Capacity planning for server resources

• US 20050005012A1
• Filed: 07/23/2004
• Published: 01/06/2005
• Est. Priority Date: 04/14/2000
• Status: Active Grant

• Current Assignee: Microsoft Technology Licensing LLC (Microsoft Corporation)
• Original Assignee: Microsoft Corporation
• Inventors: Odhner, Matt, Zizys, Giedrius, Schliiter, Kent
• Granted Patent: US 7,313,620 B2
• Time in Patent Office: Days
• US Class Current: 709/226
• CPC Class Codes: G06Q 10/06 Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling

Abstract

Methods and systems for capacity planning of server resources are described wherein fixed resources of a server cluster are used in comparison to similar server cluster benchmarks to determine the maximum load—requests per second—that can be handled by the server cluster. The maximum load is used to determine utilization of server resources and to provide estimates of server resource utilization for hypothetical loads. A recommendation as to changes to server resources to handle the hypothetical loads is displayed to the user.

Claims

1. A method, comprising:

deriving a load table that contains empirically-derived load table values, each load table value representing a maximum load handled by one or more servers having a known amount of memory and a processor having a known speed;

receiving server parameter values indicating operating parameters for one or more servers in a server cluster;

receiving a specified load value that indicates a load desired to be handled by the server cluster;

utilizing the load table with the server parameter values and the specified load value to derive server resource utilization estimates for the server resources to determine how handling the specified load will affect the utilization of server resources; and

displaying the server resource utilization estimates.

2. The method recited in claim 1, further comprising recommending a plan for possible changes to be made to the server cluster to optimize server cluster performance, the plan being based on the server resource utilization estimates.

3. The method recited in claim 2, further comprising storing the plan in non-volatile memory.

4. The method recited in claim 1, wherein the server resource utilization estimates comprise estimates for one or more of the following:

processor utilization, memory utilization, communication bandwidth utilization, and general server utilization.

5. The method recited in claim 1, wherein:

the server cluster handles a total number of multiple document types, each document type having a document type value assigned to it, the document type value for each document type indicating the amount of each document type in relation to the total amount of document types;

the deriving a load table further comprises deriving a load table for each document type, the load values in the load table being empirically-derived from servers having a known amount of memory and a processor having a known speed, and the load comprising only the document type for which the load table is derived; and

the utilizing the load table with the server parameter values and the specified load value further comprises;

for each document type, finding the closest match in the corresponding load table between the server parameter values and the entries in the load table; and

deriving server resource utilization estimates by using the load value of the closest match as the maximum load that can be handled by the server for each document type.

6. The method recited in claim 5, wherein the server resource utilization estimate derived is processor utilization, and the method further comprises:

deriving processor regression constant a and processor regression constant b for each document type by solving;

$\begin{array}{c}y=a+b·<br><br>x\\ g<br><br>\left(x\right)=\stackrel{\_}{y}+b_{\mathrm{yx}}·<br><br>\left(x-\stackrel{\_}{x}\right)\\ b_{\mathrm{xy}}=\frac{\stackrel{\_}{\left(x-\stackrel{\_}{x}\right)·<br><br>\left(y-\stackrel{\_}{y}\right)}}{\stackrel{\_}{{\left(x-\stackrel{\_}{x}\right)}^2}}\\ a=\stackrel{\_}{y}-b_{\mathrm{yx}}·<br><br>\stackrel{\_}{x}\\ b=b_{\mathrm{yx}}\end{array}$

wherein x is an independent variable corresponding to cluster load, and y is the dependent variable corresponding to processor utilization, there being multiple pairs of (x, y) values; and

deriving processor utilization by solving;

$U_{\mathrm{CPU}}=\underset{i}{\overset{\text{\hspace{1em}<br><br>}}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{a_i}{{\mathrm{e<br><br>}}^{b_i·<br><br>q_i·<br><br>L}}$

wherein U_CPU is processor utilization;

i is the document type;

a_i is the processor regression constant a for document type i;

b_i is the processor regression constant b for document type i;

q_i is the document value for document type i, expressed as a decimal percentage; and

L is the specified load.

