Computer graphics processing and selective visual display system – Computer graphics processing – Graph generating
Reexamination Certificate
2000-11-10
2003-12-16
Bazavi, Michael (Department: 2672)
Computer graphics processing and selective visual display system
Computer graphics processing
Graph generating
C345S440100
Reexamination Certificate
active
06664964
ABSTRACT:
CROSS REFERENCE TO RELATED APPLICATIONS
N/A
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT
N/A
BACKGROUND OF THE INVENTION
The present invention relates generally to computer systems, and more particularly to efficient management of data storage systems and computer system performance. The present invention relates specifically to a system and method for determining whether the activity graphs of logical volumes are correlated.
Data storage for computer systems may be provided using a variety of device types and technologies. Mass storage of computer readable data is often provided using electromagnetic storage disks, sometimes referred to as “hard disks”, or “disks”.
A device which controls and/or operates one or more disks is sometimes referred to as a “disk adapter.” A disk adapter typically controls a set of stacked storage disks, each of which has data recorded electromagnetically in “blocks” of data which are organized onto concentric circles or “tracks.” A disk “head” writes or reads the data stored on the tracks.
It is often desirable to have some form of virtual disk subsystem in order to provide flexibility in the allocation and management of disk storage. A virtual disk subsystem may be used to define what are referred to as “logical volumes”, using storage capacity from one or more disks. For example, one or more disks may be organized into a group to form a storage pool from which disk space may be allocated to form the logical volumes. Each logical volume may consist of an arbitrary-size storage space defined within the related group of storage devices. Each logical volume can then be used as a separate storage space for a file system or for raw data storage by various applications.
A problem arises with respect to mapping logical volumes onto specific physical devices, due to the fact that system performance may suffer when two or more logical volumes with correlated activity graphs are co-located on one or more physical devices. In such circumstances, shared resources of the physical device or devices storing the correlated logical volumes may impose a bottleneck on system performance during periods of coincidental high activity.
Thus, it would be desirable to have a system which determines whether the activity graphs of two logical volumes are correlated, so that appropriate action may be taken to prevent system performance degradation.
A known mathematical technique for determining the correlation of two data sequences is the “correlation coefficient” method. The correlation coefficient technique is a mathematical tool that may be employed to find linear relationships between two variables, X and Y. Correlation coefficient analysis typically results in a value from −1 to +1 describing the correlation of two data sequences over the length of interest. Therefore, correlation coefficient values close to 1 indicate a positive linear association between the variables, in that as one of the variables increases, so does the other. Conversely, correlation coefficient values close to −1 indicate a negative linear association between the variables, in that as one of the variables increases, the other decreases. Correlation coefficient values close to zero indicate a lack of linear association between the variables. As it is generally known, the correlation coefficient equation may be given as follows:
CORRELATION
COEFFICIENT
=
∑
i
(
X
i
-
X
_
)
(
Y
i
-
Y
_
)
∑
i
(
X
i
-
X
_
)
2
∑
i
(
Y
i
-
Y
_
)
2
where X
i
and Y
i
in this case are activity levels at the i
th
time samples, and {overscore (X)} and {overscore (Y)} are the means of X and Y, respectively.
The correlation coefficient technique has certain drawbacks applied to the problem of determining whether the activity graphs of logical volumes are correlated. These drawbacks stem from the fact that the correlation coefficient approach assumes that a linear correlation exists between the two sequences being compared, which is frequently not true for activity graphs of logical volumes. Moreover, the correlation coefficient approach does not consider the correlation of the absolute activity levels of the logical volumes being compared.
For the reasons stated above, it would be desirable to have a system which determines whether the activity graphs of two logical volumes are correlated, at least in part based on their absolute activity levels, so as to detect whether the logical volumes have significant periods of coincidental high activity levels. Further, it would be desirable to have a system which determines whether the activity graphs are correlated for two logical volumes, at least partly based on the magnitude of changes in the respective activity levels, so as to detect whether the logical volumes have coincidental activity level increases of a large magnitude.
BRIEF SUMMARY OF THE INVENTION
In accordance with principles of the invention, a system and method are disclosed for determining whether activity graphs for logical volumes of data storage are correlated. Activity graphs are first generated over a test period for each of the logical volumes to be compared. Each activity graph consists of a series of activity levels measured at sampling points within the test period. An activity level for a logical volume may, for example, reflect the number of read and/or write operations involving data stored within that logical volume.
In an illustrative embodiment of the disclosed system, an area ratio criteria is employed to determine whether logical volume activity graphs are correlated. The disclosed system employs the area ratio criteria to determine whether activity graphs for a selected pair of logical volumes are correlated by determining whether an area ratio of the activity graphs is at least as great as a predetermined threshold. The area ratio of the activity graphs is a ratio between a minimum area and a maximum area described by the two activity graphs. The minimum area is defined as the area lying below both the activity graphs. The maximum area is defined as the area lying below either one or the other of the activity graphs. The predetermined threshold area ratio may, for example, be determined empirically for a given application, such that pairs of activity graphs which have an area ratio at least as large as the threshold area ratio value should be considered correlated.
In another illustrative embodiment, other correlation criteria are employed to determine if the activity graphs of two logical volumes are correlated. The set of correlation criteria which may be employed further includes a peak ratio criteria. The peak ratio criteria indicates that one activity graph is correlated to another activity graph if a peak ratio described by the two activity graphs is at least as large as a predetermined peak ratio value. The peak ratio for the two activity graphs being compared is a ratio between the number of coincidental peaks in the two graphs, and the difference between the total number of peaks in the two graphs and the number of coincidental peaks. The number of coincidental peaks may, for example, be defined as the number of peaks in one of the activity graphs which occur at the same time as peaks in the other activity graph. Further for purposes of illustration, a peak within an activity graph may be defined as an activity level sample which is above the average activity level for the activity graph, plus a predetermined offset value. Alternatively, or in addition, a peak within an activity graph may be defined as an activity level at least as large as the product of the average activity level for the activity graph multiplied by a predetermined multiplier value. Appropriate predetermined offset and/or multiplier values may be determined empirically for specific applications.
The correlation criteria employed by the disclosed system may further include a sharp peak criteria. The sharp peak criteria indicates that one activity graph is correlated to another in the event that the two activity graphs have a coinc
Levin-Michael Orit
Sahin Adnan
Bazavi Michael
EMC Corporation
Gunther John M.
Havan Thu-Thao
Wilson Penelope S.
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