Abstract:
A computer data processing system and an article of manufacture for determining database workload periodicity. The computer data processing system includes a module for converting database activity samples spanning a time period from the dime domain to the frequency domain, the converting resulting in a frequency spectrum, a module for identifying fundamental peaks of the frequency spectrum, and a module for allocating database resources based on at least one of the fundamental peaks.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This is a continuation of application Ser. No. 11/015,826 filed on Dec. 17, 2004 now U.S. Pat. No. 7,509,336. The entire disclosure of the prior application, application Ser. No. 11/015,826, is hereby incorporated by reference. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to databases, and more particularly to the determination of periodicity in database workloads. 
     BACKGROUND 
     Autonomic computing is a self-managing computing model named after the human body&#39;s autonomic nervous system. An autonomic computing system is capable of controlling the functioning of computer applications and systems without input from the user, in the same way that the autonomic nervous system regulates body systems without conscious input from the individual. The goal of autonomic computing is to create self-executing systems capable of high-level functioning while shielding users from system complexity. 
     Workload characterization is a fundamental issue in autonomic computing. In order to effectively allocate system resources to a particular computing task, an autonomic system should have the ability to characterize the workload of the computing task. 
     An important aspect of workload characterization is determination of workload periodicity. Workload periodicity refers to the tendency of a workload to place cyclic demands on processing power. For example, if an e-commerce web site shows a peak load (i.e. maximum activity) between 5 PM and 8 PM, a minimum load between 5 AM and 8 AM, and decreasing/increasing loads between the two extremes, a workload periodicity analysis should reveal the workload to have a strong cyclic structure. The closer the activity pattern is to a perfect sine/cosine wave, the stronger the cyclic nature or “structure” of the workload. The strength of a cyclic structure would be decreased by the presence of random noise or by non-periodic events. 
     A workload periodicity analysis not only evidences a workload&#39;s historical characteristics, it may also be used predict workload trends into the future. Such workload forecasting may permit the processing efficiency of an autonomic computing system to be improved, as the system may be able to “preemptively” allocate resources, prior to expected peaks in processing demand. 
     As database systems move towards the autonomous computing model, a periodicity analyzer for database workloads would be desirable. 
     SUMMARY 
     In accordance with an aspect of the present invention there is provided a data processing system for determining database workload periodicity, the data processing system including a converting module for converting database activity samples spanning a time period from the time domain to the frequency domain, the converting module providing a frequency spectrum, an identifying module for identifying fundamental peaks of the frequency spectrum, and an allocating module for allocating database resources based on at least one of the fundamental peaks. 
     In accordance with another aspect of the present invention there is provided an article of manufacture for directing a data processing system to determine database workload periodicity, the article of manufacture including a program usable medium embodying one or more instructions executable by the data processing system, the one or more instructions including data processing system executable instructions for converting database activity samples spanning a time period from the time domain to the frequency domain, the converting resulting in a frequency spectrum, data processing system executable instructions for identifying fundamental peaks of the frequency spectrum, and a data processing system executable instructions for allocating database resources based on at least one of the fundamental peaks. 
     Other aspects and features of the present invention will become apparent to those ordinarily skilled in the art upon review of the following description of specific embodiments of the invention in conjunction with the accompanying figures. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In the figures which illustrate embodiments of the present invention: 
         FIG. 1  illustrates a database system exemplary of an embodiment of the present invention; 
         FIG. 2  illustrates certain components the database system of  FIG. 1  in greater detail; 
         FIG. 3  illustrates database workload data comprising samples showing 20 activity of the database system of  FIG. 1  over time; 
         FIG. 4  illustrates another representation of the workload data set of  FIG. 3  also showing database system activity over time; 
         FIG. 5  illustrates the data set of  FIG. 4  after application of a low pass filter; 
         FIG. 6  illustrates a frequency spectrum generated from the data set of  FIG. 5  using a Fourier transform; 
         FIG. 7  illustrates an energy-density spectrum generated from the frequency spectrum of  FIG. 6 ; 
         FIG. 8  illustrates the energy-density spectrum of  FIG. 7  with low frequency components having been removed; 
         FIG. 9  illustrates the application of Wold decomposition to the energydensity spectrum of  FIG. 8 ; and, 
         FIG. 10  illustrates operation of the workload periodicity analyzer of  FIG. 2 . 
     