7. The method recited in claim 5, wherein the server resource utilization estimate derived is communication bandwidth utilization, and the method further comprises:

deriving bandwidth regression constant c and bandwidth regression constant d for each document type by solving;

$\begin{array}{c}y=c+d·<br><br>x\\ g<br><br>\left(c\right)=\stackrel{\_}{d}+d_{d<br><br>\text{\hspace{1em}<br><br>}<br><br>c}·<br><br>\left(c-\stackrel{\_}{c}\right)\\ c_{c<br><br>\text{\hspace{1em}<br><br>}<br><br>d}=\frac{\stackrel{\_}{\left(c-\stackrel{\_}{c}\right)·<br><br>\left(d-\stackrel{\_}{d}\right)}}{\stackrel{\_}{{\left(c-\stackrel{\_}{c}\right)}^2}}\\ c=\stackrel{\_}{d}-d_{d<br><br>\text{\hspace{1em}<br><br>}<br><br>c}·<br><br>\stackrel{\_}{c}\\ d=d_{d<br><br>\text{\hspace{1em}<br><br>}<br><br>c}\end{array}$

wherein c is an independent variable corresponding to cluster load, and d is the dependent variable corresponding to communication bandwidth utilization, there being multiple pairs of (c, d) values; and

deriving communication bandwidth utilization by solving;

$U_B=\underset{i}{\overset{\text{\hspace{1em}<br><br>}}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{F_{\mathrm{TCP}}·<br><br>\left(c_i+d_i·<br><br>q_i·<br><br>L\right)}{B}$

wherein U_B is communication bandwidth utilization;

F_TCP is a transmission overhead factor for each document type that, when applied to a certain size page of the document type, results in the actual bandwidth necessary to transmit the page;

i is the document type;

c_i is the bandwidth regression constant c for document type i;

d_i is the bandwidth regression constant d for document type i;

q_i is the document value for document type i, expressed as a decimal percentage;

L is the specified load; and

B is the total communication bandwidth available.

8. The method recited in claim 5, wherein the server resource utilization estimate derived is memory utilization, and the method further comprises:

deriving memory utilization by solving;

$U_M=\frac{N·<br><br>\left(M_{\mathrm{TCP}}+M_{\mathrm{IISStruct}}\right)+M_{\mathrm{OS}}+M_{\mathrm{IIS}}}{M}$

wherein N is a number of concurrent connections derived by solving;

$N=\underset{i}{\overset{\text{\hspace{1em}<br><br>}}{\sum <br><br>}}<br><br>\left(\frac{q_i·<br><br>L}{\left(X_i-q_i·<br><br>L\right)}\right)+\mathrm{S1}·<br><br>q_i·<br><br>L$

wherein U_M is memory utilization;

M_TCP is an amount of memory necessary to support each connection for communications;

M_IISStruct is the amount of memory necessary to support data structures associated with each connection;

M_OS is the amount of memory required by a server operating system;

M_IIS is the amount of memory required by a server communication program;

M is the amount of total memory available;

i is the document type;

q_i is the document value for document type i, expressed as a decimal percentage;

L is the specified load;

X_i is the load value obtained from the load table for document type i; and

S1 is a connection memory factor that is the adjusted average of the incoming connections at different speeds.

9. The method recited in claim 5, wherein the server resource utilization estimate derived is general server utilization, and the method further comprises:

deriving general server utilization by solving;

$U=\underset{i}{\overset{\text{\hspace{1em}<br><br>}}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{q_i·<br><br>L}{X_i}$

wherein i is the document type;

q_i is the document value for document type i, expressed as a decimal percentage;

L is the specified load; and

X_i is the load value obtained from the load table for document type i.

10. One or more computer-readable media having computer-readable instructions thereon which, when executed by one or more computers, cause the computers to implement the method of claim 5.

11. A method for deriving server resource utilization estimates for a server cluster that handles multiple document types, the method comprising:

assigning a document type value to each document type, each document type value indicating a percentage that each document type makes up of a total amount of document types;

deriving a load table for each document type, each load table containing load table values empirically derived from a server cluster that has a known amount of memory and a processor having a known type and speed, each load table value representing a maximum load that can be handled by the server cluster when the load comprises only one of the multiple document types;

receiving one or more server cluster parameter values that indicate operating parameters for the server cluster;

receiving a specified load value that indicates a load desired to be handled by the server cluster;

utilizing the load tables to derive server resource utilization estimates to determine how handling the specified load will affect the utilization of server resources; and

recommending a plan to optimize handling of the specified load by increasing resources of the server cluster.

