Patent Publication Number: US-10310752-B1

Title: Extent selection with mapped raid

Description:
BACKGROUND 
     Technical Field 
     This application generally relates to data storage. 
     Description of Related Art 
     Systems may include different resources used by one or more host processors. Resources and host processors in the system may be interconnected by one or more communication connections, such as network connections. These resources may include, for example, data storage devices such as those included in the data storage systems manufactured by EMC Corporation. These data storage systems may be coupled to one or more host processors and provide storage services to each host processor. Multiple data storage systems from one or more different vendors may be connected and may provide common data storage for one or more host processors in a computer system. 
     A host may perform a variety of data processing tasks and operations using the data storage system. For example, a host may perform basic system I/O (input/output) operations in connection with data requests, such as data read and write operations. 
     Host systems may store and retrieve data using a data storage system containing a plurality of host interface units, disk drives (or more generally storage devices), and disk interface units. Such data storage systems are provided, for example, by EMC Corporation of Hopkinton, Mass. The host systems access the storage devices through a plurality of channels provided therewith. Host systems provide data and access control information through the channels to a storage device of the data storage system and data of the storage device is also provided from the data storage system to the host systems also through the channels. The host systems do not address the disk drives of the data storage system directly, but rather, access what appears to the host systems as a plurality of files, objects, logical units, logical devices or logical volumes. These may or may not correspond to the actual physical drives. Allowing multiple host systems to access the single data storage system allows the host systems to share data stored therein. 
     SUMMARY OF THE INVENTION 
     In accordance with one aspect of the techniques herein is a method of allocating one or more mapped RAID extents comprising: determining a pool of N physical storage devices; selecting M physical storage portions, wherein each of the M physical storage portions is selected from a different one of the N physical storage devices of the pool; and allocating a first mapped RAID extent as the selected M physical storage portions, wherein the first mapped RAID extent denotes a stripe of a RAID group. A first portion of the M physical storage portions of the stripe may store user data for the stripe and remaining ones of the M physical storage portions of the stripe, not included in the first portion, may store parity information for the stripe. N may denote a first integer value that is equal to or greater than a second integer value denoted by M. The step of selecting may be performed in accordance with a neighborhood matrix denoting a distribution of neighboring physical storage portions across the N physical storage devices of the pool. The neighborhood matrix may include N rows and N columns and each entry (I, J) of the neighborhood matrix located at row I, column J may denote a count of how many times physical storage device I of the pool has neighbored physical storage device J of the pool. The two physical storage devices I and J of the pool may be neighbors with each other each time a first physical storage portion from physical storage device I and a second physical storage portion from physical storage device J are included in a same mapped RAID extent that is allocated. The M physical storage portions on M different ones of the N physical storage devices may be a first combination, and wherein said selecting may select the first combination from a plurality of combinations using the neighborhood matrix. Selecting may use the neighborhood matrix to evaluate whether the first combination results in a first variance that is a minimum variance with respect to other variances resulting from selection of any other combination of the plurality of combinations. The first variance and the other variances may be with respect to values stored in the entries of the neighborhood matrix. The plurality of combinations may be a selected subset of all possible combinations of selecting M physical storage devices from the N physical storage devices. The selected subset may cover all N physical storage devices of the pool. A first physical storage device of the N physical storage devices may fail and a group X of remaining ones of the N physical storage devices of the pool that may not have failed. The method may include: determining a first set of one or more physical storage portions of the first mapped RAID extent stored on the first physical storage device that failed; and relocating each physical storage portion of the first set to a physical storage device of the group X, wherein said relocating is performed in accordance with criteria, said criteria including each physical storage portion of the first mapped RAID extent is stored on a different physical storage device of the group X and said criteria including evenly distributing the first set of one or more physical storage portions among the physical storage devices of group X. The one or more mapped RAID extents may include a plurality of mapped RAID extents that are stripes of the RAID group and the plurality of mapped RAID extents may include the first mapped RAID extent. Each stripe of the RAID group may include M physical storage portions comprising X, one or more physical storage portions storing user data for the stripe and Y, one or more physical storage portions storing parity information for the stripe. The RAID group may have a RAID-5 configuration and Y may denote a single physical storage portion storing parity information for the stripe. The RAID group may have a RAID-6 configuration and Y may denote two physical storage portions storing parity information for the stripe. 
