Acceptability testing for capacity planning of data storage system

• US 6,606,585 B1
• Filed: 08/21/1999
• Issued: 08/12/2003
• Est. Priority Date: 10/13/1998
• Status: Expired due to Fees

• Current Assignee: Hewlett-Packard Development Company, L.P. (HP Inc.)
• Original Assignee: Hewlett-Packard Development Company, L.P. (HP Inc.)
• Inventors: Spasojevic, Mirjana, Merchant, Arif, Wilkes, John, Golding, Richard, Borowsky, Elizabeth Lynn
• Primary Examiner(s): Broda, Esq., Samuel
• Application Number:
  US09/379,204
• Time in Patent Office: 1,452 Days
• Field of Search: 703/1-2, 703/19-22, 710/15-19, 702/179-186, 709/224
• US Class Current: 703/2
• CPC Class Codes: G06F 11/3414 Workload generation, e.g. scripts, playback
• CPC Class Codes: G06F 11/3452 Performance evaluation by statistical analysis

Abstract

Data storage devices of an enterprise system are tested to determine whether the enterprise system is optimally configured. Each data storage device is tested to determine whether it can satisfy a performance requirement for an assigned group of n workloads. A group of n inequalities are generated, and only up to n of the inequalities may be evaluated to determine whether the device satisfies the performance requirement for the assigned group of workloads. The inequalities are based on a phased, correlated model of I/O activity.

Claims

1. A method of using a computer to determine whether a data storage device satisfies a performance requirement for an assigned group of workloads, the method comprising:

determining at least one performance requirement model for each workload in the group, each model being an increasing function of request rate, the request rate of a given workload being approximated by a distribution process describing ON/OFF behavior of the given workload; and

using the computer to evaluate at least one model in the group to determine whether the device satisfies the performance requirement.

2. The method of claim 1, wherein the request rate of a given workload is further approximated by phase probabilities correlating ON/OFF behavior of the given workload to other workloads in the group.

3. The method of claim 2, wherein each phase probability represents the probability of the given workload already being ON when another workload comes ON.

4. The method of claim 2, wherein the request rate of an i^th workload is represented by p_jiΛ

_i, where Λ

_i is I/O activity rate of a modulated ON/OFF process, and p_ji is the phase probability that a i^th workload is already ON when a j^th workload comes ON, whereby the function R(p_jiΛ

₁, . . . , p_jnΛ

_n)<

C is evaluated for each j=1 to n, where R is the increasing function, and n is the number of workloads in the group.

5. The method of claim 4, wherein stability of the device is tested by evaluating:

$\underset{i=1}{\stackrel{n}{\sum <br><br>}}<br><br>p_{\mathrm{ji}}<br><br>{\mathrm{\Lambda <br><br>}}_i<br><br>a_i<<br><br>C$

for each j=1 to n, where C is a constant, a_i is mean service time of the device.

6. The method of claim 4, wherein a p-quantile of QoS for response time of the device is tested by evaluating:

$\underset{i=1}{\stackrel{n}{\sum <br><br>}}<br><br>p_{\mathrm{ji}}<br><br>{\mathrm{\Lambda <br><br>}}_i<br><br>a_i<br><br>T+{\mathrm{\Phi <br><br>}}^{-1}<br><br>\left(p\right)<br><br>\sqrt{\underset{i=1}{\stackrel{n}{\sum <br><br>}}<br><br>p_{\mathrm{ji}}<br><br>{\mathrm{\Lambda <br><br>}}_i<br><br>\left(a_i^2+b_i\right)<br><br>T+\underset{i=1}{\stackrel{n}{\sum <br><br>}}<br><br>p_{\mathrm{ji}}<br><br>\left(1-p_{\mathrm{ji}}\right)<br><br>{\mathrm{\Lambda <br><br>}}_i^2<br><br>a_i^2<br><br>T^2}<<br><br>T$

for each j=1 to n, where a_i is mean service time of the device, and b_i is variance of service time.

7. The method of claim 1, wherein the distribution process is a modulated ON/OFF process.

8. The method of claim 1, wherein the distribution process is a Poisson process.

9. The method of claim 1, further comprising the step of using the computer to indicate whether the device satisfies the performance requirement.

10. Apparatus for testing a plurality of data storage devices, the apparatus comprising:

first means for generating a configuration in which groups of workloads are assigned to the data storage devices; and

second means for determining whether each device, as configured in the configuration, satisfies a performance requirement, the second means determining at least one performance requirement model for each workload in each group, each model being an increasing function of request rate, the request rate being approximated by a distribution process describing workload ON/OFF behavior and phase probabilities correlating ON/OFF behavior of pairs of workloads in the same group; and

third means for evaluating at least one model of each group to determine whether each device as configured satisfies its performance requirement.

11. The apparatus of claim 10, further comprising fourth means for supplying the distribution processes and phase probabilities to the second means.

12. The apparatus of claim 10, further comprising fourth means, responsive to the third means, for indicating whether each device satisfied its performance requirement.

13. Apparatus for determining whether a data storage device satisfies a performance requirement for an assigned group of workloads, the apparatus comprising:

a processor;

memory encoded with a program that, when executed, instructs the processor to determine at least one performance requirement condition for each workload in the group, and determine whether any of the at least one condition is not satisfied;

each condition being an increasing function of request rate, the request rate being approximated by a distribution process describing workload ON/OFF behavior and phase probabilities correlating ON/OFF behavior of pairs of workloads in the group.

