Patent Publication Number: US-9892014-B1

Title: Automated identification of the source of RAID performance degradation

Description:
FIELD 
     Embodiments of the present invention relate generally to data storage systems. More particularly, embodiments of the invention relate to prediction of performance degradation of redundant array of inexpensive disks (RAID) disks. 
     BACKGROUND 
     RAID is a technology that employs collections of disk drives (herein referred to simply as disks) and allows them to be used as a logical unit. RAID provides greater performance and reliability (e.g., through the use of a protection scheme called “parity”) than a single disk. Data is distributed across the disks and, therefore, the performance of a RAID group is dependent on the performance of each disk. Throughout the description, a RAID group shall interchangeably be referred to as a RAID array. If a single disk experiences performance degradation the RAID group will also have performance degradation. Disks exhibiting poor performance should, therefore, be proactively removed from operation within the RAID group and replaced with a new disk drive. 
     Conventionally, a large number of statistics are available and collected for determining disk-drive performance and health. These include the industry standard Self-Monitoring, Analysis, and Reporting Technology (SMART) data for Serial Advanced Technology Attachment (SATA) disks, and various log pages for Small Computer System Interface (SCSI) disks. Analyzing this massive amount of statistics, however, can be resource intensive, and often results in false positives. Here, a false positive refers to a disk that has been erroneously identified as having performance degradation when in fact it is in normal operating condition. Thus, there is a need for a simple and efficient mechanism to check disk-drive health that will yield a low-rate of false positives. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Embodiments of the invention are illustrated by way of example and not limitation in the figures of the accompanying drawings in which like references indicate similar elements. 
         FIG. 1  is a block diagram illustrating a storage system according to one embodiment of the invention. 
         FIG. 2  is a block diagram illustrating the collection and calculation of parameters for and by a storage system according to one embodiment of the invention. 
         FIG. 3  is a timing diagram illustrating determination of performance statistics according to one embodiment. 
         FIG. 4  is a flow diagram illustrating a method for determining disks which have degraded in performance according to one embodiment. 
         FIG. 5  is a diagram illustrating a display of disks and their respective performance statistics according to one embodiment. 
         FIG. 6  is a diagram illustrating the results of a prediction of disk performance degradation according to one embodiment. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Various embodiments and aspects of the inventions will be described with reference to details discussed below, and the accompanying drawings will illustrate the various embodiments. The following description and drawings are illustrative of the invention and are not to be construed as limiting the invention. Numerous specific details are described to provide a thorough understanding of various embodiments of the present invention. However, in certain instances, well-known or conventional details are not described in order to provide a concise discussion of embodiments of the present inventions. 
     References in the specification to “one embodiment” or “an embodiment” means that a particular feature, structure, or characteristic described in conjunction with the embodiment can be included in at least one embodiment of the invention. The appearances of the phrase “in one embodiment” in various places in the specification do not necessarily all refer to the same embodiment. 
     Bracketed text and blocks with dashed borders (e.g., large dashes, small dashes, dot-dash, and dots) may be used herein to illustrate optional operations that add additional features to embodiments of the invention. However, such notation should not be taken to mean that these are the only options or optional operations, and/or that blocks with solid borders are not optional in certain embodiments of the invention. 
     In the following description and claims, the terms “coupled” and “connected,” along with their derivatives, may be used. It should be understood that these terms are not intended as synonyms for each other. “Coupled” is used to indicate that two or more elements, which may or may not be in direct physical or electrical contact with each other, co-operate or interact with each other. “Connected” is used to indicate the establishment of communication between two or more elements that are coupled with each other. 
     Techniques for predicting a RAID disk has degraded in performance are herein described. Throughout the description, a RAID disk that has degraded in performance shall simply be referred to as a degraded disk. Throughout the description, disk performance degradation prediction is described as being performed by a management system. It shall be understood, however, that similar predictions can be performed the RAID storage system itself. According to one embodiment, the management system analyzes disk performance statistics collected during storage of data from a source storage system to the RAID storage system. The performance statistics include, but not limited to, usage observations, read-byte-counts, write-byte-counts, or any combination thereof. 
     As used herein, a “usage observation” refers to a numeric value that indicates how busy a disk was during a particular time period (e.g., during a time interval). The usage observation may be a ratio between the total time that the disk utilized to process requests (e.g., read, write, replicate requests, etc.) and the time of the interval. For example, assuming a time interval of 24 hours, a usage observation of 0.5 indicates that the disk spent a total of 12 out of 24 hours processing requests. As used herein, a “read-byte-count” refers to a count that indicates how many bytes were read from the disk during a particular time interval. As used herein, a “write-byte-count” refers to a count that indicates how many bytes were written to the disk during a particular time interval. 
     According to one embodiment, the management system analyzes the performance statistics in order to identify degraded disks of a RAID group/array. Identifying degraded disks includes determining a population mean of the usage observations of all disks that belong to the same RAID group. Here, a “RAID group” refers to a collection of disks on a RAID storage system that appears as a single physical disk to the source storage system. A RAID array is a set of disks where data is written in “striped” form across all the disks at once, and for which parity is calculated and written with the data. The population mean is determined for a population data set. A data set refers to all performance statistics that are observed during the same time interval (e.g., 60 minutes, 24 hours, etc.) In one embodiment, the management system then determines a population standard deviation of the usage observations based on the determined population mean. According to one embodiment, for each disk of the RAID group, the management system then determines a Z-score based on the disk&#39;s usage observation, the determined population mean, and the population standard deviation. As used herein, a Z-score refers to the number of standard deviations that a particular observation is above or below the mean of the data set. Thus, in this context, the Z-score of a disk refers to how many standard deviations its usage observation is above or below the population mean. 