     In accordance with another aspect of techniques herein is a system comprising: at least one processor; and a memory comprising code stored thereon that, when executed, performs a method of allocating one or more mapped RAID extents comprising: determining a pool of N physical storage devices; selecting M physical storage portions, wherein each of the M physical storage portions is selected from a different one of the N physical storage devices of the pool; and allocating a first mapped RAID extent as the selected M physical storage portions, wherein the first mapped RAID extent denotes a stripe of a RAID group. 
     In accordance with another aspect of techniques herein is a computer readable medium comprising code stored thereon that, when executed, performs a method of allocating one or more mapped RAID extents comprising: determining a pool of N physical storage devices; selecting M physical storage portions, wherein each of the M physical storage portions is selected from a different one of the N physical storage devices of the pool; and allocating a first mapped RAID extent as the selected M physical storage portions, wherein the first mapped RAID extent denotes a stripe of a RAID group. The selecting may be performed in accordance with a neighborhood matrix denoting a distribution of neighboring physical storage portions across the N physical storage devices of the pool. The neighborhood matrix may include N rows and N columns and each entry (I, J) of the neighborhood matrix located at row I, column J may denote a count of how many times physical storage device I of the pool has neighbored physical storage device J of the pool. The two physical storage devices I and J of the pool are may be neighbors with each other each time a first physical storage portion from physical storage device I and a second physical storage portion from physical storage device J are included in a same mapped RAID extent that is allocated. The M physical storage portions on M different ones of the N physical storage devices may be a first combination, and selecting may select the first combination from a plurality of combinations using the neighborhood matrix. Selecting may use the neighborhood matrix to evaluate whether the first combination results in a first variance that is a minimum variance with respect to other variances resulting from selection of any other combination of the plurality of combinations. The first variance and the other variances may be with respect to values stored in the entries of the neighborhood matrix. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Features and advantages of the present invention will become more apparent from the following detailed description of exemplary embodiments thereof taken in conjunction with the accompanying drawings in which: 
         FIG. 1  is an example of components that may be included in a system in accordance with techniques described herein; 
         FIGS. 2 and 3  are examples illustrating a traditional RAID group configuration; 
         FIGS. 4 and 4B  are examples illustrating mapped RAID extents of a RAID group in an embodiment in accordance with techniques herein; 
         FIG. 5  is an example illustrating a neighborhood matrix that may be used in an embodiment in accordance with techniques herein; 
         FIG. 6  is an example illustrating a good relatively even distribution of mapped RAID extents; 
         FIG. 7  is an example illustrating a relatively uneven distribution of mapped RAID extents across storage devices of a pool; 
         FIG. 8  is a flowchart of processing steps that may be performed in an embodiment in accordance with techniques herein; 
         FIG. 9  is an example of pseudocode outlining steps that may be performed in an embodiment in accordance with techniques herein; and 
         FIGS. 10A-10C  illustrate different distributions of values of the neighborhood matrix for different RAID group configurations in an embodiment in accordance with techniques herein. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENT(S) 
     Referring to  FIG. 1 , shown is an example of an embodiment of a system that may be used in connection with performing the techniques described herein. The system  10  includes a data storage system  12  connected to host systems  14   a - 14   n  through communication medium  18 . In this embodiment of the computer system  10 , and the n hosts  14   a - 14   n  may access the data storage system  12 , for example, in performing input/output (I/O) operations or data requests. The communication medium  18  may be any one or more of a variety of networks or other type of communication connections as known to those skilled in the art. The communication medium  18  may be a network connection, bus, and/or other type of data link, such as a hardwire or other connections known in the art. For example, the communication medium  18  may be the Internet, an intranet, network (including a Storage Area Network (SAN)) or other wireless or other hardwired connection(s) by which the host systems  14   a - 14   n  may access and communicate with the data storage system  12 , and may also communicate with other components included in the system  10 . 
