SYSTEM

The present invention is directed to a method, apparatus and computer program product for the analysis of metrics of performance for a computer system. In particular, the present invention is directed to a method, apparatus and computer program for the estimation of performance characteristics estimation of performance characteristics for a computer system, especially a computer system with high priory uncertainty in performance behaviour.

The estimation of the regression of a computer system performance metric with high level of priory uncertainty and the automatic identification of system performance metric discontinuities and the removal of outliers have been attempted in the art via mean and median mode estimation, via linear or non-linear regression models or via the application of wavelet approach to computer performance data.

D.J. Lilja discusses in detail in "Measuring computer performance, A practitioner's guide" at least in the chapters dedicated to "Average performance and variability" and "Linear regression models" both mean and median mode estimation, via linear or non-linear regression, models. Further, S. Papadimitriou et al., in "Multiresolution analysis and de-noising of computer performance evaluation data with the wavelet transform" discusses the application of wavelet approach to computer performance data.

None of the approaches mentioned above provides a reliable solution for the estimation of performance characteristics for a computer system, especially a computer system with high priory uncertainty in performance behaviour.

The present invention aims to provide a reliable solution for the estimation of performance characteristics for a computer system, especially a computer system with high priory uncertainly in performance behaviour via the method for analysis of metrics of performance for a computer system of claim 1, via the apparatus for analysis of metrics of performance for a computer system of claim 5, and via the computer program product of claim 6.

Therefore, the present invention provides for a method for analysis of metrics of performance for a computer system comprising constructing a time-scale data distribution for the computer system, removing data distribution outliers, detecting data discontinuities, and performing a coefficient dependent wavelet thresholding algorithm between points of detected data discontinuities, so that regression oscillation near the points of data discontinuity is removed.

In accordance with the present invention removing the data distribution outliers is realized via estimating a variance of data from a median absolute deviation of the differences between observations y, at time points tj , wherein i is the number of observations from 1 to n, estimating a local median over a window containing a point of interest and its k left and right neighbors, indentifying an outlier if a difference between data point and median is greater that 3 σ, , wherein σ _; is the estimated signal variance, and removing the identified outlier.

In accordance with the present invention, the step of detecting data discontinuities comprises estimating a wavelet coefficient d,, wherein i is the number of observations from 1 to n, comparing the estimated wavelet coefficient with the condition for discontinuity, and detecting points of data discontinuity.

In accordance with the present invention, performing a coefficient dependent wavelet thresholding algorithm between points of detected data discontinuities comprises estimating a signal variance in a window that 0,2 times the signal length, creating a bandlimited covariance matrix, estimating the covariance matrix for other levels of the signal, performing coefficient dependent universal wavelet thresholding, and performing an inverse discrete wavelet transform.

In accordance with the present invention is also proposed an apparatus for analysis of metrics of performance for a computer system comprising means for constructing a time-scale data distribution for a computer system who's performance metrics are studied, means for removing data distribution outliers, means for detecting data discontinuities, and means for performing a coefficient dependent wavelet thresholding algorithm between points of detected data discontinuities, so that regression oscillation near the points of data discontinuity is removed.

In accordance with the present invention is further proposed a computer program product for analysis of metrics of performance for a computer system, comprising a tangible computer usable medium including computer usable program code for performing analysis of metrics of performance for a computer system, the computer usable program code being used for constructing a time-scale data distribution for the computer system, removing data distribution outliers, detecting data discontinuities, and performing a coefficient dependent wavelet thresholding algorithm between points of detected data discontinuities, so that regression oscillation near the points of data discontinuity is removed.

In order to assist the understanding of embodiments of the invention, reference will now be made to the appended drawings, in which like reference numerals refer to like elements. The drawings are exemplary only, and should not be construed as limiting the invention.

Fig. 1 represents exemplary load data;

Fig. 2 represents another exemplary load data test;

Fig. 3 represents two curves, a representation of the measurements and a representation of the regression of data;

Fig. 4 represents the curves of Fig. 3 with highlighted areas;

Fig. 5 represents a flow chart of the method 100 for analysis of metrics of performance metrics for a computer system, as proposed in accordance with an embodiment of the present invention;

Fig. 6 represents an algorithm for outliers removal;

Fig. 7 is a flowchart of a coefficient dependent wavelet thresholding algorithm, in accordance with the present invention;

Fig. 8 is another flow chart representation of the method of the present invention;

Fig. 9 represents the result of the application of the algorithm, including outliers removal and discontinuities detection, and

Fig. 10 is an embodiment of a data processing system 800 in which the method of the present invention may be implemented.