12. The method recited in claim 11, wherein the utilizing the load tables to derive server resource utilization estimates further comprises:

for each document type, finding the closest match in the corresponding load table between the memory and processor of the server cluster with the memory and processor entries in the load table; and

deriving server resource utilization estimates by using the load value of the closest match as the maximum load that can be handled by the server cluster for each document type.

13. The method recited in claim 12, wherein the server resource utilization estimate derived is processor utilization, and the method further comprises:

displaying the server resource utilization estimates;

deriving a first processor regression constant and a second processor regression constant for each document type by;

(1) finding a functional dependency approximation between processor utilization and load for each document type;

(2) transforming the functional dependency into linear form by using logarithmic transformation;

(3) deriving the first and second processor regression constants using linear regression methodology;

finding a partial processor utilization for each document type by dividing the first processor regression constant for a particular document type by e to the power of the product of the specified load, the document type value, and the second processor regression constant for the document type; and

summing the partial processor utilizations to derive the processor utilization of the server cluster for the specified load.

14. The method recited in claim 12, wherein the server resource utilization estimate derived is communication bandwidth utilization, and the method further comprises:

deriving a first bandwidth regression constant and a second bandwidth regression constant for each document type by;

(1) finding a functional dependency approximation between communication bandwidth utilization and load for each document type;

(2) transforming the functional dependency into linear form by using logarithmic transformation;

(3) deriving the first and second bandwidth regression constants using linear regression methodology;

determining a transmission overhead factor for each document type that, when applied to a certain size page of the document type, results in the actual bandwidth necessary to transmit the page;

finding a raw partial bandwidth utilization for each document type utilizing the document type value, the specified load, and the first and second bandwidth regression constants for the document type;

finding a weighted partial bandwidth utilization for each document type utilizing the raw partial bandwidth utilization for a document type and the transmission overhead factor for the document type;

finding a partial bandwidth utilization for each document type that is a function of the weighted partial bandwidth utilization for each document type and the total communication bandwidth available; and

summing the partial bandwidth utilizations to derive the communication bandwidth utilization.

15. The method recited in claim 12, wherein the server resource utilization estimate derived is communication bandwidth utilization, and the method further comprises:

deriving a first bandwidth regression constant and a second bandwidth regression constant for each document type by;

(1) finding a functional dependency approximation between communication bandwidth utilization and load for each document type;

(2) transforming the functional dependency into linear form by using logarithmic transformation;

(3) deriving the first and second bandwidth regression constants using linear regression methodology;

determining a transmission overhead factor for each document type that, when applied to a certain size page of the document type, results in the actual bandwidth necessary to transmit the page;

finding a raw partial bandwidth utilization for each document type by multiplying the document type value by a product of the specified load and the second bandwidth regression constant for the document type, and adding the first bandwidth regression constant for the document type;

finding a weighted partial bandwidth utilization for each document type by multiplying the raw partial bandwidth utilization for a document type by the transmission overhead factor for the document type;

finding a partial bandwidth utilization for each document type by dividing the weighted partial bandwidth utilization for each document type by the total communication bandwidth available; and

summing the partial bandwidth utilizations to derive the communication bandwidth utilization.

16. The method recited in claim 12, wherein the server resource utilization estimate derived is memory utilization, the method further comprising:

for each document type, deriving a connection memory factor as a function of the incoming connections at different speeds;

for each document type, deriving a weighted connection memory factor as a function of the connection memory factor, the specified load and the document type value;

for each document type, deriving a page load ratio utilizing the document type value, the specified load, the load value obtained from load table for the document type and the document type value;

for each document type, deriving a number of concurrent connections from the weighted connection memory factor and the page load ratio;

summing the number of concurrent connections for each document type to derive a total number of concurrent connections; and

deriving the memory utilization by multiplying from the total number of concurrent connections, the amount of memory necessary to support each connection for communications, the amount of memory necessary to support data structures associated with each connection, the amount of memory required by a server operating system, the amount of memory required by the server communication program, and the total memory available.