     Each of the host systems  14   a - 14   n  and the data storage system  12  included in the system  10  may be connected to the communication medium  18  by any one of a variety of connections as may be provided and supported in accordance with the type of communication medium  18 . The processors included in the host computer systems  14   a - 14   n  may be any one of a variety of proprietary or commercially available single or multi-processor system, such as an Intel-based processor, or other type of commercially available processor able to support traffic in accordance with each particular embodiment and application. 
     It should be noted that the particular examples of the hardware and software that may be included in the data storage system  12  are described herein in more detail, and may vary with each particular embodiment. Each of the host computers  14   a - 14   n  and data storage system may all be located at the same physical site, or, alternatively, may also be located in different physical locations. Examples of the communication medium that may be used to provide the different types of connections between the host computer systems and the data storage system of the system  10  may use a variety of different communication protocols such as block-based protocols (e.g., SCSI, Fibre Channel, iSCSI), file system-based protocols (e.g., NFS), and the like. Some or all of the connections by which the hosts and data storage system may be connected to the communication medium may pass through other communication devices, such switching equipment that may exist such as a phone line, a repeater, a multiplexer or even a satellite. 
     Each of the host computer systems may perform different types of data operations in accordance with different types of tasks. In the embodiment of  FIG. 1 , any one of the host computers  14   a - 14   n  may issue a data request to the data storage system  12  to perform a data operation. For example, an application executing on one of the host computers  14   a - 14   n  may perform a read or write operation resulting in one or more data requests to the data storage system  12 . 
     It should be noted that although element  12  is illustrated as a single data storage system, such as a single data storage array, element  12  may also represent, for example, multiple data storage arrays alone, or in combination with, other data storage devices, systems, appliances, and/or components having suitable connectivity, such as in a SAN, in an embodiment using the techniques herein. It should also be noted that an embodiment may include data storage arrays or other components from one or more vendors. In subsequent examples illustrated the techniques herein, reference may be made to a single data storage array by a vendor, such as by EMC Corporation of Hopkinton, Mass. However, as will be appreciated by those skilled in the art, the techniques herein are applicable for use with other data storage arrays by other vendors and with other components than as described herein for purposes of example. 
     The data storage system  12  may be a data storage array including a plurality of data storage devices  16   a - 16   n . The data storage devices  16   a - 16   n  may include one or more types of physical data storage devices (PDs or physical devices) such as, for example, one or more rotating disk drives and/or one or more solid state drives (SSDs). An SSD is a data storage device that uses solid-state memory to store persistent data. An SSD using SRAM or DRAM, rather than flash memory, may also be referred to as a RAM drive. SSD may refer to solid state electronics devices as distinguished from electromechanical devices, such as hard drives, having moving parts. Flash devices or flash memory-based SSDs are one type of SSD that contains no moving mechanical parts. 
     The flash devices may be constructed using nonvolatile semiconductor NAND flash memory. The flash devices may include one or more SLC (single level cell) devices and/or MLC (multi level cell) devices. 
     The data storage array may also include different types of adapters or directors, such as an HA  21  (host adapter), RA  40  (remote adapter), and/or device interface  23 . Each of the adapters may be implemented using hardware including a processor with local memory with code stored thereon for execution in connection with performing different operations. The HAs may be used to manage communications and data operations between one or more host systems and the global memory (GM). In an embodiment, the HA may be a Fibre Channel Adapter (FA) or other adapter which facilitates host communication. The HA  21  may be characterized as a front end component of the data storage system which receives a request from the host. The data storage array may include one or more RAs that may be used, for example, to facilitate communications between data storage arrays. The data storage array may also include one or more device interfaces  23  for facilitating data transfers to/from the data storage devices  16   a - 16   n . The data storage interfaces  23  may include device interface modules, for example, one or more disk adapters (DAs) (e.g., disk controllers), adapters used to interface with the flash drives, and the like. The DAs may also be characterized as back end components of the data storage system which interface with the physical data storage devices. 
     One or more internal logical communication paths may exist between the device interfaces  23 , the RAs  40 , the HAs  21 , and the memory  26 . An embodiment, for example, may use one or more internal busses and/or communication modules. For example, the global memory portion  25   b  may be used to facilitate data transfers and other communications between the device interfaces, HAs and/or RAs in a data storage array. In one embodiment, the device interfaces  23  may perform data operations using a cache that may be included in the global memory  25   b , for example, when communicating with other device interfaces and other components of the data storage array. The other portion  25   a  is that portion of memory that may be used in connection with other designations that may vary in accordance with each embodiment. 