     According to one embodiment, the management system determines that a disk with a high Z-score has degraded in performance. Here, a high Z-score refers to a Z-score that is greater than a predetermined Z-score threshold (e.g., 3 standard deviations). In one embodiment, in order to minimize false positives, the management system determines whether there was an imbalanced workload during the time interval. Here, an imbalanced workload refers to a phenomenon where certain disks of the RAID group are utilized more frequently than other disks of the same RAID group. In such an embodiment, the management system determines a standard deviation of the read-byte-counts of all disks of the RAID group, and a standard deviation of the write-byte-counts of all disks of the RAID group. In one embodiment, if the sum of these 2 standard deviations are not within a predetermined percentage (e.g., 10%) of the standard deviation of the usage observations, the management system determines that there was an imbalanced workload during the sample time period, and discards the entire set of observations without performing any prediction. 
     According to one embodiment, in order to minimize false positives, the management system determines whether a predicted degraded disk has a high Z-score for at least a first predetermined amount of time out of a second consecutive predetermined amount of time. For example, the management system determines that a high Z-score disk is a degraded disk only if it has a high Z-score for at least 3 out of 5 consecutive days. In yet another embodiment, in order to minimize false positives, the management system determines whether the predicted degraded disk has a usage observation that is greater than a predetermined usage threshold. Thus, for example, the management system may determine that a disk has not degraded even though it has a high Z-score because its usage observation is below the usage threshold. 
     Throughout the description, performance statistics are described as being collected and analyzed by the management system for illustrative purposes. One having ordinary skill in the art would recognize that these operations can be performed by any system in the network. For example, the RAID system itself may collect and/or analyze the performance statistics and locally determine whether any of the disks has degraded. Further, the management system may be configured to determine the usage observations, read-byte-counts, write-byte-counts, etc., rather than collecting them from the RAID storage system. In such an embodiment, the RAID storage system is configured to transmit raw operating statistics (e.g., time logs of when read/writes occur, etc.) to the management system. Various embodiments of the present invention shall become apparent through the description of various other figures below. 
       FIG. 1  is a block diagram illustrating a storage system according to one embodiment of the invention. Referring to  FIG. 1 , system  100  includes, but is not limited to, one or more client systems  101 - 102  communicatively coupled to storage system  104  over network  103 . Clients  101 - 102  may be any type of clients such as a server, a personal computer (e.g., desktops, laptops, and tablets), a “thin” client, a personal digital assistant (PDA), a Web enabled appliance, a gaming device, a media player, or a mobile phone (e.g., Smartphone), etc. Network  103  may be any type of networks such as a local area network (LAN), a wide area network (WAN) such as Internet, a corporate intranet, a metropolitan area network (MAN), a storage area network (SAN), a bus, or a combination thereof, wired and/or wireless. 
     Storage system  104  may include any type of server or cluster of servers, such as storage systems available from EMC® Corporation of Hopkinton, Mass. For example, storage system  104  may be a storage server used for any of various different purposes, such as to provide multiple users with access to shared data and/or to back up mission critical data. Storage system  104  may be, for example, a file server (e.g., an appliance used to provide network attached storage (NAS) capability), a block-based storage server (e.g., used to provide SAN capability), a unified storage device (e.g., one which combines NAS and SAN capabilities), a nearline storage device, a direct attached storage (DAS) device, a tape backup device, or essentially any other type of data storage device. Storage system  104  may have a distributed architecture, or all of its components may be integrated into a single unit. Storage system  104  may be implemented as part of an archive and/or backup system such as a deduplicating storage system available from EMC® Corporation of Hopkinton, Mass. 
     In one embodiment, storage system  104  includes, but is not limited to, deduplication storage engine  107 , and one or more storage units  108 - 109  communicatively coupled to each other. Storage units  108 - 109  may be implemented locally (e.g., single node operating environment) or remotely (e.g., multi-node operating environment) via interconnect  120 , which may be a bus and/or a network. In one embodiment, one of the storage units  108 - 109  operates as an active storage to receive and store external or fresh user data, while the other storage unit operates as a target storage unit to periodically archive data from the active storage unit according to an archiving policy or scheme. Storage units  108 - 109  may be, for example, conventional magnetic disks, optical disks such as CD-ROM or DVD based storage, magnetic tape storage, magneto-optical (MO) storage media, solid state disks, flash memory based devices, or any other type of non-volatile storage devices suitable for storing large volumes of data. Storage units  108 - 109  may also be a combination of such devices. The storage units  108 - 109  may be organized into one or more volumes of Redundant Array of Inexpensive Disks (RAID). 
     In response to a data file to be stored in storage units  108 - 109 , optional deduplication storage engine  107  is configured to segment the data file into multiple chunks according to a variety of segmentation policies or rules. Deduplication storage engine  107  may choose not to store a chunk in a storage unit if the chunk has been previously stored in the storage unit. In the event that deduplication storage engine  107  chooses not to store the chunk in the storage unit, it stores metadata enabling the reconstruction of the file using the previously stored chunk. As a result, chunks of data files are stored in a deduplicated manner, either within each of storage units  108 - 109  or across at least some of storage units  108 - 109 . Data stored in the storage units may be stored in a compressed form (e.g., lossless compression: Huffman coding, Lempel-Ziv Welch coding; delta encoding: a reference to a chunk plus a difference; etc.). In one embodiment, different storage units may use different compression methods (e.g., main or active storage unit from other storage units, one storage unit from another storage unit, etc.). 