In the following the present invention is presented in connection with computer testing or rough testing of the computer performance.

For example, if what is tested is the performance of the web site, the use of a web site is simulated so that many users will access the web site during a period of time. During the testing, performance metrics of the computer system hosting the web are gathered, such as the central processing unit (CPU) utilization of the tested client server unit. The metrics are gathered as a time function. During a set period of time, a certain number of metrics is gathered.

Figure 1 represents exemplary load data, such as the number of transactions occurring on the CPU in a certain period of time, or the number of transaction that take place in a period of time in the client-server system. In other words, figure 1 represents the initial raw data gathered for an exemplary period of 5 seconds at the time.

Figure 2 represents as well an exemplary load data test, this time over a longer period of time, of 2 minutes.

As shown in figure 2, that represents the CPU usage in a longer period of time, the measurements are summarized in a mean curve of the signal. The curve represented in figure 2 exhibits a mean curve with peaks of the signal.

In order to obtain useful information from the curve, such as the performance metrics of the CPU, the peaks exhibited need to be eliminated. It is of note that the curve of figure 2 exhibits several high frequency phenomena due to peaks or outliers. The present invention will discuss among others a procedure to remove the outliers and the extreme observations, that may have been introduced either by measurement errors or by malfunctioning of the system. These regions of the curve are not relevant for the interpretation of the results and may introduce errors in the interpretation of the results.

Others observations that may be made regarding the exemplary load data tests represented in figures 1 and 2 are that they represent a non-stationary process, since when queuing the system in a stationary working mode, the resulting representation should have has a gamma distribution. It is further of note that the variance and the mean of the process change over time. As such, the curves of figures 1 and 2 are indicative of a high priory uncertainty in performance behaviour.

Referring now specifically to the curves illustrated in Fig. 3, the curves are a representation of the measurements and of the regression of a network throughput data in Mb per second versus the id of the measurement, which represents time. Each value of id corresponds to 30 seconds, for an exemplary CPU who's metrics are aimed to be analyzed.

In figure 3, the solid line refers to the plotted regression, while the line with lower contrast refers to the actual measurements performed, and is similar to the exemplary curve illustrated in Fig. 2.

In the art by regression analysis is understood any technique for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables. More specifically, regression analysis aids in understanding how the typical value of the dependent variable changes when any one of the independent variables is varied, while the other independent variables are held fixed. Most commonly, regression analysis estimates the conditional expectation of the dependent variable given the independent variables, that is, the average value of the dependent variable when the independent variables are held fixed. Less commonly, the focus is on a quantile, or other location parameter of the conditional distribution of the dependent variable given the independent variables. In all cases, the estimation target is a function of the independent variables called the regression function. In regression analysis, it is also of interest to characterize the variation of the dependent variable around the regression function, which can be described by a probability distribution.

Regression analysis is used for prediction and forecasting, where its use has substantial overlap with the field of machine learning. Regression analysis is also used to understand which among the independent variables are related to the dependent variable, and to explore the forms of these relationships. Regression analysis is used to infer causal relationships between the independent and dependent variables.

A large body of techniques for carrying out regression analysis has been developed. Methods such as linear regression and ordinary least squares regression are parametric, in that the regression function is defined in terms of a finite number of unknown parameters that are estimated from the data. Nonparametric regression refers to techniques that allow the regression function to lie in a specified set of functions, which may be infinite-dimensional.

The performance of regression analysis methods in practice depends on the form of the data generating process, and how it relates to the regression approach being used. Since the true form of the data- generating process is in general not known, regression analysis often depends to some extent on making assumptions about this process. These assumptions are sometimes (but not always) testable if a large amount of data is available. Regression models for prediction are often useful even when the assumptions are moderately violated, although they may not perform optimally.

Referring further to the curves represented in Fig. 3, the following equation is characteristic for the represented measurements: wherein

y represent the number of i measurements plotted on the curve;

e is a noise like component of the observed data, and

f represents the regression of y, and it is time dependent.

