Method and system for software rejuvenation via flexible resource exhaustion prediction

• US 20020144178A1
• Filed: 03/30/2001
• Published: 10/03/2002
• Est. Priority Date: 03/30/2001
• Status: Active Grant

• Current Assignee: International Business Machines Corporation
• Original Assignee: International Business Machines Corporation
• Inventors: Heidelberger, Philip, Castelli, Vittorio, Harper, Richard E.
• Granted Patent: US 6,810,495 B2
• Time in Patent Office: Days
• US Class Current: 714/15
• CPC Class Codes: G06F 11/1438 Restarting or rejuvenating

Abstract

A method (and computer system in which at least one software component thereof is restarted based on projection of resource exhaustion), for selecting the most suitable projection method from among a class of projection methods, includes providing M fitting modules which take measured symptom data associated with the system as input and produce M scores, wherein M is an integer, selecting the fitting module producing the best score, and from the selected module, producing a prediction of the resource exhaustion time.

Claims

1. In a computer system where at least one software component thereof is restarted based on projection of resource exhaustion, a method for selecting the most suitable projection method from among a class of projection methods, comprising:

providing M fitting modules which take measured symptom data associated with said system as input and produce M scores, wherein M is an integer;

selecting the fitting module producing the best score; and

from the selected module, producing a prediction of the resource exhaustion time.

2. The method of claim 1, further comprising:

monitoring a system; and

producing a dataset of recently measured symptom data of said system.

3. The method of claim 1, further comprising:

scheduling a rejuvenation of the monitored system, based upon the predicted resource exhaustion time.

4. The method of claim 3, wherein said scheduling further considers another factor including a time of a non-prime shift of said computer system.

5. The method of claim 1, further comprising:

creating a data set of measured symptoms, denoted by X, which includes observations taken during a time interval, wherein observations are taken at different times within the time interval and measure at least one aspect of the system, including any of a virtual memory usage, a disk usage, and a number of processes;

representing a fitting module number j by a class of models having k(j) parameters;

letting a(j)=[a(j,1), . . . , a(j,k(j))] denote a set of parameters for class j, calculating a penalty function P1(j,a(j), X), which measures a goodness of fit of the fitting model; and

selecting best parameter values, b(j) for model class j, such that said best parameter values b(j) minimize P1(j,a(j),X) over all possible values of the parameters a(j).

6. The method of claim 5, further comprising:

calculating a second penalty function P2(j,b(j),X) which incorporates any of a penalty for the lack of fit of the model class j with parameter values b(j) to the data and a penalty for complexity of the model.

7. The method of claim 1, further comprising:

associating, with each fitting module j, a score and assigning the score to be P2(j,b(j),X), such that with the plurality of scores, the best fitting module J is selected, where J is the index that minimizes penalty functions P2(1,b(1),X), . . . , P2(M,b(M),X).

8. The method of claim 7, further comprising:

selecting a model class J, wherein the parameter values selected for that model class are b(J).

9. The method of claim 8, further comprising:

predicting the resource exhaustion time from the best fitting model using model class J with parameter values b(J),

wherein said selecting and predicting is applied to each measured symptom.

10. The method of claim 1, wherein said selecting a fitting module comprises:

measuring a symptom at times T(1), . . . , T(N) during a time window, where X(i) is a data value of a measured symptom at time T(i);

smoothing, with a smoothing filter, data values to produce a smoothed signal, wherein if the median width is k, and n=m*k, then the output of the filter is to produce m medians Y(1), . . . , Y(m) which is associated to sampling times'"'"' t(1), . . . , t(m) such that Y(1)=median (X(1), . . . , X(k)), Y(2)=median(X(k+1), . . . , X(2k)), . . . and the sampling times of the medians are defined as t(1)=median (T(1), . . . , T(k)), t(2)=median(T(k+1), . . . T(2k)), . . . ; and

selecting h breakpoint times c(1), . . . , c(h), wherein the fitting module uses the model

Y(j)=a1(k)*t(j)+a0(k)+error if c(k−

1)t(j)c(k)

 

where c(0)=t(0) and c(k+1)=t(m).

11. The method of claim 10, wherein said selecting a fitting module further comprises:

imposing an additional constraint so as to make the fitted function continuous at the breakpoints such that a1(k)*c(k)+a0(k)=a1(k+1)*c(k)+a0(k+1), wherein the parameters are;

a=[a0(1), . . . , a0(h), a1(1), . . . , a1(h), c(1), . . . , c(h)]=[a0,a1,c].

12. The method of claim 11, wherein said selecting a fitting module further comprises:

finding the best parameter values b, said finding the best parameter values including;

fixing breakpoint times c at one of a possible sets of breakpoint times such that given c, the best values for a0 and a1, a0*(c) and a1*(c) are found by minimizing the Penalty P1(a0,a1,c,X) over a0 and a1;

finding a best location for the breakpoints by finding that c* that minimizes P1(a0*(c),a1*(c),c,X) over the set of all possible breakpoints c; and

setting the best parameter values with h breakpoints to;

b=[a0*(c*),a1*(c*),c*]

 

and setting the score to P2(b,X)=P2(a0*(c*),a1*(c*),c*,X).