     The particular data storage system as described in this embodiment, or a particular device thereof, such as a disk or particular aspects of a flash device, should not be construed as a limitation. Other types of commercially available data storage systems, as well as processors and hardware controlling access to these particular devices, may also be included in an embodiment. 
     Host systems provide data and access control information through channels to the storage systems, and the storage systems may also provide data to the host systems also through the channels. The host systems do not address the drives or devices  16   a - 16   n  of the storage systems directly, but rather access to data may be provided to one or more host systems from what the host systems view as a plurality of logical devices, logical volumes (LVs) which may also referred to herein as logical units (e.g., LUNs). A logical unit (LUN) may be characterized as a disk array or data storage system reference to an amount of disk space that has been formatted and allocated for use to one or more hosts. A logical unit may have a logical unit number that is an I/O address for the logical unit. As used herein, a LUN or LUNs may refer to the different logical units of storage which may be referenced by such logical unit numbers. The LUNs may or may not correspond to the actual or physical disk drives or more generally physical storage devices. For example, one or more LUNs may reside on a single physical disk drive, data of a single LUN may reside on multiple different physical devices, and the like. Data in a single data storage system, such as a single data storage array, may be accessed by multiple hosts allowing the hosts to share the data residing therein. The HAs may be used in connection with communications between a data storage array and a host system. The RAs may be used in facilitating communications between two data storage arrays. The DAs may be one type of device interface used in connection with facilitating data transfers to/from the associated disk drive(s) and LUN (s) residing thereon. A flash device interface may be another type of device interface used in connection with facilitating data transfers to/from the associated flash devices and LUN(s) residing thereon. It should be noted that an embodiment may use the same or a different device interface for one or more different types of devices than as described herein. 
     In an embodiment in accordance with techniques herein, the data storage system as described may be characterized as having one or more logical mapping layers in which a logical device of the data storage system is exposed to the host whereby the logical device is mapped by such mapping layers of the data storage system to one or more physical devices. Additionally, the host may also have one or more additional mapping layers so that, for example, a host side logical device or volume is mapped to one or more data storage system logical devices as presented to the host. 
     The device interface, such as a DA, performs I/O operations on a physical device or drive  16   a - 16   n . In the following description, data residing on a LUN may be accessed by the device interface following a data request in connection with I/O operations that other directors originate. The DA which services the particular physical device may perform processing to either read data from, or write data to, the corresponding physical device location for an I/O operation. 
     Also shown in  FIG. 1  is a management system  22   a  that may be used to manage and monitor the system  12 . In one embodiment, the management system  22   a  may be a computer system which includes data storage system management software or application such as may execute in a web browser. A data storage system manager may, for example, view information about a current data storage configuration such as LUNs, storage pools, and the like, on a user interface (UI) in a display device of the management system  22   a . Alternatively, and more generally, the management software may execute on any suitable processor in any suitable system. For example, the data storage system management software may execute on a processor of the data storage system  12 . 
     Each of the different adapters, such as HA  21 , DA or disk interface, RA, and the like, may be implemented as a hardware component including, for example, one or more processors, one or more forms of memory, and the like. Code may be stored in one or more of the memories of the component for performing processing. 
     An embodiment of a data storage system may include components having different names from that described herein but which perform functions similar to components as described herein. Additionally, components within a single data storage system, and also between data storage systems, may communicate using any suitable technique that may differ from that as described herein for exemplary purposes. For example, element  12  of  FIG. 1  may be a data storage system, such as the VNXe® data storage system by EMC Corporation of Hopkinton, Mass., that includes multiple storage processors (SPs). Each of the SPs  27  may be a CPU including one or more “cores” or processors and each may have their own memory used for communication between the different front end and back end components rather than utilize a global memory accessible to all storage processors. In such embodiments, memory  26  may represent memory of each such storage processor. 