In order to obtain an accurate characterization of the CPU in question, the noise like components of the observed data need to be eliminated and f, indicative of the property of the signal, needs to be estimated. As a result, the performance metrics of the CPU may be obtained.

Therefore, via the methods and apparatuses of the present invention, it is aimed to calculate or clearly estimate the regression of the signal, so the performance metrics of the tested system may be estimated. As showed in the above, the regression of the signal represents the actual value of the signal minus the noise, caused by different causes. Therefore the noise needs to be removed so that the signal can be accurately estimated.

The various methods available in the art for the estimation of the regression operate based on estimations that have been already made regarding the system. In the real systems there are parts who's behaviors is rather difficult to predict. Therefore, more sensitive methods for the estimation of the regression for real systems are necessary.

Referring now to the representation made in Fig. 4, it is of note that the figure represents the curve represented in Fig. 3 with two highlighted areas, each representative respectively of an outlier 202 and of a discontinuity 204.

By an outlier is understood an observation that is numerically distant from the rest of the data. An outlier observation, or an outlier, may be defined as one that appears to deviate markedly from other members of the sample in which it occurs.

Outliers can occur by chance in any distribution, but they are often indicative either of measurement error or that the population has a heavy-tailed distribution. In the former case one wishes to discard them or use statistics that are robust to outliers, while in the latter case they indicate that the distribution has high kurtosis and that one should be very cautious in using tools or intuitions that assume a normal distribution. A frequent cause of outliers is a mixture of two distributions, which may be two distinct sub-populations, or may indicate 'correct trial' versus 'measurement error'; this is modeled by a mixture model.

In most larger samplings of data, some data points will be further away from the sample mean than what is deemed reasonable. This can be due to incidental systematic error or flaws in the theory that generated an assumed family of probability distributions, or it may be that some observations are far from the center of the data. Outlier points can therefore indicate faulty data, erroneous procedures, or areas where a certain theory might not be valid. However, in large samples, a small number of outliers is to be expected (and not due to any anomalous condition).

Outliers, being the most extreme observations, may include the sample maximum or sample minimum, or both, depending on whether they are extremely high or low. However, the sample maximum and minimum are not always outliers because they may not be unusually far from other observations.

Estimators capable of coping with outliers are said to be robust: the median is a robust statistic, while the mean is not.

In the case of normally distributed data, roughly 1 in 22 observations will differ by twice the standard deviation or more from the mean, and 1 in 370 will deviate by three times the standard deviation, as estimated via the three sigma rule. In a sample of 1000 observations, the presence of up to five observations deviating from the mean by more than three times the standard deviation is within the range of what can be expected, being less than twice the expected number and hence within 1 standard deviation of the expected number and are not indicative of an anomaly. If the sample size is only 100, however, just three such outliers are already reason for concern, being more than 1 1 times the expected number.

In general, if the nature of the population distribution is known a priori, it is possible to test if the number of outliers deviate significantly from what can be expected: for a given cutoff (so samples fall beyond the cutoff with probability p) of a given distribution, the number of outliers will follow a binomial distribution with parameter p, which can generally be well-approximated by the Poisson distribution with λ = pn. Thus if one takes a normal distribution with cutoff 3 standard deviations from the mean, p is approximately .3%, and thus for 1 ,000 trials one can approximate the number of samples whose deviation exceeds 3 sigmas by a Poisson distribution with λ = 3.

Outliers can have many anomalous causes. A physical apparatus for taking measurements may have suffered a transient malfunction. There may have been an error in data transmission or transcription. Outliers arise due to changes in system behaviour, fraudulent behaviour, human error, instrument error or simply through natural deviations in populations. A sample may have been contaminated with elements from outside the population being examined. Alternatively, an outlier could be the result of a flaw in the assumed theory, calling for further investigation by the researcher. Additionally, the pathological appearance of outliers of a certain form appears in a variety of datasets, indicating that the causative mechanism for the data might differ at the extreme end.

Unless it can be ascertained that the deviation is not significant, it is ill-advised to ignore the presence of outliers. Outliers that cannot be readily explained demand special attention. ^J

Outlier detection and removal is used to remove anomalous observations from data. Outlier detection can identify system faults and fraud before they escalate with potentially catastrophic consequences.