     The metadata, such as metadata  110 - 111 , may be stored in at least some of storage units  108 - 109 , such that files can be accessed independent of another storage unit. Metadata of each storage unit includes enough information to provide access to the files it contains. In one embodiment, metadata may include fingerprints contained within data objects  112 - 113 , where a data object may represent a data chunk, a compression region (CR) of data chunks, or a container of one or more CRs. Fingerprints are mapped to a particular data object via metadata  110 - 111 , enabling the system to identify the location of the data object containing a chunk represented by a particular fingerprint. When an active storage unit fails, metadata contained in another storage unit may be utilized to recover the active storage unit. When one storage unit is unavailable (e.g., the storage unit has failed, or is being upgraded, etc.), the system remains up to provide access to any file not stored in the failed storage unit. When a file is deleted, the metadata associated with the files in the system is updated to reflect that the file has been deleted. 
     In one embodiment, the metadata information includes a file name, a storage unit where the chunks associated with the file name are stored, reconstruction information for the file using the chunks, and any other appropriate metadata information. In one embodiment, a copy of the metadata is stored on a storage unit for files stored on a storage unit so that files that are stored on the storage unit can be accessed using only the information stored on the storage unit. In one embodiment, a main set of metadata information can be reconstructed by using information of other storage units associated with the storage system in the event that the main metadata is lost, corrupted, damaged, etc. Metadata for a storage unit can be reconstructed using metadata information stored on a main storage unit or other storage unit (e.g., replica storage unit). Metadata information further includes index information (e.g., location information for chunks in storage units, identifying specific data objects). 
     In one embodiment, the storage system as shown in  FIG. 1  may be used as a tier of storage in a storage hierarchy that comprises other tiers of storage. One or more tiers of storage in this hierarchy may utilize different kinds of storage devices and/or may be optimized for different characteristics such as random update performance. Files are periodically moved among the tiers based on data management policies to achieve a cost-effective match to the current storage requirements of the files. For example, a file may initially be stored in a tier of storage that offers high performance for reads and writes. As the file ages, it may be moved into a tier of storage according to one embodiment of the invention. In various embodiments, tiers include different storage technologies (e.g., tape, hard drives, semiconductor-based memories, optical drives, etc.), different locations (e.g., local computer storage, local network storage, remote network storage, distributed storage, cloud storage, archive storage, vault storage, etc.), or any other appropriate storage for a tiered data storage system. 
     According to one embodiment, storage system  104  further includes backup application/software (SW)  106  configured to perform backup from source storage systems (e.g., clients  101 - 102 ) to storage system  104  (i.e., the target storage). Backup SW  106  is also configured to perform restore from target storage system  104  to the source storage systems. In one embodiment, backup SW  106  is configured to periodically collect and transmit performance statistic data representing at least some of storage system  104  operating statistics, to management system  150  and/or data collection server  160  over network  103 . One having ordinary skill in the art would recognize that backup SW  106  can be implemented as part of the source storage servers (e.g., clients  101 - 102 ) and/or a dedicated backup server (e.g., backup server  170 ). In one embodiment, backup SW  106  can be implemented as part of a host application (e.g., host application  171 ). For example, backup SW  106  can be implemented as part of the Oracle® Database (DB) application. 
     In one embodiment, storage system  104  further includes operation manager  105  configured to periodically collect and transmit performance statistic data representing at least some of storage system  104  operating statistics, to management system  150  and/or data collection server  160  over network  103 . This may be the case, for example, in embodiments where backup SW  106  is not implemented as part of storage system  104 . In one embodiment, the performance statistic data collected by backup SW  106  and/or operation manager  105  includes, but not limited to, usage observations, read-byte-counts, write-byte-counts, or any combination thereof. 
     In the example illustrated in  FIG. 1 , storage system  104  may be located at a client site and utilized by a client such as an enterprise or corporation, where the storage system  104  may be provided by a storage provider or vendor such as EMC Corporation. In one embodiment, management system  150  is associated with a storage provider or vendor that provides storage system  104  to a client. For example, management system  150  may be operated or owned by the storage provider or alternatively, it may be operated by a third-party vendor on behalf of the storage provider. 
     According to one embodiment, management system  150  includes data collector  151 , predictor  152 , and predictive model  155 . Data collector  151  is employed to communicate with operation manager  105  and/or backup SW  106  to collect statistic data described above. Note that although one storage system is shown, data collector  151  may communicate with multiple operation managers and/or multiple backup applications of multiple storage systems to collect statistic data concerning the respective storage systems, which may be located at the same or different geographical locations (e.g., same or different client sites). For example, management system  150  may be a centralized management server or cluster of servers for single or multiple clients or customers. In one embodiment, some operations of the backup applications may be running as part of the application that the backup applications protect, for example, Oracle, VMware, etc. 
     The collected performance statistic data is stored in a storage device as part of statistic logs  154 . In one embodiment, degradation predictor  152  is to perform an analysis on statistic logs  154  to generate predictive model  155  for predicting disk performance degradation. Note that data collector  151  is optional here, as statistic logs  154  can be collected by a third party entity, such as another server (e.g., data collection server  160 ), and transmitted to management server  150  for processing. Management system  150  and/or data collection server  160  may represent a cloud server or a cluster of cloud servers. Further, in an embodiment where disk performance degradation is determined locally by degradation predictor  118 , the performance statistics may be collected and stored as part of statistic logs  119 , which is stored in a storage device accessible by storage system  104 . In such an embodiment, degradation predictor  118  may perform an analysis on statistic logs  119  to generate predictive model  121  for predicting disk performance degradation. Thus, although throughout the description disk degradation prediction is described as being performed by management system  150 , it shall be understood that similar operations can be performed by RAID storage system  104  (e.g., degradation predictor  118  may perform operations similar to those performed by degradation predictor  152 , predictive model  121  may include modelling information similar to those included as part of predictive model  155 , and statistic logs  119  may include statistics similar to those included as part of statistic logs  154 ). 