    
    
     DETAILED DESCRIPTION 
     An embodiment of the present invention analyzes database workload data to identify any periodic (i.e. cyclic) patterns in workload intensity that may be present. If periodic patterns are detected, workload period duration information may be extracted from the data along with a confidence metric estimating the strength of the cyclic structure. A high level of confidence indicates that the periodic pattern is likely to repeat. The analysis may be used by autonomous database components to predict the time and approximate intensities of peak workload levels occurring in the future, so that database system resources may be allocated accordingly. 
     Briefly, an embodiment of the database workload periodicity analysis is performed as follows. Initially, a set of database activity samples is converted from the time domain to the frequency domain. The resulting frequency spectrum is then used to create an energy-density spectrum which reflects the energy of workload components at different frequencies. Fundamental peaks in the energy-density spectrum are identified. The power of identified fundamental peaks is computed, accounting for associated harmonics. The power of a fundamental peak and associated harmonics reflects the degree to which a workload period corresponding to the peak dominates the database workload. A confidence metric indicative of the degree to which the workload cycle approximates a sinusoid may be produced by dividing the peak power by the sum of the peak power and non-peak power, Fundamental peaks may be identified within the frequency spectrum rather than the energy-density spectrum in some embodiments. 
     Referring to  FIG. 1 , a database system  10  is illustrated. Database system  10  comprises a computer system  20  executing a database management system (DBMS)  12 . The computer system  20  may be a server such as the IBM® eServer 325 for example. The computer system includes a processor (not shown) interconnected with memory including non-volatile memory  16 , which may be used to store data comprising the database. The DBMS  12  may be a commercially available relational database management system modified to operate as described herein. In the present embodiment, the DMBS  12  is a modified version of the IBM® DB2 Universal Database Version 8.1. The modifications provide the system with the ability to perform database workload periodicity analysis, in a manner that will be described. The DBMS  12  may be loaded into the computer system  20  from a machine-readable medium  14 , which could be a disk, a tape, a chip or a random access memory containing a file downloaded from a remote source. 
       FIG. 2  illustrates certain components of the database system  10 , namely DBMS  12  and non-volatile memory  16 , in greater detail. 
     As shown in  FIG. 2 , DBMS  12  includes a performance monitor  30  and a workload periodicity analyzer (abbreviated “WORPAZ”)  32 . Other components of DBMS  12  are omitted for clarity. 
     The performance monitor  30  is a module responsible for monitoring the performance of the database system  10 . The performance monitor  30  is configured to sample database activity at regular intervals in time and to store these samples in a file  18  in non-volatile memory  16 . In the present embodiment, the performance monitor  30  is the DB2 “Snapshot Monitor’ interface. As known to those skilled in the art, the DB2 Snapshot Monitor is a software component which allows samples (i.e. “snapshots”) of the state of database activity to be taken at particular points in time. The samples may capture various metrics indicative of database activity at the sampled moments, such as the number of database commands (e.g. Structured Query Language (SQL) statements) executed in a preceding time period for example. From the perspective of characterizing load, the metrics should encompass activity in respect of lower level objects such as tables (e.g. rows_deleted, rows_inserted, rows updated, rows_selected, rows_read, and rows_written, or sums of these). A list illustrative of various types of database metrics that could be employed can be found in the DB2 System Monitor Guide and Reference, published by IBM®. 
     The workload periodicity analyzer  32  is a module responsible for analyzing the periodicity of the workload of database system  10 . The WORPAZ  32  reads the database activity samples stored in file  18  and uses this workload data to analyze workload periodicity. The WORPAZ  32  may be part of an autonomic computing database component which controls the behavior of the database system  10  based on anticipated workload. The workload periodicity analyzer  32  executes periodically on database system  10  (e.g. at regular time intervals, which may be 10 minutes intervals for example). 
       FIGS. 3 to 9  illustrate exemplary database workload data at various stages of workload periodicity analysis. 
       FIG. 3  illustrates a set of samples  300  representing activity of the database system  10  over a 120-minute time period. Although the data  300  is illustrated in the form of a continuous line graph, it actually consists of a set of discrete samples. More specifically, the exemplary data set  300  consists of 120 samples, each representing a snapshot of database activity taken at a 1-minute interval. Each sample in  FIG. 3  is a cumulative measure of the number of SQL statements executed by the DBMS  12  since the beginning of the 120-minute time period. The workload data shown in  FIG. 3  forms the input to the WORPAZ  32 . 