The detection and identification of outliers may be performed at least in 3 ways:

Determine the outliers with no prior knowledge of the data. This is essentially a learning approach analogous to unsupervised clustering. The approach processes the data as a static distribution, pinpoints the most remote points, and flags them as potential outliers.

Model both normality and abnormality. This approach is analogous to supervised classification and requires pre-labeled data, tagged as normal or abnormal.

Model only normality (or in a few cases model abnormality). This is analogous to a semi-supervised recognition or detection task. It may be considered semi-supervised as the normal class is taught but the algorithm learns to recognize abnormality.

Even when a normal distribution model is appropriate to the data being analyzed, outliers are expected for large sample sizes and should not automatically be discarded if that is the case. The application should use a classification algorithm that is robust to outliers to model data with naturally occurring outlier points.

In regression problems, an alternative approach may be to only exclude points which exhibit a large degree of influence on the parameters, using a measure such as Cook's distance.

While reviewing the behavior of the curve represented in figure 4, it is of note that the curve exhibits several discontinuities, such as the ones indicated by box 204. As known in the art, if a function is not continuous at a point in its domain, said function has a discontinuity there.

Analogue to the outliers 202, the points of discontinuity are also indicative of unusual behavior of the system and for the purposes of obtaining a correct estimation of the system behavior, the points of discontinuity need to be detected and properly handled.

In accordance with the present invention a method is proposed for the automatic identification of system performance. As it will be explained in detail bellow the identification of system performance metrics relies on the removal of outliers and the identification of discontinuities and analysis of system performance metric between the points of discontinuity.

In accordance with the method for analysis of metrics of performance for a computer system proposed by the present invention, a time-scale data distribution is first constructed for the computer system. Further, the data distribution outliers are removed, the data discontinuities are detected and a coefficient dependent wavelet thresholding algorithm is performed between points of detected data discontinuities, so that regression oscillation near the points of data discontinuity is removed.

Referring now to the illustration made in Fig. 5, that represents a flow chart of the method 100 for analysis of metrics of performance for a computer system proposed by the present invention, the present invention comprises at least the step of constructing 102 a time-scale data distribution for the computer system. Further, the data distribution outliers are removed in a step 104, the data discontinuities are detected, in a step 106 and a coefficient dependent wavelet thresholding algorithm is performed, in a step 108, between points of detected data discontinuities, so that regression oscillation near the points of data discontinuity is removed. As such, the curve obtained in step 110 is free of errors and provides an accurate representation of the studied computer system performance. Further, it is of note that the above method, as opposed to the methods known in the art, does not comprise or rely on any assumptions regarding the state of the system. As a result, as it will be shown in detail bellow, the present method provides for more accurate results.

In the following, the steps of the method 100 referring to outliers removal 104, discontinuities detection 106 and thresholding 108 will be described in detail. It is of note that the performance of the steps of the method in combination is leading to the accurate attainment of the performance metrics for the studied system. It is further of note that in the following the steps of the method will each be described as a special wavelet technique. A person skilled in the art would be aware that other techniques are as well suitable for the implementation of steps 104 to 108 of the method.

Referring now to the representation made in Fig. 6, Fig. 6 represents an algorithm for outliers removal.

Wavelet methods are known for having been used in non-parametric regression problem of estimating a function f on the basis of observations yi at time points tj, modeled as

Wherein i=l, 2, n, and ej is noise.

To remove the outliers and the extreme observations the following procedure may be carried out:

For a number of observations i from 1 to n, where n is the number of observations, the variance of the data is estimated from a median absolute deviation of the differences d _t =

obtaining in step 104.2 an estimate signal variance of

σ, = 1.96 · 4Ζ ⁾ (^ , ₊ , ) ,

wherein MAD is the median absolute deviation

The median absolute deviation (MAD) is a robust measure of the variability of a univariate sample of quantitative data. It can also refer to the population parameter that is estimated by the MAD calculated from a sample.

For a univariate data set X _\ , Xi,..., X _n , the MAD is defined as the median of the absolute deviations from the data's median:

MAD median _j -( ) | ) . that is, starting with the residuals (deviations) from the data's median, the MAD is the median of their absolute values.

The median absolute deviation is a measure of statistical dispersion. It is a more robust estimator of scale than the sample variance or standard deviation. It thus behaves better with distributions without a mean or variance, such as the Cauchy distribution.