17. The method recited in claim 12, wherein the server resource utilization estimate derived is memory utilization, the method further comprising:

for each document type, deriving a connection memory factor that is the adjusted average of the incoming connections at different speeds;

for each document type, deriving a weighted connection memory factor by multiplying the connection memory factor by a product of the specified load and the document type value;

for each document type, deriving a page load ratio by dividing the product of the document type value and the specified load by the difference between the load value obtained from load table for the document type and the product of the document type value and the specified load;

for each document type, adding the weighted connection memory factor and the page load ratio to derive a number of concurrent connections for each document type;

summing the number of concurrent connections for each document type to derive a total number of concurrent connections; and

deriving the memory utilization by multiplying the total number of concurrent connections by the sum of the amount of memory necessary to support each connection for communications and the amount of memory necessary to support data structures associated with each connection, and adding the amount of memory required by a server operating system and the amount of memory required by the server communication program, and dividing the result thereof by total memory available.

18. The method recited in claim 12, wherein the server resource utilization estimate derived is general server utilization, and wherein the method further comprises:

deriving a partial load for each document type from the document type value for a document type and the specified load;

deriving a partial utilization value for each document type from the partial load for a document type and the load table value for the document type; and

deriving the general server utilization by summing the partial utilization values.

19. The method recited in claim 12, wherein the server resource utilization estimate derived is general server utilization, and wherein the method further comprises:

deriving a partial load for each document type by multiplying the document type value for a document type by the specified load;

deriving a partial utilization value for each document type by dividing the partial load for a document type by the load table value for the document type; and

deriving the general server utilization by summing the partial utilization values.

20. One or more computer-readable media having computer-readable instructions thereon which, when executed by one or more computers, cause the computers to implement the method of claim 12.

21. A method for deriving server resource utilization estimates for a server cluster, the method comprising:

collecting one or more server cluster parameter values at different times during operation of the server cluster, the server cluster parameters indicating utilization of server resources;

extrapolating the collected values to determine the maximum load value that can be handled by the server cluster;

receiving a specified load value that indicates a load desired to be handled by the server cluster;

utilizing the extrapolated maximum load value to determine if the collected values are of sufficient accuracy to use in deriving server resource utilization estimates;

deriving server resource utilization estimates to determine how handling the specified load will affect the utilization of server resources if the collected values have been determined to provide sufficient accuracy;

displaying the server resource utilization estimates; and

recommending a plan to optimize handling of the specified load by increasing resources of the server cluster, if necessary.

22. The method as recited in claim 21, wherein the collected values include one or more of the following parameters:

incoming server load;

CPU utilization;

number of bytes transmitted by server cluster;

available communication bandwidth;

processor type;

processor speed;

available memory;

types of documents transmitted; and

types of client connections.

23. The method as recited in claim 21, wherein the collecting server parameter values is performed over a user-defined period of time.

24. The method as recited in claim 21, wherein the extrapolating the collected values to determine the maximum load value that can be handled by the server cluster further comprises:

deriving first and second processor regression constants using regression analysis with a CPU utilization value for an incoming server load collected at a certain time; and

utilizing the first and second processor regression constants to determine the maximum load value that can be handled by the server cluster.

25. The method as recited in claim 21, wherein the specified load value is input by a user as a total number of requests per second that the user desires the server cluster to handle, or as a percentage increase over the current number of request per second that the server cluster can handle.

26. The method as recited in claim 21, wherein the utilizing the extrapolated maximum load value to determine if the collected values are of sufficient accuracy further comprises:

determining the first derivative of CPU utilization as a function of the specified load;

determining the value of the function at the point of the largest collected incoming server load value to obtain a slope value;

comparing the slope value with a pre-determined value and, if the slope value is larger than the pre-determined value, then assuming the collected values are of sufficient accuracy to proceed; and

determining the specified load value at which the CPU utilization equals one hundred percent, and using that load value as the maximum load value that can be handled by the server cluster for further calculations.

27. The method as recited in claim 21, wherein the server resource utilization is processor utilization, the method further comprising:

finding a functional dependency approximation between processor utilization and load;

transforming functional dependency into linear form by using logarithmic transformation;

deriving first and second processor regression constants using linear regression methodology;

dividing the first processor regression constant by e to the power of the product of the second processor regression constant and the specified load to obtain the processor utilization estimate.