     According to one embodiment, management system  150  further includes prediction reporter  126  configured to send notifications indicating certain predetermined predictions have occurred. For example, prediction reporter  126  is configured to send notifications when a disk degradation is predicted. Similar reporting mechanisms can be implemented as part of RAID storage system  104  (not shown). 
       FIG. 2  is a block diagram illustrating a storage system according to one embodiment of the invention. The storage system illustrated in  FIG. 2  is similar to the storage system illustrated in  FIG. 1 . Certain details have been omitted in  FIG. 2 , however, in order to avoid obscuring the invention. Certain details have also been added in  FIG. 2  in order to better illustrate the invention. 
       FIG. 2  illustrates RAID storage system  104  comprising of RAID groups (i.e., arrays)  1 - 2 . RAID storage system  104 , however, can include more or less RAID groups (i.e., arrays). A typical RAID storage system can include, for example, up to 56 RAID groups. Each RAID group includes multiple disks. A typical RAID group can include, for example, up to 14 disks. In the illustrated example, RAID group  1  includes disks  220 , and RAID group  2  includes disks  221 . 
       FIG. 2  illustrates RAID storage system  104  comprising of system-tick-counter  210 , disk-tick-counter(s)  211 , read-byte-counter(s)  212 , and write-byte-counter(s)  213 . System-tick-counter  210  contains the number system ticks that have occurred/elapsed since RAID storage system  104  was booted up. As used herein, a “system tick” (herein referred to simply as a “tick”) is a Unix term for a time unit (e.g., 1 millisecond), which in the Linux kernel is referred to as a “Jiffy”. Disk-tick-counters  211  represent disk tick counters, each counter corresponding to a disk on RAID storage system  104 . Each counter of disk-tick-counters  211  contains the number of ticks that the respective disk spent processing one or more requests since the time the disk was discovered by RAID storage system  104 . As used herein, “discovering” a disk refers to RAID storage system  104  detecting the presence of the disk (e.g., when RAID storage system boots up, when the disk is inserted into RAID storage system  104 , etc.) By way of example, a disk-tick-counter with an observation of 100 indicates that the respective disk spent  100  ticks processing one or more requests since the time the disk was discovered. 
     Read-byte-counters  212  represent read byte counters, each counter corresponding to a disk on RAID storage system  104 . Each counter of read-byte-counters  212  contains the number of bytes that have been read from the respective disk since the time the disk was discovered by RAID storage system  104 . By way of example, a read-byte-counter with an observation of 100 indicates that 100 bytes have been read from the respective disk since the time the disk was discovered. 
     Write-byte-counters  213  represent write byte counters, each counter corresponding to a disk on RAID storage system  104 . Each counter of write-byte-counters  213  contains the number of bytes that have been written to the respective disk since the time the disk was discovered by RAID storage system  104 . By way of example, a write-byte-counter with an observation of 100 indicates that 100 bytes have been written to the respective disk since the time the disk was discovered. 
     Disk drives in RAID storage system  104 , in one embodiment, are “hot-pluggable” and can be swapped in and out at any time. All the disk-specific counters (e.g., disk-tick-counters  211 , read-byte-counters  212 , and write-byte-counters  213 ) are set to zero when the disk is discovered, when RAID storage system  104  itself is booted up, or the disk is hot-inserted any time after system booted up. 
     According to one embodiment, performance statistics of the disks are collected and stored as part of statistic logs  154 . In the illustrated example, performance statistics Usage diski , Read-byte-count diski , and Write-byte-count diski  are collected and stored as part of statistic logs  154 . The determination of these statistics are illustrated in  FIG. 3 . 
       FIG. 3  is a timing diagram illustrating the computation of Usage diski , Read-byte-count diski , and Write-byte-count diski , according to one embodiment.  FIG. 3  illustrates two sets of data for two time intervals. Throughout the description, disk performance degradation prediction is described in the context of the time interval that extends from time T 1  to T 2 . One having ordinary skill in the art would recognize that similar predictions can be made based on statistics collected for any set of observations. 
     At transaction  3 - 01 , storage system  104  (e.g., operation manager  105  of storage system  104 ) logs/samples the current system tick count and stores it as system-tick-count T1 . For example, storage system  104  samples the current observation system-tick-counter  210  and stores it as system-tick-count T1 . As part of transaction  3 - 01 , storage system  104  also samples the current disk tick count corresponding to Disk i  and stores it as disk i -tick-count T1 . For example, storage system  104  samples the current observation of a disk-tick-counter  211  that corresponds to Disk, and stores it as disk i -tick-count T1 . 
     As part of transaction  3 - 01 , storage system  104  also samples the current read byte count corresponding to Disk, and stores it as read-byte-count diskiT1 . For example, storage system  104  samples the current observation of a read-byte-counter  211  that corresponds to Disk, and stores it as read-byte-count diskT1 . As part of transaction  3 - 01 , storage system  104  also samples the current write byte count corresponding to Disk, and stores it as write-byte-count diskT1 . For example, storage system  104  samples the current observation of a write-byte-counter  211  that corresponds to Disk, and stores it as write-byte-count diskiT1 . 
     At transaction  3 - 02 , storage system  104  logs/samples the current system tick count and stores it as system-tick-count T2 . For example, storage system  104  samples the current observation system-tick-counter  210  and stores it as system-tick-count T2 . As part of transaction  3 - 02 , storage system  104  also samples the current disk tick count corresponding to Disk, and stores it as disk i -tick-count T2 . For example, storage system  104  samples the current observation of a disk-tick-counter  211  that corresponds to Disk, and stores it as disk i -tick-count T2 . 
     As part of transaction  3 - 02 , storage system  104  also samples the current read byte count corresponding to Disk, and stores it as read-byte-count diskiT2 . For example, storage system  104  samples the current observation of a read-byte-counter  211  that corresponds to Disk, and stores it as read-byte-count diskiT2 . As part of transaction  3 - 02 , storage system  104  also samples the current write byte count corresponding to Disk, and stores it as write-byte-count diskiT2 . For example, storage system  104  samples the current observation of a write-byte-counter  211  that corresponds to Disk, and stores it as write-byte-count diskiT2 . 
     In one embodiment, storage system  104  determines Usage diski  (i.e., the usage observation of Disk i ) of the sample by determining the ratio of the total amount of time Disk i  utilized to process all access requests during the time interval. In this example, storage system  104  determines Usage diski  by applying the following equation: 
     