For instance, the MAD is a robust statistic, being more resilient to outliers in a data set than the standard deviation. In the standard deviation, the distances from the mean are squared, so on average, large deviations are weighted more heavily, and thus outliers can heavily influence it. In the MAD, the magnitude of the distances of a small number of outliers is irrelevant.

The estimated signal variance corresponds to the usual variance estimation via a wavelet decomposition using the Haar basis. It is assumed that k represents the window length.

Further, in a subsequent step 104.4 it is estimated the local median over a window containing the point itself and its k left and right neighbors. If the difference between data point and median is greater that 3 σ, , the point represents an outlier, as identified in step 104.6 and will be removed in step 104.8.

The above may be performed via software available in the art, exemplarily via a software tool called VisuShrink using a specifically elected wavelet basis. The variances of the wavelet coefficients may be determined under the assumption that the non-deleted data points are independent with variance σ, . It is possible to base the variance estimation of a higher order wavelet basis expansion than the Haar basis, but the resulting wavelet coefficient would be more contaminated with outliers. A re- estimation of the variance from the data from which outliers have been removed will typically underestimate the noise level, and is not recommended.

Therefore, to summarize, the step 104 of removing data distribution outliers comprises at least estimating a variance of data from a median absolute deviation of the differences between observations yj at time points tj , wherein i is the number of observations from 1 to n, estimating a local median over a window containing a point of interest and its k left and right neighbors, indentifying an outlier if a difference between data point and median is greater that 3 σ, , wherein σ, is the estimated signal variance, and removing the identified outlier.

The subsequent step in accordance with the method 100 of the present invention is the detection of data discontinuities 106. Referring now to Fig. 4, step 106, it is of note that the figure provides a flow chart representation of the detection of data discontinuities 106.

In accordance with the sequence of steps illustrated in figure 6, for a number of observations i from 1 to n, where n is the number of observations, the wavelet coefficients d, are calculated with the Haar wavelet, assuming that the minimum length between discontinuities is m, as follows:

i i+

« , = ( ∑y _j -∑ _yj )/ j2^i σ = MAD(d)

In accordance with the algorithm the condition of detection of discontinuities is

If the wavelet coefficient is larger than the condition for discontinuity, a discontinuity point has been detected.

Therefore, to summarize, the step of detecting (106) data discontinuities comprises at least estimating a wavelet coefficient dj, wherein i is the number of observations from 1 to n, comparing the estimated wavelet coefficient with the condition for discontinuity, and detecting the points of data discontinuity.

Referring now to the illustration made in Fig. 7, Fig. 7 is a flowchart of a coefficient dependent wavelet thresholding algorithm, in accordance with the present invention.

In accordance with Fig. 7 the algorithm is performed for data intervals between the change points detected in step 106. The illustrated algorithm comprises at least an estimation 108.2 of the signal variance in a window that 0,2 times the signal length, creating a bandlimited covariance matrix 108.4, estimating the covariance matrix for other levels 108.6, coefficient dependent universal wavelet thresholding 108, , and performing an inverse discrete wavelet transform 108.10. In accordance with the algorithm summarized above, the wavelet coefficients are filtered depending on the signal variance, which is calculated in a window 0,2 times the signal length. The application of the algorithm leads to obtaining the final regression of the data.

In step 108.2 wavelet coefficients at first level of decomposition are calculated using Haar basis.

The estimated local standard deviation σ, of the i-th data point is based on the median of the absolute values over a small window of width 0.2 signal length around of each point.

Estimated local standard deviations σ, in step 108.4 are used as diagonals elements of initial bandlimited covariance: matrix∑ .

∑,, = σ,

Using matrices of discrete wavelet transform H _} (approximation coefficients calculation), G _j (detail coefficients calculation) estimation of bandlimited covariance matrix∑' on other levels is performed:

∑J = H ^J+] '∑ ^j+] - (H ^J+] ) ^T

∑J = G ^J+] -∑ ^J+] ■(G ^l+ ) ^r

This gives variances σ of individual wavelet coefficients d[ at each level, step 108.6. These values of variances are used for coefficient dependent wavelet thresholding with threshold level τ{ of each coefficient.