       FIG. 4  illustrates another representation  400  of the workload data set  300  of  FIG. 3 . In this representation, database activity is represented by the number of SQL statements executed by the DBMS  12  since the last sample (rather than since the beginning of the 120-minute time period). The data set  400  is generated by applying a difference operator to adjacent samples in the data set  300  of  FIG. 3 . 
       FIG. 5  illustrates a workload data set  500  which consists of the set of database activity samples  400  of  FIG. 4  after application of a low pass filter. 
       FIG. 6  illustrates a frequency spectrum  600  which is generated by converting the data set  500  of  FIG. 5  from the time domain to the frequency domain. The frequency spectrum  600  has a real component  610  and an imaginary component  620 . As will be appreciated by a person of ordinary skill in the art, the frequency spectrum of  FIG. 6  represents the same information as is represented in  FIG. 5 , except that the X-axes in  FIG. 6  represents the frequency domain while the X-axis of  FIG. 5  represents the time domain. 
       FIG. 7  illustrates an energy-density spectrum  700  generated from the frequency spectrum  600  of  FIG. 6 . The amplitude associated with a frequency indicated on the X-axis represents the energy of the database workload at that frequency. The energy units Joules (J) are applied to the Y-axis of  FIG. 6 . 
       FIG. 8  illustrates the energy-density spectrum of  FIG. 7  with low frequency components removed, i.e., after application of a high-pass filter. 
       FIG. 9  illustrates the filtered energy-density spectrum of  FIG. 8  with a sole fundamental peak  902  being indicated in dashed lines. 
     Operation  1000  of the workload periodicity analyzer  32  of  FIG. 2  is illustrated in  FIG. 10 . 
     Initially, a set of samples of the activity of the database system  10  over time is generated (S 1002 ). In the present embodiment, generation of this set of samples involves two steps. 
     First, the workload data set  300  of  FIG. 3  is created. Creation of data set  300  entails sampling a running total of the number SQL statements executed by the DBMS  12  at 1-minute intervals over a sampling time period of 120 minutes. The sampling time period should preferably be at least twice as long as the longest expected cycle in the workload, to ensure that at least two representative cycles are sampled (if no information is known about expected workload cycle durations, the sampling period should simply be made very long). The performance monitor  30  controls the sampling. The samples are stored in file  18  within the non-volatile memory  16  of database system  10  ( FIG. 2 ). 
     Second, the workload data set  400  of  FIG. 4  is created from the workload data set  300  of  FIG. 3 . This step entails applying a difference operator to adjacent samples in the data set  300  of  FIG. 3  to generate samples representative of the number of SQL statements executed by the DBMS  12  since the last sample. The data set  400  of  FIG. 4  is generated by the workload periodicity analyzer  32  based on the data stored in file  18 . 
     It will be appreciated that the data set  400  could be created without the initial creation of data set  300  and application of a difference operator thereto, if the performance monitor has the capability to directly sample the number of SQL statements executed since the previous sample. 
     Next, a low-pass filter is applied to the samples  400  of  FIG. 4  (S 1004 — FIG. 10 ). This may be achieved by computing a moving average for samples in the workload data set  400  ( FIG. 4 ). For example, the moving average may use a neighborhood of width  5  centered on the point in question (i.e. two points on either side as well as the center point). The result is a filtered data set  500  ( FIG. 5 ) in which rapid variations which are assumed to represent noise have been removed. 
     Thereafter, the filtered set  500  of database activity samples is converted from the time domain to the frequency domain (S 1006 — FIG. 10 ) to create a frequency spectrum  600  ( FIG. 6 ). Conversion may be performed using a Fast Fourier Transform (FFT). The FFT may be a software-based function from a library, such as the “Fastest Fourier Transform in the West’ (FFTW) library available at http://www.fftw.org/ for example, or a similar function. 
     From the frequency spectrum  600 , an energy-density spectrum  700  ( FIG. 7 ) is generated (S 1008 — FIG. 10 ). Individual energy components of the energy density spectrum  700  are generated by squaring the magnitude of corresponding frequency components of the frequency spectrum  600  ( FIG. 6 ). 
     In particular, an energy component of the energy density spectrum  700  is the sum of the squares of the magnitudes of the corresponding real component (from  610 ) and imaginary component (from  620 ). For example, if the complex number for one element of the frequency array is 3−4*i (with 3 being the real component and −4*i being the imaginary component (i being the square root of negative −1)) then the corresponding entry in the energy density spectrum array is:
 