28. The method as recited in claim 21, wherein the server resource utilization is communication bandwidth utilization, the method further comprising:

finding a functional dependency approximation between communication bandwidth utilization;

transforming functional dependency into linear form by using logarithmic transformation;

deriving first and second bandwidth regression constants using linear regression methodology;

deriving a transmission overhead factor that, when applied to a certain size web page, results in the actual capacity necessary to transmit the web page;

deriving a weighted communication overhead factor from the transmission overhead factor and the available communication bandwidth;

deriving an adjusted communication load from the specified load and the first and second bandwidth regression constants; and

determining the communication bandwidth utilization estimate utilizing the weighted communication overhead factor and the adjusted communication load.

29. The method as recited in claim 21, wherein the server resource utilization is communication bandwidth utilization, the method further comprising:

finding a functional dependency approximation between communication bandwidth utilization;

transforming functional dependency into linear form by using logarithmic transformation;

deriving first and second bandwidth regression constants using linear regression methodology;

deriving a transmission overhead factor that, when applied to a certain size web page, results in the actual capacity necessary to transmit the web page;

deriving a weighted communication overhead factor by dividing the transmission overhead factor by the available communication bandwidth;

deriving an adjusted communication load by adding the first bandwidth regression constant to the product of the specified load and the second bandwidth regression constant; and

determining the communication bandwidth utilization estimate by multiplying the weighted communication overhead factor by the adjusted communication load.

30. The method as recited in claim 21, wherein the server resource utilization is memory utilization, the method further comprising:

deriving a connection memory factor that is the adjusted average of the incoming connections at different speeds;

deriving a weighted connection memory factor by multiplying the connection memory factor by the specified load;

deriving a page load ratio by dividing the specified load by the difference of the maximum load value and the specified load;

deriving a total number of concurrent connections from the weighted connection memory factor and the page load ratio; and

deriving a gross memory utilization using the total number of concurrent connections, the amount of memory necessary to support each connection for communications, the amount of memory necessary to support data structures associated with each connection, the amount of memory required by a server operating system, and the amount of memory required by the server communication program; and

deriving the memory utilization estimate from the gross memory utilization and total memory available.

31. The method as recited in claim 21, wherein the server resource utilization is memory utilization, the method further comprising:

deriving a connection memory factor that is the adjusted average of the incoming connections at different speeds;

deriving a weighted connection memory factor by multiplying the connection memory factor by the specified load;

deriving a page load ratio by dividing the specified load by the difference of the maximum load value and the specified load;

deriving a total number of concurrent connections by adding the weighted connection memory factor and the page load ratio; and

deriving a gross memory utilization by multiplying the total number of concurrent connections by the sum of the amount of memory necessary to support each connection for communications and the amount of memory necessary to support data structures associated with each connection, and adding the amount of memory required by a server operating system and the amount of memory required by the server communication program; and

deriving the memory utilization estimate by dividing the gross memory utilization by total memory available.

32. The method as recited in claim 21, wherein the server resource utilization is general server utilization, the method further comprising, deriving the general server utilization estimate as a function of the specified load and the maximum load.

33. The method as recited in claim 21, wherein the server resource utilization is general server utilization, the method further comprising:

dividing the specified load by the maximum load to derive the general server utilization estimate.

34. One or more computer-readable media having computer-readable instructions thereon which, when executed by one or more computers, cause the computers to implement the method of claim 21.

35. A method, comprising:

collecting one or more server cluster parameter values at different times during operation of the server cluster, the server cluster parameters indicating utilization of server resources;

extrapolating the collected values to determine the maximum load value that can be handled by the server cluster;

receiving a specified load value that indicates a load desired to be handled by the server cluster;

utilizing the extrapolated maximum load value to determine if the collected values are of sufficient accuracy to use in deriving server resource utilization estimates;

deriving server resource utilization estimates to determine how handling the specified load will affect the utilization of server resources if the collected values have been determined to provide sufficient accuracy;

displaying the server resource utilization estimates;

recommending a plan to optimize handling of the specified load by increasing resources of the server cluster, if necessary; and

wherein the collected values include one or more of the following parameters;

incoming server load;

CPU utilization;

number of kilobytes transmitted by server cluster;

available communication bandwidth;

processor type;

processor speed;

available memory;

types of documents transmitted; and

types of client connections.