Application of an inverse discrete wavelet transform to thresholded coefficients produce an estimation of signal regression.

The method for analyzing the metrics of performance for a computer system proposed in accordance with the present invention is particularly suitable for the analysis of system performance data, where the system has high levels of prior uncertainty since it may accurately detect and remove the noise and errors comprised by said systems. Further, the method of the invention allows the identification of system stability intervals, that are defied between two identified points of discontinuity. The method of the invention may be implemented in a robust way with the usage of statistical packages.

The method of the present invention offers the possibility to automate the analysis of the system performance data for almost every type of load tests and system behavior, and as a result lots of manual effort of system characterization may be saved. The system load test data may be easily integrated into automated test execution, that significantly increases the product quality. Further, the method of analysis proposed by the present invention permits that many performance metrics of the system to be analyzed, increasing therefore the quality of performance analysis.

The method 100 of the present invention is presented in a summary view in connection with the flowchart of figure 8. The method (100) for analysis of metrics of performance for a computer system, comprises constructing a time-scale data distribution (102) for the computer system, removing (104) data distribution outliers, detecting (106) data discontinuities, and performing (108) a coefficient dependent wavelet thresholding algorithm between points of detected data discontinuities, so that regression oscillation near the points of data discontinuity is removed.

The step of removing (104) data distribution outliers comprises estimating a variance of data from a median absolute deviation of the differences between observations j at time points tj , wherein i is the number of observations from 1 to n, estimating a local median over a window containing a point of interest and its k left and right neighbors, indentifying an outlier if a difference between data point and median is greater that 3 σ, ,

wherein σ, is the estimated signal variance, and removing the identified outlier.

The step of detecting (106) data discontinuities comprises estimating a wavelet coefficient d|, wherein i is the number of observations from 1 to n, comparing the estimated wavelet coefficient with the condition for discontinuity, and detecting points of data discontinuity.

The step of performing (108) a coefficient dependent wavelet thresholding algorithm between points of detected data discontinuities comprises estimating a signal variance in a window that 0,2 times the signal length, creating a bandlimited covariance matrix,

estimating the covariance matrix for other levels of the signal, performing coefficient dependent universal wavelet thresholding, and performing an inverse discrete wavelet transform.

The steps 102 to 108 of the method of the present invention are performed in combination.

An exemplary application of the method of the present invention may be observed in connection with the signal representation made in Fig. 9.

The result of the application of the algorithm, including outliers removing and discontinuities detection, may be seen in the figure 9. The signal representation made in Fig. 9 above is the signal representation prior to the removal of outliers and the detection of discontinuities. The representation provided bellow in Fig. 9 the resulting signal after the outliers removing and discontinuities detection. The algorithm provides much better results near the outliers and the points of discontinuities, since the regression oscillation near these points is completely removed.

The present application is also directed to an apparatus for performing the method proposed by the present invention. The present invention may be implemented via a data processing system in which the method for analysis of metrics of performance for a computer system of the present invention may be implemented.

FIG. 10 is an embodiment of a data processing system 800 in which the method of the present invention may be implemented. The data processing system of FIG. 10 may be located and/or otherwise operate at any node of a computer network, that may exemplarily comprise clients 810 and/or 820, servers 840 and/or 850, etc. In the embodiment illustrated in FIG. 8, data processing system 800 includes communications fabric 802, which provides communications between processor unit 804, memory 806, persistent storage 808, communications unit 810, inpiit/output (I/O) unit 812, and display 814.

Processor unit 804 serves to execute instructions for software that may be loaded into memory 806. Processor unit 804 may be a set of one or more processors or may be a multi-processor core, depending on the particular implementation. Further, processor unit 804 may be implemented using one or more heterogeneous processor systems in which a main processor is present with secondary processors on a single chip. As another illustrative example, processor unit 804 may be a symmetric multiprocessor system containing multiple processors of the same type.

In some embodiments, memory 806 may be a random access memory or any other suitable volatile or non-volatile storage device. Persistent storage 808 may take various forms depending on the particular implementation. For example, persistent storage 808 may contain one or more components or devices. Persistent storage 808 may be a hard drive, a flash memory, a rewritable optical disk, a rewritable magnetic tape, or some combination of the above. The media used by persistent storage 808 also may be removable such as, but not limited to, a removable hard drive.