13. The method of claim 12, wherein said selecting a fitting module further comprises:

preventing overfitting of said data

14. The method of claim 13, wherein said preventing includes:

with a fitting module having p parameters, computing a penalty P2 using weights w=[w(1), . . . , w(m)] and a parameter penalty d; and

computing fitted values Z=[Z(1), . . . , Z(m)] using the fitting module with the parameter values b at times [t(1), . . . , t(m)], wherein weighted residual sum of squares (WSS) is computed as;

WSS=w(1)(Z(1)−

Y(1))^ 2+ . . . +w(m)(Z(m)−

y(m))^ 2

 

such that w is selected so as to give less weight to those fitted values further in the past.

15. The method of claim 14, wherein a penalty is included for the number of parameters used such that one of:

P2(b,X)=Wp=WSS*(1+d)^ (p−

p0)

where p is the number of parameters used in the fitting module and p0 is the minimum number of parameters used by any of the fitting modules, and

P2(b,X)=Cp=RSS/s^ 2−

(m−

2p)

is used, where p is the number of parameters in the model, s^ 2 is the residual mean square error (RSS/m) from the largest model considered, and m is the number of samples in the smoothed signal, wherein the fitting model with a smallest value of Cp is selected.

16. The method of claim 1, wherein said fitting modules include any of a Linear Regression Module, a Piecewise Linear Regression Module with 1 breakpoint, a Piecewise Linear Regression Module with at least 2 breakpoints, a Log Linear Regression Module, a Piecewise Log Linear Regression Module with 1 breakpoint, and a Piecewise Log Linear Regression Module with at least 2 breakpoints.

17. The method of claim 1, wherein, when a resource approaches a danger level, the computer system should be rejuvenated, and

wherein a time tr at which the resource is estimated to become exhausted is determined by extrapolating the best fitting module into the future and detecting where the danger level is reached, such that a potential rejuvenation is scheduled for a time just prior to tr.

18. The method of claim 1, further comprising:

estimating approximate confidence intervals for fitted parameters; and

constructing, based on said confidence intervals, a confidence band for an extrapolated prediction.

19. The method of claim 18, wherein a potential rejuvenation time of said system is determined when the confidence band first reaches a danger level, and a potential rejuvenation is scheduled for said potential rejuvenation time.

20. The method of claim 1, wherein said at least one software component includes an operating system of said computer system.

21. A computer system where at least one software component thereof is restarted based on projection of resource exhaustion, comprising:

a selector for selecting a most suitable projection method from among a class of projection methods.

22. The system of claim 21, wherein said selector comprises:

a plurality of M fitting modules which take measured symptom data associated with said system as input and produce M scores, wherein M is an integer; and

a selecting unit for selecting the fitting module producing the best score.

23. The system of claim 22, wherein said selector further comprises:

a predictor for producing a prediction of the resource exhaustion time, based on the module selected by said selecting unit.

24. The system of claim 21, wherein said at least one software component includes an operating system of said computer system.

25. The system of claim 23, further comprising:

a monitor for monitoring the system, said monitor producing a dataset of recently measured symptom data of said system.

26. The system of claim 23, further comprising:

a scheduler for scheduling a rejuvenation of the monitored system, based upon the predicted resource exhaustion time.

27. The system of claim 26, wherein said scheduler further considers another factor including a time of a non-prime shift of said computer system.

28. The system of claim 23, further comprising:

means for creating a data set of measured symptoms, denoted by X, which includes observations taken during a time interval,

wherein observations are taken at different times within the time interval and measure at least one aspect of the system, including any of a virtual memory usage, a disk usage, and a number of processes;

means for representing a fitting module number j by a class of models having k(j) parameters;

letting a(j)=[a(j,1), . . . , a(j,k(j))] denote a set of parameters for class j, a calculator for calculating a penalty function P1(j,a(j), X), which measures a goodness of fit of the fitting model; and

means for selecting best parameter values, b(j) for model class j, such that said best parameter values b(j) minimize P1(j,a(j),X) over all possible values of the parameters a(j).

29. The system of claim 28, further comprising:

means for calculating a second penalty function P2(j,b(j),X) which incorporates any of a penalty for the lack of fit of the model class j with parameter values b(j) to the data and a penalty for complexity of the model.

30. The system of claim 23, further comprising:

means for associating, with each fitting module j, a score and assigning the score to be P2(j,b(j),X), such that with the plurality of scores, the best fitting module J is selected, where J is the index that minimizes penalty functions P2(1,b(1),X), . . . , P2(M,b(M),X).

31. The system of claim 30, further comprising:

means for selecting a model class J, wherein the parameter values selected for that model class are b(J).

32. The system of claim 31, wherein said predictor predicts the resource exhaustion time from the best fitting model using model class J with parameter values b(J),

wherein said selecting and predicting is applied to each measured symptom.