       
         
           
             
               
                 
                   
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     In one embodiment, storage system  104  determines Read-byte-count diski  (i.e., the total number of bytes read from Disk, during the time interval) by determining the difference between the running total of bytes read from Disk, at the end of the time interval and the running total of bytes read from Disk, at the beginning of the time interval. In this example, storage system  104  determines Read-byte-count diski  by applying the following equation:
 
Read-byte-count diski =(read-byte-count diskT2 −read-byte-count diskiT1 )  Equation (2).
 
     In one embodiment, storage system  104  determines Write-byte-count diski  (i.e., the total number of bytes written to Disk i  during the sample) by determining the difference between the running total of bytes written to Disk i  at the end of time interval and the running total of bytes written to Disk, at the beginning of the time interval. In this example, storage system  104  determines Write-byte-count diski  by applying the following equation:
 
Write-byte-count diski =(write-byte-count diskiT2 −write-byte-count diskiT1 )  Equation (3).
 
     One having ordinary skill in the art would recognize that Usage disci , Read-byte-count diski , and/or Write-byte-count diski  can be computed by other systems in the network. For example, Usage disci , Read-byte-count diski , and/or Write-byte-count diski  can be computed by management system  150 . In such an embodiment, storage system  104  can transmit raw operating statistics (e.g., observations of counters and/or the deltas of the counters, etc.) to management system  150 , and management system  150  can compute Usage disci , Read-byte-count diski , and/or Write-byte-count diski  based on the raw statistics. In other words, the operations illustrated in  FIG. 3  can be performed in a distributed manner. 
     Referring now back to  FIG. 2 . In one embodiment, predictor  152  generates predictive model  155  using performance statistics stored as part of statistic logs  154 . In one embodiment, predictor  152  generates the population mean of the usage observations (μ) by adding up all the usage observations of the observations, and dividing the sum by the number of usage observations in the population. In this example, predictor  152  can determine population mean of usage observations by applying the following equation: 
     
       
         
           
             
               
                 
                   
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                     ) 
                   
                 
               
             
           
         
       
     
     Throughout the description, various equations are described which reference the variable “n”. As used herein, “n” refers the number of disks in the disk group (i.e., array) for which the prediction is being made. A RAID array is one set of disks where data is written in “striped” form across all the disks at once, and for which parity is calculated and written with the data. Typical storage systems, such as those provided by EMC®, have 1 to 56 or more such arrays. The mechanism for predicting degraded disks described herein is effective in part because it looks at just the family of disks in the disk group (i.e. array), and for the vast majority of cases they are receiving very similar workloads, and thus their relative performance can be determined. 
     In one embodiment, predictor  152  is further configured to generate the population standard deviation of the usage observations (σ usage ) by first determining the population variance of the usage observations (σ 2   usage ). The population variance of the usage observations is determined by determining a difference of the population mean of the usage observations and each usage observation, adding up the square of each difference, and then dividing the sum by the number of usage observations in the population. In this example, predictor  152  can determine the population variance of the usage observations by applying the following equation: 
     