(3)^2+(−4) A 2=9+16=25
 
     This technique for generating an energy-density spectrum is described in “Signals and Systems, 2 nd  Edition” by Oppenheim, Willsky and Nawab (published by Nawab) (p. 312), which is hereby incorporated by reference hereinto. The amplitude associated with each energy component of the resultant energydensity spectrum  700  represents the energy of the database workload at the associated frequency, which reflects the degree to which a workload period corresponding to the frequency dominates the database workload. 
     Next, a high-pass filter is applied to the energy-density spectrum  700  (S 1010 — FIG. 10 ) to create a filtered energy-density spectrum  800  ( FIG. 8 ). In the present embodiment, application of the high-pass filter is effected by removing the three lowest frequency components of the energy-density spectrum  700 , which are assumed to constitute low frequency noise. 
     It will be appreciated that the moving average computation performed in S 1004  and low frequency component removal performed in S 1010  in combination have the same effect of as would the application of a bandpass frequency filter to the workload data set  400  ( FIG. 4 ). 
     Next, fundamental peaks and associated harmonics in the filtered energy-density spectrum  800  are identified (S 1012 ). A fundamental peak is defined as the largest set of contiguous array elements in the energy-density spectrum  800  in which each element exceeds a threshold set at 5% percent of the highest amplitude element in the spectrum  800 . Fundamental peaks represent concentrations of periodicity within the workload data, i.e., frequencies at which cycles in the workload data are strongest. 
     In the exemplary energy-density spectrum  900  of  FIG. 9  (which is simply energy-density spectrum  800  with the sole fundamental peak indicated at  902 ), only one fundamental peak is found. This fundamental peak is shown in dashed lines in  FIG. 9  at  902 . The fundamental peak  902  spans the third to the tenth data points. The energy-density spectrum  900  components which comprise the peak (i.e. energy components at frequency bins  4 - 8 ) are marked with squares in  FIG. 9 . The center frequency of the fundamental peak  902 , which is deemed to be the frequency at which the maximum energy value within the contiguous set occurs, is at the seventh data point. 
     It will be noted that the endpoints of the peak are defined in the present embodiment to be the first data points on either side of the center which are below the threshold. Summation is then performed from these endpoints (inclusively). Thus, both of the “left tail” of the peak (i.e. the energy component between the third and fourth data points) and the “right tail” of the peak (i.e. the energy component at between the eleventh and twelfth data points) are considered to be part of the peak. 
     Harmonics associated with each fundamental peak are also identified in S 1012 . A harmonic is a fundamental peak whose center frequency is an even multiple (plus or minus an adjustable tolerance) of a known fundamental peak. In the present embodiment, a peak should be at least 20% of the strength of the highest recorded energy density to be recognized as a harmonic. Based on this criterion, no harmonics strong enough to be recognized by the WORPAZ  32  exist in the energy-density spectrum  900  of the present example. 
     Thereafter, referring again to  FIG. 10 , for each identified fundamental peak (S 1014 ), the power of the peak and any associated harmonics is computed (S 1016 ). 
     The power of a fundamental peak is computed by summing the amplitude of each individual energy component comprising the peak. The power of the fundamental peak indicates the degree to which corresponding workload period dominates the workload of the database system  10 . 
     For example, the power of fundamental peak  902  of  FIG. 9  is computed by summing the energy of the energy-density spectrum components at frequency bins  4 ,  5 ,  6 ,  7  and  8 . The power of each harmonic would be computed in the same manner. If no harmonics exist, as in the present case, the power of “the peak and any associated harmonics” will simply be the power of the peak. 
     A confidence metric indicating the degree to which the workload frequency associated with the fundamental peak dominates the database workload is then 15 computed (S 1018 ). 
     To facilitate computation of the confidence metric for a fundamental peak, the power of non-peak components of the energy-density spectrum  900  is first computed. To identify which components of the energy-density spectrum are the “non-peak” components, a technique known as Wold decomposition is used. In this technique, energy-density spectrum components comprising either a fundamental peak or a harmonic are deemed to be peak (i.e. periodic) components, and the remaining components are deemed to be non-peak (i.e. random) components. 
     In the present example, the components of energy-density spectrum  900  which comprise the sole fundamental peak  902  are classified as peak components, while the remaining components are classified as non-peak components (in view of the fact that only one fundamental peak  902  and no harmonics exist). 
     The sum of the power over the non-peak spectrum is then calculated by summing the energy of each individual non-peak component. This results in a computed “total non-peak power”. 
     The confidence metric for a fundamental peak may then be computed by dividing the power of the peak and any associated harmonics (as computed in S 1016 ) by the sum of the peak-plus-harmonics power (again from S 1016 ) and the computed total non-peak power. The value of the confidence metric will vary from zero to one, with one corresponding to a perfect sine wave at the relevant frequency, which frequency reflects the length of the cycle. 
     In the present example, the confidence metric computed for the sole fundamental peak  902  is 0.898. This is computed based on peak and non-peak power values of 151464701 and 17214044 (respectively), as follows: 
     