33. The system of claim 23, wherein said selector for selecting a fitting module comprises:

means for measuring a symptom at times T(1), . . . , T(N) during a time window, where X(i) is a data value of a measured symptom at time T(i);

a smoothing filter for smoothing data values to produce a smoothed signal, wherein if the filter width is k, and n=m*k, then the output of the filter is to produce m medians Y(1), . . . , Y(m) which is associated to sampling times'"'"' t(1), . . . , t(m) such that Y(1)=median (X(1), . . . , X(k)), Y(2)=median(X(k+1), . . . , X(2k)), . . . and the sampling times of the medians are defined as t(1)=median (T(1), . . . , T(k)), t(2)=median(T(k+1), . . . , T(2k)), . . . ; and

means for selecting h breakpoint times c(1), . . . , c(h), wherein the fitting module uses the model

Y(j)=a1(k)*t(j)+a0(k)+error if c(k−

1)t(j)c(k)

 

where c(0)=t(0) and c(k+1)=t(m).

34. The system of claim 33, wherein said selector for selecting a fitting module further comprises:

means for imposing an additional constraint so as to make the fitted function continuous at the breakpoints such that a1(k)*c(k)+a0(k)=a1(k+1)*c(k)+a0(k+1), wherein the parameters are;

a=[a0(1), . . . , a0(h), a1(1), . . . , a1(h), c(1), . . . , c(h)]=[a0,a1,c].

35. The system of claim 34, wherein said selector for selecting a fitting module further comprises:

means for finding the best parameter values b, said finding the best parameter values including;

means for fixing breakpoint times c at one of a possible sets of breakpoint times such that given c, the best values for a0 and a1, a0*(c) and a1*(c) are found by minimizing the Penalty P1(a0,a1,c,X) over a0 and a1;

means for finding a best location for the breakpoints by finding that c* that minimizes P1(a0*(c),a1*(c),c,X) over the set of all possible breakpoints c; and

means for setting the best parameter values with h breakpoints to;

b=[a0*(c*),a1*(c*),c*]

 

and setting the score to P2(b,X)=P2(a0*(c*),a1*(c*),c*,X).

36. The system of claim 35, wherein said selector for selecting a fitting module further comprises:

means for preventing overfitting of said data.

37. The system of claim 36, wherein said means for preventing includes:

means for computing, with a fitting module having p parameters, a penalty P2 using weights w=[w(1), . . . , w(m)] and a parameter penalty d; and

means for computing fitted values Z=[Z(1), . . . , Z(m)] using the fitting module with the parameter values b at times [t(1), . . . , t(m)], wherein weighted residual sum of squares (WSS) is computed as;

WSS=w(1)(Z(1)−

Y(1)) ^ 2+ . . . +w(m)(Z(m)−

y(m)) ^ 2

 

such that w is selected so as to give less weight to those fitted values further in the past.

38. The system of claim 37, wherein a penalty is included for the number of parameters used such that one of:

P2(b,X)=Wp=WSS*(1+d) ^ (p−

p0)

where p is the number of parameters used in the fitting module and p0 is the minimum number of parameters used by any of the fitting modules, and

P2(b,X)=Cp=RSS/s^ 2−

(m−

2p)

is used, where p is the number of parameters in the model, s^ 2 is the residual mean square error (RSS/m) from the largest model considered, and m is the number of samples in the smoothed signal, wherein the fitting model with a smallest value of Cp is selected.

39. The system of claim 22, wherein said fitting modules include any of a Linear Regression Module, a Piecewise Linear Regression Module with 1 breakpoint, a Piecewise Linear Regression Module with at least 2 breakpoints, a Log Linear Regression Module, a Piecewise Log Linear Regression Module with 1 breakpoint, and a Piecewise Log Linear Regression Module with at least 2 breakpoints.

40. The system of claim 22, wherein, when a resource approaches a danger level, the computer system should be rejuvenated, and

wherein a time tr at which the resource is estimated to become exhausted is determined by extrapolating the best fitting module into the future and detecting where the danger level is reached, such that a potential rejuvenation is scheduled for a time just prior to tr.

41. The system of claim 22, further comprising:

an estimator for estimating approximate confidence intervals for fitted parameters; and

means for constructing, based on said confidence intervals, a confidence band for an extrapolated prediction.

42. The system of claim 41, wherein a potential rejuvenation time of said system is determined when the confidence band first reaches a danger level, and a potential rejuvenation is scheduled for said potential rejuvenation time.

43. A signal-bearing medium tangibly embodying a program of machine-readable instructions executable by a digital processing apparatus to perform a method for, in a computer system where at least one software component thereof is restarted based on projection of resource exhaustion, selecting the most suitable projection method from among a class of projection methods, said method comprising:

providing M fitting modules which take measured symptom data associated with said system as input and produce M scores, wherein M is an integer;

selecting the fitting module producing the best score; and

from the selected module, producing a prediction of the resource exhaustion time.