     As known in the art, a RAID (redundant array of independent disks) group is a group of physical storage devices or members providing different levels of protection and fault tolerance within the RAID group. A RAID group provides an associated level of protection based on a particular configuration of the physical drives comprising the RAID group. The particular level of protection provided by a RAID group may be one of standard and/or well known levels and configurations (e.g., RAID-0, RAID-1, RAID-5, RAID-6, and the like). In at least one embodiment, physical drives may be configured into RAID groups of one or more RAID levels. As known in the art, LUNs may have storage provisioned from, or built on top of, the RAID groups. 
     Described in following paragraphs are techniques that may be used to layout mapped RAID extents evenly (or approximately evenly) to all physical storage devices (PDs) of a pool. One benefit of using mapped RAID as described herein is better rebuild performance than using traditional RAID. As described in more detail below, in order to obtain improved rebuild performance with mapped RAID, techniques herein attempt to distribute mapped RAID extents as evenly as possible to the PDs. In this way, when one PD fails fails, all the other PDs may be involved in the rebuilding procedure. In accordance with techniques herein, processing may be performed to evenly layout RAID extents to the PDs independent of the number of PDs in the pool, independent of the number of RAID extents to be allocated, and independent of RAID extent width (e.g. number of PDs, M, in the RAID group). In at least one embodiment in accordance with techniques herein, a neighborhood matrix may be used to evaluate whether the mapped RAID extents are evenly distributed to PDs of the pool, or not. Furthermore, as described in more detail below, in at least one embodiment in accordance with techniques herein, a small subset of selection combinations may be used rather than all possible combinations to improve processing efficiency and reduce computing complexity. 
     As noted above, RAID may be characterized in one aspect as a data storage virtualization technology that combines multiple PDs into a single logical unit for the purposes of data redundancy, performance improvement, or both. Data is distributed across the drives in one of several ways, referred to as RAID levels, depending on the required level of redundancy and performance. 
     With reference now to  FIG. 2 , shown is an example illustrating traditional RAID 5 layout of a RAID group with  5  member PDs including 4 data PDs and 1 parity PD. As known in the art, RAID 5 provides block level striping with distributed parity. Parity information is distributed among the PDs. In the example  1200  of  FIG. 2 , each stripe includes 5 blocks, which includes 4 data blocks (denoted as D 0 , D 1 , D 2 , D 3  and D 4 ) and 1 parity block (denoted as P). Upon failure of a single PD, such as failure of PD 3   206  as illustrated with reference to the example  200  of  FIG. 3 , subsequent reads can be calculated from the distributed parity such that no data is lost. Additionally, a hot spare PD  202  may be selected to replace the failed PD 3   206  and all the data of the failed PD 3   206  may be rebuilt  204  and written to the new PD  202 . 
     With the new physical storage technologies (e.g. shingled media disk) emerging, the storage capacity of a single PD increases year by year and the rebuild time is increased accordingly. In other words, a customer may face an increased risk of double PD failure, which may result in lost data if RAID group rebuild time is not reduced. However, the rebuild time is subject to the write bandwidth of the hot spare PD replacing the failed PD. With the traditional RAID group such as in  FIGS. 2 and 3 , the write bandwidth of the hot spare PD may currently be a bottleneck and it may accordingly be difficult using such traditional RAID to reduce the rebuild time. As a result, mapped RAID technology described in following paragraphs may be used as described in following paragraphs. 
     Referring to  FIG. 4 , shown is an example illustrating use of mapped RAID techniques in an embodiment in accordance with techniques herein. The example  300  includes a pool of N PDs, where N is an integer having a minimum value depending on the particular RAID configuration and drive members. The N PDs may be referred to using indices 0 through N−1, inclusively. For example, consider a RAID 5 configuration such as described above in connection with  FIG. 2  having M=5 members including 4 data members and 1 parity member. The minimum number of PDs in the pools used for mapped RAID may be at least M, the number of RAID group members, which is 5 in this example. Thus, the number of PDs N is greater than or equal to M. It should be noted that the foregoing M may also denote the RAID extent width or number of disk extents in each mapped RAID extent as described in more detail elsewhere herein. Generally, mapped RAID is created on top of a pool of the N PDs. Each PD of the pool used for configuring mapped RAID may be viewed as a set of continuous non-overlapping fixed sized disk (PD) extents or portions. 