       
         
           
             
               
                 
                   metric 
                   = 
                     
                   ⁢ 
                   
                     151464701 
                     / 
                     
                       ( 
                       
                         151464701 
                         + 
                         17214044 
                       
                       ) 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     151464701 
                     / 
                     147425795 
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   0.898 
                 
               
             
           
         
       
     
     This represents a high degree of confidence that peaks of workload intensity will occur in the future at a frequency of 0.00086 Hz, or approximately every 21 minutes, assuming future database workload is similar to historical workload. 
     As will be appreciated by those skilled in the art, modifications to the above-described embodiment can be made without departing from the essence of the invention. For example, performance monitor  30  need not necessary store database workload data in a file  18 . Rather, the data could alternatively be stored in SQL tables or in appropriate data structures in memory. 
     In another alternative, the application of a low-pass filter and high-pass filter to workload data need not be performed during periodicity analysis if workload data is known to be relatively free of noise. If filtering is performed, either or both of a low-pass filter and a high-pass filter may be applied. 
     Alternatively, a bandpass filter having the same effect could be used. In the case of the high-pass filter, the described approach of dropping three lowest-frequency components is but one approach of many that could be used. Filtration may be performed in either of the time domain or the frequency domain. 
     It will also be appreciated that database workload data in alternative embodiments may not take the form of samples indicating a number of SQL statements executed over a time period. Rather, workload periodicity analyses may be based on other database performance metrics (e.g. as described above). The analysis can be applied to any single metric or mathematical combinations of metrics. 
     As well, it will be appreciated that workload periodicity analysis need not be performed in a target environment based on real-time data samples taken during actual database system operation. Rather, workload periodicity analysis may be performed in a factory simulation environment based on representative sets of data samples which approximate real-world database system activity, so as to create one or more “pre-fabricated models” of expected workload periodicity data. These models, which may comprise confidence metrics, expected workload frequencies, and/or other workload periodicity data generated by the method described herein, may be shipped “canned” along with the database system  10  for use as-needed in the target environment. That is, once the database system is activated in its target environment, the system may select the pre-fabricated model that best suits its current environment, and allocate system resources according to that model. This approach may alleviate some of the computational and data management burdens which may be introduced when sampling is performed real-time as described above. 
     Fundamentally, those skilled in the art will recognize that identifying fundamental peaks in the energy-density spectrum is equivalent to identifying fundamental peaks in the frequency spectrum, in the sense that the same peaks can be identified regardless of which spectrum is examined. Of course, when a threshold is set at a percentage X of a maximum element when examining the energy-density spectrum, to identify the same peak in the corresponding frequency spectrum, the threshold would need to be set at a percentage that is the square root of X of the maximum frequency spectrum element (e.g. if the threshold were set at 64% of the maximum element in the energy-density spectrum, it would need to be set at 80% of the maximum element in the frequency spectrum). Of course, both of the real and imaginary components of the frequency spectrum should be taken into account when identifying fundamental peaks. 
     Other modifications will be apparent to those skilled in the art and, therefore, the invention is defined in the claims.