14. The apparatus of claim 13, wherein the request rate of an i^th workload is represented by p_jiΛ

_i, where Λ

_i is I/O activity rate of a Poisson process, and p_ji is the phase probability that a i^th workload is already ON when a j^th workload comes ON, whereby the function R(p_jiΛ

₁, . . . , p_jnΛ

_n)<

C is evaluated for each j=1 to n, where R is the increasing function, and n is the number of workloads in the group.

15. The apparatus of claim 14, wherein whether the device satisfies a stability requirement is determined by evaluating:

$\underset{i=1}{\stackrel{n}{\sum <br><br>}}<br><br>p_{\mathrm{j1}}<br><br>{\mathrm{\Lambda <br><br>}}_i<br><br>a_i<<br><br>C$

for each j=1 to n, where C is a constant, and a_i is mean service time of the device.

16. The apparatus of claim 14, wherein whether the device satisfies a p-quantile of QoS for response time requirement is determined by evaluating:

$\underset{i=1}{\stackrel{n}{\sum <br><br>}}<br><br>p_{\mathrm{ji}}<br><br>{\mathrm{\Lambda <br><br>}}_i<br><br>a_i<br><br>T+{\mathrm{\Phi <br><br>}}^{-1}<br><br>\left(p\right)<br><br>\sqrt{\underset{i=1}{\stackrel{n}{\sum <br><br>}}<br><br>p_{\mathrm{ji}}<br><br>{\mathrm{\Lambda <br><br>}}_i<br><br>\left(a_i^2+b_i\right)<br><br>T+\underset{i=1}{\stackrel{n}{\sum <br><br>}}<br><br>p_{\mathrm{ji}}<br><br>\left(1-p_{\mathrm{ji}}\right)<br><br>{\mathrm{\Lambda <br><br>}}_i^2<br><br>a_i^2<br><br>T^2}<<br><br>T$

for each j=1 to n, where a_i is mean service time of the device, and b_i is variance of service time.

17. The apparatus of claim 13, wherein each condition is represented as an inequality, and wherein the performance requirement is not satisfied if any inequality is not satisfied.

18. The apparatus of claim 13, wherein each phase probability represents the probability of the given workload already being ON when another workload comes ON.

19. The apparatus of claim 13, wherein the distribution process is a modulated ON/OFF process.

20. The apparatus of claim 13, wherein the distribution process is a Poisson process.

21. An article for causing a configuration engine to model a performance requirement of a data storage device with respect to an assigned group of workloads, the article comprising:

computer memory; and

a program encoded in the computer memory, the program, when executed, causing the configuration engine to determine a performance requirement model as an increasing function of request rate, the request rate approximated by a distribution process describing workload ON/OFF behavior and phase probabilities correlating ON/OFF behavior of pairs of workloads in the group.

22. The article of claim 21, wherein the request rate of an i^th workload is represented by p_jiΛ

_i, where Λ

_i is I/O request rate of a Poisson process, and p_ji is the phase probability that a i^th workload is already ON when a j^th workload comes ON, whereby the function R(p_jiΛ

₁, . . . , p_jnΛ

_n)<

C is evaluated for each j=1 to n, where R is the increasing function, and n is the number of workloads in the group.

23. The article of claim 22, wherein whether the device satisfies a stability requirement is determined by evaluating:

$\underset{i=1}{\stackrel{n}{\sum <br><br>}}<br><br>p_{\mathrm{j1}}<br><br>{\mathrm{\Lambda <br><br>}}_i<br><br>a_i<<br><br>C$

for each j=1 to n, where C is a constant, a_i is mean service time of the device, Λ

_i is the I/O request rate of the process, and p_ji is the phase probability that a i^th workload is already ON when a j^th workload comes ON.

24. The article of claim 22, wherein whether the device satisfies a p-quantile of QoS for response time requirement is determined by evaluating:

$\underset{i=1}{\stackrel{n}{\sum <br><br>}}<br><br>p_{\mathrm{ji}}<br><br>{\mathrm{\Lambda <br><br>}}_i<br><br>a_i<br><br>T+{\mathrm{\Phi <br><br>}}^{-1}<br><br>\left(p\right)<br><br>\sqrt{\underset{i=1}{\stackrel{n}{\sum <br><br>}}<br><br>p_{\mathrm{ji}}<br><br>{\mathrm{\Lambda <br><br>}}_i<br><br>\left(a_i^2+b_i\right)<br><br>T+\underset{i=1}{\stackrel{n}{\sum <br><br>}}<br><br>p_{\mathrm{ji}}<br><br>\left(1-p_{\mathrm{ji}}\right)<br><br>{\mathrm{\Lambda <br><br>}}_i^2<br><br>a_i^2<br><br>T^2}<<br><br>T$

for each j=1 to n, where a_i is mean service time of the device, b_i is variance of service time, Λ

_i is the I/O request rate of the process, and p_ji is the phase probability that a i^th workload is already ON when a j^th workload comes ON.

25. The article of claim 21, wherein each phase probability represents the probability of the given workload already being ON when another workload comes ON.

26. The article of claim 21, wherein the distribution process is a modulated ON/OFF process.

27. The article of claim 21, wherein the distribution process is a Poisson process.

28. The article of claim 21, wherein the article further causes the configuration engine to test the model to determine whether the model is satisfied.

29. The article of claim 21, wherein the model comprises a series of inequalities, and wherein the model is satisfied if all of the inequalities are satisfied.