36. The method as recited in claim 35, wherein the extrapolating the collected values to determine the maximum load value that can be handled by the server cluster further comprises:

deriving processor regression constant a and processor regression constant b for each document type by solving the linear equation;

y=a+b·

x

for multiple pairs of (x, y) values;

giving;

$\begin{array}{c}g<br><br>\left(x\right)=\stackrel{\_}{y}+b_{\mathrm{yx}}·<br><br>\left(x-\stackrel{\_}{x}\right)\\ \mathrm{and}\\ b_{\mathrm{xy}}=\frac{\stackrel{\_}{\left(x-\stackrel{\_}{x}\right)·<br><br>\left(y-\stackrel{\_}{y}\right)}}{\stackrel{\_}{{\left(x-\stackrel{\_}{x}\right)}^2}}\end{array}$

to derive the processor regression constants;

a={overscore (y)}−

b_yx·

{overscore (x)}
b=b_yx

wherein x is an independent variable corresponding to an incoming server load value collected at time i; and

y is the dependent variable corresponding to CPU utilization collected at time i; and

determining the maximum load value that can be handled by the server cluster by determining a first derivative of U_CPU as a function of L, by solving;

U′

_CPU=e^a′

·

b′

·

e<sup>b′

·

L</sup>

wherein L is a value at which U′

_CPU is one hundred percent, or the maximum load that can be handled by the server cluster.

37. The method as recited in claim 36, wherein the utilizing the extrapolated maximum load value to determine if the collected values are of sufficient accuracy further comprises:

determining the first derivative of CPU utilization as a function of the specified load by solving;

U′

_CPU=e^a′

·

b′

·

e<sup>b′

·

L</sup>

wherein L is the largest incoming load value collected; and

comparing the tangent of U′

_CPU with a pre-determined value and, if the tangent of U′

_CPU is larger than the pre-determined value, then assuming the collected values are of sufficient accuracy to proceed with further calculations.

38. The method as recited in claim 36, wherein the server resource utilization is general server utilization, the method further comprising:

deriving general server utilization by solving;

$U=\frac{L}{X}$

wherein X is the maximum load that can be handled by the server cluster and L is the specified load.

39. The method as recited in claim 35, wherein the server resource utilization is communication bandwidth utilization, the method further comprising:

deriving bandwidth regression constant c and bandwidth regression constant d by solving;

y=c+d·

x

for multiple pairs of (x, y), giving;

$\begin{array}{c}g<br><br>\left(c\right)=\stackrel{\_}{d}+d_{d<br><br>\text{\hspace{1em}<br><br>}<br><br>c}·<br><br>\left(c-\stackrel{\_}{c}\right)\\ \mathrm{and}\\ c_{c<br><br>\text{\hspace{1em}<br><br>}<br><br>d}=\frac{\stackrel{\_}{\left(c-\stackrel{\_}{c}\right)·<br><br>\left(d-\stackrel{\_}{d}\right)}}{\stackrel{\_}{{\left(c-\stackrel{\_}{c}\right)}^2}}\end{array}$

wherein solving for c and d gives;

c={overscore (d)}−

d_dc·

{overscore (c)} and d=d_dc

wherein x is an independent variable corresponding to an incoming server load value collected at time i, and y is the dependent variable corresponding to communication bandwidth utilization collected at time i; and

deriving communication bandwidth utilization by solving;

$U_B=\frac{F_{\mathrm{TCP}}}{B}·<br><br>\left(c+d·<br><br>L\right)$

wherein U_B is communication bandwidth utilization;

F_TCP is a transmission overhead factor that, when applied to a certain size page, results in the actual bandwidth necessary to transmit the page;

L is the specified load; and

B is the total communication bandwidth available.

40. The method as recited in claim 35, wherein the server resource utilization is memory utilization, the method further comprising:

deriving memory utilization by solving;

$U_M=\frac{N·<br><br>\left(M_{\mathrm{TCP}}+M_{\mathrm{IISStruct}}\right)+M_{\mathrm{OS}}+M_{\mathrm{IIS}}}{M}$

wherein N is a total number of concurrent connections derived by solving;

$N=\frac{L}{\left(X-L\right)}+\mathrm{S1}·<br><br>L$

wherein U_M is memory utilization;

M_TCP is a an amount of memory necessary to support each connection for communications;

M_IISStruct is the amount of memory necessary to support data structures associated with each connection;

M_OS is the amount of memory required by a server operating system;

M_IIS is the amount of memory required by a server communication program;

M is the total amount of memory available;

L is the specified load;

X is the maximum load that can be handled by the server cluster; and

S1 is a connection memory factor that is the adjusted average of the incoming connections at different speeds.