       
         
           
             
               
                 
                   
                     σ 
                     usage 
                     2 
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             n 
                           
                           ⁢ 
                           
                             
                               ( 
                               
                                 
                                   μ 
                                   usage 
                                 
                                 - 
                                 
                                   Usage 
                                   diski 
                                 
                               
                               ) 
                             
                             2 
                           
                         
                         ) 
                       
                       n 
                     
                     . 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     5 
                     ) 
                   
                 
               
             
           
         
       
     
     Predictor  152  then determines the population standard deviation of the usage observations by taking the square root of the population variance of the usage observations. In this example, predictor  152  can determine the population standard deviation of usage observations by applying the following equation:
 
σ usage =square root(σ 2   usage )  Equation (6).
 
     According to one embodiment, in order to determine whether one or more disks of RAID storage system  104  has degraded in performance, predictor  152  generates a Z-Score for each of the disks. Predictor  152  generates a Z-Score of a disk by determining a difference between its usage observation and the population mean of usage observations, and dividing the difference by the population standard deviation of the usage observations. For example, predictor  152  can determine Z-Score diski  by applying the following equation: 
     
       
         
           
             
               
                 
                   
                     Z 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     
                       Score 
                       diski 
                     
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             Usage 
                             diski 
                           
                           - 
                           
                             μ 
                             usage 
                           
                         
                         ) 
                       
                       
                         σ 
                         usage 
                       
                     
                     . 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     7 
                     ) 
                   
                 
               
             
           
         
       
     
     In one embodiment, predictor  152  determines that a disk has degraded in performance if it has a high Z-Score. Here, a high Z-Score refers to a Z-Score that is greater than a predetermined Z-Score threshold (e.g., 3 or more standard deviations). In this example, predictor  152  can predict whether Disk i  has degraded in performance by applying the following equations:
 
Disk i  degraded= Z -Score diski &gt;predetermined  Z -Score threshold  Equation (8).
 
     As described above, a high Z-Score indicates that the disk has degraded in performance. For example, if the population standard deviation is 5%, and the population mean is 50%, then a disk with a Z-Score of 3 has 15% more usage (i.e., 65% usage), for the same work load. A RAID group/array is only as fast as its slowest disk. By applying mechanisms of the present invention, a degraded disk can be identified and replaced with another disk in order to prevent the entire RAID storage system from slowing down or failing. 
     According to one embodiment, predictor  152  is configured to minimize false positives (i.e., to minimize the probability of falsely identifying a degraded disk) by ensuring that the workload is well balanced between the disks of the RAID group during the sample period. In one embodiment, if the workload is not well balanced, predictor  152  discards the set of observations without performing any prediction. In one embodiment, predictor  152  determines whether the workload is well balanced between the disks by generating the population mean of the read-byte-counts of the observations (μ read-byte-count ), by applying the following equation: 
     
       
         
           
             
               
                 
                   
                     μ 
                     
                       read 
                       ⁢ 
                       
                         - 
                       
                       ⁢ 
                       byte 
                       ⁢ 
                       
                         - 
                       
                       ⁢ 
                       count 
                     
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             n 
                           
                           ⁢ 
                           
                             read 
                             ⁢ 
                             
                               - 
                             
                             ⁢ 
                             byte 
                             ⁢ 
                             
                               - 
                             
                             ⁢ 
                             
                               count 
                               diski 
                             
                           
                         
                         ) 
                       
                       n 
                     
                     . 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     9 
                     ) 
                   
                 
               
             
           
         
       
     
     In one embodiment, predictor  152  is further configured to generate the population standard deviation of the read-byte-counts of the observations (σ read-byte-count ) by first determining the population variance of the read-byte-counts (σ read-byte-count   2 ). The population variance of the read-byte-counts is determined by determining a difference of the population mean of the read-byte-counts and each read-byte-count observation, adding up the square of each difference, and then dividing the sum by the number of read-byte-counts in the population. In this example, predictor  152  can determine the population variance of the read-byte-counts by applying the following equation: 
     
       
         
           
             
               
                 
                   
                     σ 
                     
                       read 
                       ⁢ 
                       
                         - 
                       
                       ⁢ 
                       byte 
                       ⁢ 
                       
                         - 
                       
                       ⁢ 
                       count 
                     
                     2 
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             n 
                           
                           ⁢ 
                           
                             
                               ( 
                               
                                 
                                   μ 
                                   
                                     read 
                                     ⁢ 
                                     
                                       - 
                                     
                                     ⁢ 
                                     byte 
                                     ⁢ 
                                     
                                       - 
                                     
                                     ⁢ 
                                     count 
                                   
                                 
                                 - 
                                 
                                   read 
                                   ⁢ 
                                   
                                     - 
                                   
                                   ⁢ 
                                   byte 
                                   ⁢ 
                                   
                                     - 
                                   
                                   ⁢ 
                                   
                                     count 
                                     diski 
                                   
                                 
                               
                               ) 
                             
                             2 
                           
                         
                         ) 
                       
                       n 
                     
                     . 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     10 
                     ) 
                   
                 
               
             
           
         
       
     
     Predictor  152  then determines the population standard deviation of the read-byte-counts (σ read-byte-count ) by taking the square root of the population variance of the read-byte-counts. In this example, predictor  152  can determine population standard deviation of the read-byte-counts by applying the following equation:
 
σ read-byte-count =square root(σ read-byte-count   2 )  Equation (11).
 