     Each mapped RAID extent (also referred to herein as simply RAID extent) may include M different disk extents (e.g., PD extents or portions) whereby each disk extent is selected from a different one of the N PDs. For example, a first RAID extent A may include 5 disk extents  302   a - e ; a second RAID extent B may include 5 disk extents  304   a - e ; a third RAID extent C may include 5 disk extents  306   a - e ; and a fourth RAID extent D may include 5 disk extents  308   a - e . In this example  300 , each disk or PD extent used for storing user data is denoted Dn, where n is an integer in the range of 0-3. Each disk or PD extent used for storing parity information is denote P. Disk or PD extents which are free (unallocated) or otherwise reserved may not include any P or Dn designation in  FIG. 4 . 
     Some of the disk extents may be reserved on each of the N PDs for use as hot spare disk extents rather than reserve an entire PD as a hot spare as in traditional RAID groups. Techniques herein may select the disk extents used in forming the mapped RAID extents with a goal of evenly distributing the RAID extents to all N PDs of the pool. When one of the N PDs of the pool fails, for each disk extent on the failed PD that is included in a mapped RAID extent, a replacement disk extent may be obtained by selecting another replacement disk extent from one of the other remaining active/live/healthy PDs of the pool. Such selection may be based on specified criteria. When selecting disk extents for inclusion in a mapped RAID extent for such replacement due to a failed PD, the selection criteria may include selecting the replacement disk extents so as to guarantee that each mapped RAID extent includes disk extents on 5 different PDs. Additionally, selecting replacement disk extents for dead disk extents of the failed PD may be performed in manner based on another selection criteria that distributes the dead disk extent replacements evenly among the remaining N−1 PDs of the pool. 
     For example, with reference to  FIG. 4B , assume PD 4  fails whereby disk extents  302   d  and  308   c  may be relocated to another one of the N PDs. In accordance with the criteria noted above, disk extent  302   d  may be relocated to disk extent X 1  on PD 3 , and disk extent  308   c  may be relocated to disk extent Y 1  on PD N−1. 
     As may be appreciated by those skilled in the art, with mapped RAID techniques such as illustrated in  FIGS. 4 and 4B , there no longer exists the limitation of the single spare PD write bandwidth, since techniques herein replace dead disk extents with extents on different PDs. Additionally, in order to maximize rebuild performance, as many PDs as possible should participate in the rebuilding procedure (as performed in connection with rebuilding or reconstructing dead disk extents using well known techniques known in the art that vary with the particular RAID level and configuration). To achieve an improved rebuild performance, techniques herein may include processing to evenly distribute (as evenly as possible) mapped RAID extents across all PDs of the pool when creating/forming mapped RAID extents. 
     In at least one embodiment in accordance with techniques herein, the disk extent selection processing (e.g., performed to select disk extents for a mapped RAID extent) may take into account the number N of PDs in the pool, the RAID extent width, and the RAID capacity in terms of the count or number of RAID extents that can be allocated from the pool (e.g., mapped RAID extent capacity of number of mapped RAID extents possibly formed from the pool of N PDs). Described in following paragraphs are techniques that may be performed to further adapt mapped RAID for use which makes mapped RAID more scalable and efficient. Such further techniques may be used no matter how many PDs are in the pool, no matter how many RAID extents are going to be allocated, and no matter what the RAID extent width is. 
     Before describing details of processing that may be performed in an embodiment in accordance with techniques herein, what will now be described is how to evaluate/determine whether the RAID extent distribution among the N PDs of the pool is even or not. In at least one embodiment, a neighborhood matrix may be used. 
     As illustrated in  FIG. 5 , a neighborhood matrix is an N*N square matrix, where N is the number of PDs in the pool as described above. Each entry or cell of the matrix may be identified using a pair of coordinates, i, j, where “i” denotes the row of the matrix and “j” denotes the column of the matrix. An entry or cell of the matrix located in row i, column j, may be referred to as NW(i, j), whereby the contents of the entry or cell may be a numeric quantity identifying how many times PD i of the pool has ever neighbored with PD j of the pool. Two disk or PD extents, such as from two different PDs, may be defined as neighbor extents if both such disk or PD extents are included in the same mapped RAID extent. Thus, NW(i,j) denotes the number of times a disk extent from PDi has been selected or included in the same mapped RAID extent as a disk extent from PDi (e.g., how many times PDi and PDj have been neighbors or included in the same mapped RAID extent). While allocating a mapped RAID extent, processing includes selecting disk extents from different PDs. We define PDs in this same mapped RAID extent as neighbors with each other one time. The neighborhood matrix is symmetric, since based on the foregoing definition of “neighbor”, NW(i, j) should be equal to NW(j, i). 
     To further illustrate and with reference back to  FIG. 4 , consider an example of processing performed when selecting 5 disk extents for a single mapped RAID extent Q being allocated from the pool Assume the 5 disk extents selected for forming mapped RAID extent Q have been selected from PD  0 , PD  1 , PD  2 , PD  3  and PD  4  (e.g., 1 disk extent selected from each of PDs  0 - 4 ). In this case, the neighborhood matrix may be updated as a result of the foregoing selection of 5 disk extents whereby the following entries of the matrix may each be incremented by one (1): 
     
