 1 -1 1 -1 1 1 -1 0.010876000 0.011029000 -1 1 1 1 1 1 -1 0.000000000 0.000000000 1 1 1 -1 -1 -1 1 0.003879000 0.004089000 -1 -1 -1 1 -1 -1 1 0.000000000 0.000000000 1 -1 -1 -1 1 -1 1 0.000018650 0.000021390 -1 1 -1 1 1 -1 1 0.000000000 0.000000000 1 1 -1 -1 -1 1 1 0.001151000 0.001227000 -1 -1 1 1 -1 1 1 0.000000000 0.000000000 1 -1 1 -1 1 1 1 0.000008970 0.000002070 -1 1 1 1 1 1 1 0.000000000 0.000000000 1 1 1

When design of experiments performed, factors affecting each of the objective function and standard deviation of them are obtained as follows.

1600014000120001000080006000400020000

99

95

90

80

7060504030

20

10

5

1

Effect

Perc

ent

A AB BC CD D

Factor Name

Not SignificantSignificant

Effect Type

ADAB

D

CB

A

Normal Plot of the Effects(response is total cost, Alpha = 0.05)

Lenth's PSE = 254.522

403020100-10-20-30-40-50

99

95

90

80

7060504030

20

10

5

1

Effect

Perc

ent

A AB BC CD D

Factor Name


Effect Type

A

Normal Plot of the Effects(response is Standard deviation_c, Alpha = 0.05)

Lenth's PSE = 13.9010

0.030.020.010.00-0.01-0.02-0.03

99

95

90

80

7060504030

20

10

5

1

Effect

Per

cen

t

A AB BC CD D

Factor Name


Effect Type

AD

D

A

Normal Plot of the Effects(response is Reject, Alpha = 0.05)

Lenth's PSE = 0.00804849

0.00030.00020.00010.0000-0.0001-0.0002-0.0003

99

95

90

80

7060504030

20

10

5

1

Effect

Per

cen

t

A AB BC CD D

Factor Name


Effect Type

Normal Plot of the Effects(response is Standard deviation_R, Alpha = 0.05)

Lenth's PSE = 0.000102437

Figure 3. Factors affecting on answers Based on above results and the factors affecting them, we have estimated the value of the objective function which is as follows. Due to factors affecting overall cost as well as the results of the design of experiments (figure 3), total cost is to be calculated from the equation (10).

)10( 푦 = 110703 + 7642푥 + 4234푥 + 1286푥 + 7390푥 + 542푥 + 511푥



Table 9. Experiment design results in relation to the total cost Term Effect Coef Constant 110703 A 15284 7642 B 8468 4234 C 2572 1286 D 14780 7390 A*B 1083 542 A*C 190 95 A*D 1023 511 B*C -148 -74 B*D 359 180 C*D 177 88 A*B*C 137 68 A*B*D 35 18 A*C*D -98 -49 B*C*D 181 91 A*B*C*D -170 -85

Equation (11) is used to estimate the standard deviation of total cost with respect to the factors influencing and results of experiments.

Table 10. Experiment design results in respect to standard deviation of total cost Term Effect Coef Constant 41.88 A -43.95 -21.98 B -5.84 -2.92 C 2.08 1.04 D -17.24 -8.62 A*B 8.27 4.14 A*C 0.18 0.09 A*D -10.26 -5.13 B*C 20.05 10.02 B*D 2.86 1.43 C*D 3.60 1.80 A*B*C -24.10 -12.05 A*B*D -13.17 -6.59 A*C*D -7.99 -3.99 B*C*D -16.44 -8.22 A*B*C*D 18.28 9.14

)11( 푦 = 41.88− 21.98푥 Estimation of return rate from the system is performed using equation (12) and with respect to the factors affecting and experiments’ results.

)12( 푦 = 0.01389− 0.01388푥 − 0.01324푥 + 0.011323푥

The same process is used to estimate the standard deviation of returned users and equation (13) can be used.

Table 11. Experiment design results, standard deviation of return percentage

Term Effect Coef Constant 0.000129 A -0.000247 -0.000124 B -0.000112 -0.000056 C -0.000035 -0.000017 D -0.000223 -0.000111 A*B 0.000100 0.000050 A*C 0.000025 0.000013 A*D 0.000211 0.000106 B*C 0.000072 0.000036 B*D 0.000080 0.000040 C*D 0.000021 0.000011 A*B*C -0.000063 -0.000032 A*B*D -0.000068 -0.000034 A*C*D -0.000012 -0.000006 B*C*D -0.000059 -0.000029 A*B*C*D 0.000049 0.000025

)13( 푦 = 0.000129− 0.000124푥 − 0.000111푥

Now that each of the functions was estimated and standard deviation is obtained, our aim is to minimize their standard deviation in addition of to minimize the primary objective functions (return percentage and cost). The overall objective function is shown by equation (14).