Communications unit 810 provides for communications with other data processing systems or devices. In these examples, communications unit 810 is a network interface card. Modems, cable modem and Ethernet cards are just a few of the currently available types of network interface adapters. Communications unit 810 may provide communications through the use of either or both physical and wireless communications links.

Input/output unit 812 enables input and output of data with other devices that may be connected to data processing system 800. In some embodiments, input/output unit 812 may provide a connection for user input through a keyboard and mouse. Further, input/output unit 812 may send output to a printer. Display 814 provides a mechanism to display information to a user.

Instructions for the operating system and applications or programs are located on persistent storage 808. These instructions may be loaded into memory 806 for execution by processor unit 804. The processes in accordance with the different embodiments of the method of the present invention may be performed by processor unit 804 using computer implemented instructions, which may be located in a memory, such as memory 806. These instructions are referred to as program code, computer usable program code, or computer readable program code that may be read and executed by a processor in processor unit 404. The program code in the different embodiments may be embodied on different physical or tangible computer readable media, such as memory 406 or persistent storage 808.

Program code 816 is located in a functional form on computer readable media 818 that is selectively removable and may be loaded onto or transferred to data processing system 800 for execution by processor unit 804. Program code 816 and computer readable media 818 form computer program product 820 in these examples. In one example, computer readable media 818 may be in a tangible form, such as, for example, an optical or magnetic disc that is inserted or placed into a drive or other device that is part of persistent storage 808 for transfer onto a storage device, such as a hard drive that is part of persistent storage 808. In a tangible form, computer readable media 818 also may take the form of a persistent storage, such as a hard drive, a thumb drive, or a flash memory that is connected to data processing system 800. The tangible form of computer readable media 818 is also referred to as computer recordable storage media. In some instances, computer readable media 818 may not be removable.

Alternatively, program code 816 may be transferred to data processing system 800 from computer readable media 818 through a communications link to communications unit 810 and/or through a connection to input/output unit 812. The communications link and/or the connection may be physical or wireless in the illustrative examples. The computer readable media also may take the form of non- tangible media, such as communications links or wireless transmissions containing the program code.

The different components illustrated for data processing system 800 are not meant to provide architectural limitations to the manner in which different embodiments may be implemented. The different illustrative embodiments may be implemented in a data processing system including components in addition to or in place of those illustrated for data processing system 800. Other components shown in FIG. 8 can be varied from the illustrative examples shown. For example, a storage device in data processing system 800 is any hardware apparatus that may store data. Memory 806, persistent storage 808, and computer readable media 818 are examples of storage devices in a tangible form.

Accordingly, the disclosed embodiments present an apparatus for analysis of metrics of performance for a computer system comprising means for constructing a time-scale data distribution for a computer system who's performance metrics are studied, means for removing data distribution outliers, means for detecting data discontinuities, and means for performing a coefficient dependent wavelet thresholding algorithm between points of detected data discontinuities, so that regression oscillation near the points of data discontinuity is removed. The above referenced means may be implemented either via hardware, exemplarily via the elements of apparatus 800 discussed above or via software residing in and processed by the elements of apparatus 800, or via a combination of the two.

The present invention is also directed to a computer program product for analysis of metrics of performance for a computer system, comprising a tangible computer usable medium including computer usable program code for performing analysis of metrics of performance for a computer system, the computer usable program code being used for:

constructing a time-scale data distribution for the computer system, removing data distribution outliers, detecting data discontinuities, and performing a coefficient dependent wavelet thresholding algorithm between points of detected data discontinuities, so that regression oscillation near the points of data discontinuity is removed.

The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the disclosure. As used herein, the singular forms "a", "an" and "the" are. intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. The corresponding structures, materials, acts, and equivalents of all means or step plus function elements in the claims below are intended to include any structure, material, or act for performing the function in combination with other claimed elements as specifically claimed. The description of the present disclosure has been presented for purposes of illustration and description, but is not intended to be exhaustive or limited to the disclosure in the form disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the disclosure. The embodiment was chosen and described in order to best explain the principles of the disclosure and the practical application, and to enable others of ordinary skill in the art to understand the disclosure for various embodiments with various modifications as are suited to the particular use contemplated.

In addition, the flowchart and block diagrams in the Figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present disclosure. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems that perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.