     Predictor  152  then generates the population mean of the write-byte-counts (μ write-byte-count ), by applying the following equation: 
     
       
         
           
             
               
                 
                   
                     μ 
                     
                       write 
                       ⁢ 
                       
                         - 
                       
                       ⁢ 
                       byte 
                       ⁢ 
                       
                         - 
                       
                       ⁢ 
                       count 
                     
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             n 
                           
                           ⁢ 
                           
                             write 
                             ⁢ 
                             
                               - 
                             
                             ⁢ 
                             byte 
                             ⁢ 
                             
                               - 
                             
                             ⁢ 
                             
                               count 
                               diski 
                             
                           
                         
                         ) 
                       
                       n 
                     
                     . 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     12 
                     ) 
                   
                 
               
             
           
         
       
     
     In one embodiment, predictor  152  is further configured to generate the population standard deviation of the write-byte-counts of the observations (σ write-byte-count ) by first determining the population variance of the write-byte-counts of the observations (α write-byte-count   2 ). The population variance of the write-byte-counts is determined by determining a difference of the population mean of the write-byte-counts and each write-byte-count, adding up the square of each difference, and then dividing the sum by the number of write-byte-counts in the population. In this example, predictor  152  can determine the population variance of the write-byte-counts by applying the following equation: 
     
       
         
           
             
               
                 
                   
                     σ 
                     
                       write 
                       ⁢ 
                       
                         - 
                       
                       ⁢ 
                       byte 
                       ⁢ 
                       
                         - 
                       
                       ⁢ 
                       count 
                     
                     2 
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             n 
                           
                           ⁢ 
                           
                             
                               ( 
                               
                                 
                                   μ 
                                   
                                     write 
                                     ⁢ 
                                     
                                       - 
                                     
                                     ⁢ 
                                     byte 
                                     ⁢ 
                                     
                                       - 
                                     
                                     ⁢ 
                                     count 
                                   
                                 
                                 - 
                                 
                                   write 
                                   ⁢ 
                                   
                                     - 
                                   
                                   ⁢ 
                                   byte 
                                   ⁢ 
                                   
                                     - 
                                   
                                   ⁢ 
                                   
                                     count 
                                     diski 
                                   
                                 
                               
                               ) 
                             
                             2 
                           
                         
                         ) 
                       
                       n 
                     
                     . 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     13 
                     ) 
                   
                 
               
             
           
         
       
     
     Predictor  152  then determines the population standard deviation of the write-byte-counts of the observations (σ write-byte-count ) by taking the square root of the population variance of the write-byte-counts. In this example, predictor  152  can determine population standard deviation of the write-byte-counts by applying the following equation:
 
σ write-byte-count =square root(σ write-byte-count   2 )  Equation (14).
 
     Next, predictor  152  adds the population standard deviation of the read-byte-counts and the population standard deviation of the write-byte-counts, by applying the following equation:
 
Sum=σ read-byte-count +σ write-byte-count   Equation (15).
 
     In one embodiment, predictor  152  determines that the workload was balanced well among the disks of the RAID group if the sum is within a predetermined percentage (e.g., 10%) of the population standard deviation of the usage observations. In this example, predictor  152  can determine that the workload was balanced by applying the following equation:
 
Workload was balanced=sum&lt;(σ usage /predetermined percentage threshold)  Equation (16).
 
     By way of example, assume that the predetermined percentage threshold is 10%, if the population standard deviation of the usage observations is 2%, and the sum of the standard deviation of the read-byte-counts and write-byte-counts is 0.3%, then the workload was not balanced because the sum exceeds the 10% threshold. As described above, if the workload was not balanced when the observations were taken, predictor  152  simply discards the observations without performing any prediction. 
     In one embodiment, predictor  152  is configured to minimize false positives by determining that the disk with a high Z-Score has a usage observation that is greater than a predetermined usage threshold. In such an embodiment, in addition to determining that Disk, has a high Z-Score, predictor  152  can determine whether Disk, has degraded in performance by applying the following equations in order to minimize false positives:
 
Disk i degraded=Usage diski &gt;predetermined usage threshold  Equation (17).
 