)14(

Min (푦 ,푦 ,푦 ,푦 ) S.t

푦 = 110703 + 7642푥 + 4234푥 + 1286푥 + 7390푥 + 542푥 + 511푥 푦 = 41.88− 21.98푥 푦 = 0.01389 − 0.01388푥 − 0.01324푥 + 0.011323푥 푦 = 0.000129− 0.000124푥 − 0.000111푥 푥 , 푥 , 푥 ,푥 ∈ ⌊−1,1⌋

Various techniques of multi-criteria decision can be used to optimize the problem. But given that the rate of return shouldn’t exceed the permissible limit the reliability function approach is used for optimization. Simple weighted method has been used too.

3.4 Reliability function According to the description provided about the method used in the reliability function, it is calculated for each objective function. First, up and down limits of each objective function is identified, table 12 represents it.

Table 12. Up and down limits of optimization

High reliability Lower reliability 95000 90000 Total cost 0.001 0 Percent Return

50 0 Standard deviation of total costs 0.00001 0 Standard deviation of returns

Then with respect to equations 15-18, reliability function of each objective function is obtained.

(15) 푑 (y ) = 95000 − y

5000

(16) 푑 (y ) = 0.001 − y

0.001

(17) 푑 (y ) = 50 − d

50

(18) 푑 (y ) = 0.00001 − d

0.00001

Overall reliability is obtained according to equation (19).

(19) 퐷 =

95000 − y5000

.0.001 − y

0.001.

50 − d50

.

0.00001 − d0.00001

Since the goal of this projection is to maximize the reliability function, mathematical optimization model is shown by equation (19).

3.5 Optimization Using Lingo 11 mentioned problem is solved and results are shown in Table (13).

Table 13. Reliability function results

Server Asia Server Europe Server Australia Server America Total Cost Returns 28095 12000 2650 24000 94999 0.00010

These results are also simulated using Arena software and the results of the simulation are shown in Table (14).

Table 14. Simulation results

Server Asia Server Europe Server Australia Server America Total Cost Returns 28095 12000 2650 24000 100939 0.0070

3.5.1 Simple weighted optimization approach In this approach, a weight of wi is determined for each objective function, so that the sum up of the weights should be equal to 1. All weights of above problem are assumed to be equal and the results are as follows.

Table 15. Results obtained from simple weighted approach

37500 0 푥 12000 0 푥 2650 0 푥 24000 0 푥

Results in table (15) indicate that a fairly good answer is buying up and down limit of each server so that, we can reduce transfer costs.



4. Conclusions In this study, we have investigated a new issue in the literature and providing a methodology tried to obtain optimal results. Presented methodology consists of five phases, including mathematical modeling phase, data collection and modeling, experiment design, use of reliability function approach and optimization. We have first presented a mathematical model for the problem, and showed that this model cannot be solved by conventional methods. Then we simulated the model using Arena software. The simulated model was used then, to obtain the results of each stage of experiments. Finally, using the reliability function approach and Lingo software, we have obtained the optimal solutions to the problem and compared them with simple weighted method

References [1] Bhaskar, V. and P. Lallement. "Modeling a supply chain using a network of queues Vidhyacharan Bhaskar." Applied Mathematical Modelling 34: 2074–

2088,2010. [2] Cong Duc Nguyen, Farzad Safaei, and Paul Boustead ,Computer Communications ,29.2006. [3] DFC Intelligence, The Online Game Market California, USA, , available at http://www.dfcint.com/ [4] Del Castilo, E., Montgomery, D.C., "A Nonlinear programming Solution to the Dual Response Problems" Journal of Quality Technology,pp.199-204,1993. [5] Derriger ,g., Suish, R., "Simultaneous Optimization of several response Variables" Journal of Quality Technology,12,1980. [6] Kang-Won Lee a, Bong-Jun Ko b, and Seraphin Calo Computer Networks 49, 2005. [7] Khuri, A., Colon, m., " Simultaneous Optimization of several response Represented by polynomial regression functions" , Technometrices, 23 , pp 363-375,

1981. [8] Leite, S. C. and M. D. Fragoso. "Heavy traffic analysis of state-dependent parallel queues with triggers and an application to web search systems."

Performance Evaluation 67: Haag, Burlington, Mass, Academic press,2010. [9] O. Jouini, Y. Dallery and Z. Aksin, “Queueing models for full-flexible multi-class call centers with real-time anticipated delays”, International Journal of

Production Economics 120(2): 389-399, 2009 [10] Mandelbaum and S. Zeltyn, “Staffing many-server queues with impatient customers: constraint satisfaction in call centers”, Working Paper, Thechnion, Haifa,

Israel, 2008 [11] Miller, B. M. ,"Optimization of queuing system via stochastic control." Automatica 45: 1423-1430,2009. [12] Montgomery, D.c., "Design and Analysis of Experiments", 6th Edition, john Wiley & sons,2006 [13] Myers, R.h., "response Surface Methodology – Current Status and Future Direction", Journal of Quality Technology,31(1) ,pp.30-44,1999



Multi-objective Optimization of Servers used in Online Games using Response Surface Methodology and...

Documents

Transcript of Multi-objective Optimization of Servers used in Online Games using Response Surface Methodology and...