     According to one embodiment, predictor  152  is configured to minimize false positives by determining that the disk with a high Z-Score has a high Z-Score for at least a first predetermined amount of time (e.g., 3 days) out of a second consecutive predetermined amount of time (e.g., 5 consecutive days). The unit of time described above (i.e., days) are for illustrative purposes. One having ordinary skill in the art would recognize that other units can be used. For example, predictor  152  can be configured such that a disk must have a high Z-Score for 3 out of 5 consecutive samples taken. 
     The mechanisms for minimizing false positives described above assume that a set of high Z-scores are determined, and one or more high Z-scores are then removed from the set if the criteria are not satisfied (e.g., the usage observation is not greater than the predetermined usage threshold). One having ordinary skill in the art would recognize that the set of high Z-scores can be determined after it has been determined that the criteria are satisfied. For example, a disk with a usage observation that is not greater than the predetermined usage threshold can be removed as a candidate without determining its Z-score. Further, one having ordinary skill in the art would recognize that the criteria for minimizing false positives described above can be used in any combination thereof. 
       FIG. 4  is a flow diagram illustrating method  400  for determining performance degradation of one or more disks at a RAID storage system. For example, method  400  can be performed by predictor  152 , which can be implemented in software, firmware, hardware, or any combination thereof. 
     Referring now to  FIG. 4 . At block  405 , a predictor determines a population mean of usage observations associated with a plurality of disks of a RAID storage system. For example, predictor  152  applies Equation (4). At block  410 , the predictor determines a population standard deviation of usage observations associated with the plurality of disks of the RAID storage system based on the determined population mean. For example, predictor  152  applies Equation (6). At block  415 , the predictor, for each disk of the plurality of disks of the RAID storage system, determines a Z-Score based on its usage observation, the determined population mean, and the determined population standard deviation. For example, predictor  152  applies Equation (7). 
     At block  420 , the predictor identifies a set of disks with a high Z-Score (e.g., Z-Score that is greater than a predetermined Z-Score threshold). For example, predictor  152  applies Equation (8). At block  425 , the predictor optionally determines that a sum of a read and write standard deviation associated with the plurality of disks of the RAID storage system is within a predetermined percentage of the determined population standard deviation of usage observations. For example, predictor  152  applies Equation (16). 
     At block  430 , the predictor optionally removes, from the set, disks which do not have a usage observation that is greater than a predetermined usage threshold. For example, predictor  152  applies Equation (17) to determine whether Disk, should be removed from the set of candidates. At block  435 , the predictor removes, from the set, disks which do not have a high Z-Score for at least a first predetermined amount of time (e.g., 3 days) out of a second consecutive predetermined amount of time (e.g., 5 consecutive days). At block  440 , the predictor determines that the set includes disks which have degraded in performance. 
     Although the processes or methods are described above in terms of some sequential operations, it should be appreciated that some of the operations described may be performed in a different order. Moreover, some operations may be performed in parallel rather than sequentially. Further, some operations may not be performed in some embodiments. For example, blocks  425 ,  430 , and  435  are optional, and can be performed in different orders than as described above. 
       FIG. 5  is a diagram illustrating an example of a graphical user interface (GUI) for displaying disks and their respective performance statistics. For example, the GUI may be generated prediction reporter  126  of management system  150 , or a prediction reporter of RAID storage system  104  (not shown). In the illustrated GUI, the reporter has predicted that disk 2.1 has degraded in performance because it has a Z-score of 3.6. 
       FIG. 6  is a diagram illustrating the effectiveness of the present mechanisms for predicting disk performance degradation.  FIG. 6  illustrates that most of the disks that had a high Z-score 30 days ago still have a high Z-score today (and on average, even higher). 
     Some portions of the preceding detailed descriptions have been presented in terms of algorithms and symbolic representations of operations on data bits within a computer memory. These algorithmic descriptions and representations are the ways used by those skilled in the data processing arts to most effectively convey the substance of their work to others skilled in the art. An algorithm is here, and generally, conceived to be a self-consistent sequence of operations leading to a desired result. The operations are those requiring physical manipulations of physical quantities. 
     It should be borne in mind, however, that all of these and similar terms are to be associated with the appropriate physical quantities and are merely convenient labels applied to these quantities. Unless specifically stated otherwise as apparent from the above discussion, it is appreciated that throughout the description, discussions utilizing terms such as those set forth in the claims below, refer to the action and processes of a computer system, or similar electronic computing device, that manipulates and transforms data represented as physical (electronic) quantities within the computer system&#39;s registers and memories into other data similarly represented as physical quantities within the computer system memories or registers or other such information storage, transmission or display devices. 
     Embodiments of the invention also relate to an apparatus for performing the operations herein. Such a computer program is stored in a non-transitory computer readable medium. A machine-readable medium includes any mechanism for storing information in a form readable by a machine (e.g., a computer). For example, a machine-readable (e.g., computer-readable) medium includes a machine (e.g., a computer) readable storage medium (e.g., read only memory (“ROM”), random access memory (“RAM”), magnetic disk storage media, optical storage media, flash memory devices). 
     The processes or methods depicted in the preceding figures may be performed by processing logic that comprises hardware (e.g. circuitry, dedicated logic, etc.), software (e.g., embodied on a non-transitory computer readable medium), or a combination of both. Although the processes or methods are described above in terms of some sequential operations, it should be appreciated that some of the operations described may be performed in a different order. Moreover, some operations may be performed in parallel rather than sequentially. 
     Embodiments of the present invention are not described with reference to any particular programming language. It will be appreciated that a variety of programming languages may be used to implement the teachings of embodiments of the invention as described herein. 
     In the foregoing specification, embodiments of the invention have been described with reference to specific exemplary embodiments thereof. It will be evident that various modifications may be made thereto without departing from the broader spirit and scope of the invention as set forth in the following claims. The specification and drawings are, accordingly, to be regarded in an illustrative sense rather than a restrictive sense.