       
         
           
               
               
               
               
               
             
               
                   
                   
               
             
            
               
                   
                 0,1 
                 0,2 
                 0,3 
                 0,4 
               
               
                   
                 1,0 
                 1,2 
                 1,3 
                 1,4 
               
               
                   
                 2,0 
                 2,1 
                 2,3 
                 2,4 
               
               
                   
                 3,0 
                 3,1 
                 3,2 
                 3,4 
               
               
                   
                 4,0 
                 4,1 
                 4,2 
                 4,2 
               
               
                   
                   
               
            
           
         
       
     
     If mapped RAID extents are distributed evenly among the N PDs of the pool, the values stored in cells or entries of the matrix should be the same, or approximately so (e.g., within some specified tolerance or amount of one another) and also excluding the diagonal. Therefore, techniques herein may select different disk extents when allocating to form a mapped RAID extent where such selection results in the values stored across entries in the matrix almost the same after completing RAID extent allocation. Generally, any suitable technique may be used which attempts to have a goal of such even distribution to minimize differences or variances between values of entries in the neighborhood matrix. Described in more detail below is one particular technique that may be used in at least one embodiment. Before describing the particular technique, what will now be described are examples illustrating good or desired distribution of values in the neighborhood matrix and also bad or undesired distribution of values in the neighborhood matrix. 
     Referring to  FIG. 6 , shown is an example  500  illustrating a good or desired distribution of values in the in the neighborhood matrix in an embodiment in accordance with techniques herein. Element  510  illustrates the matrix have values in entries which are relatively close to one another, such as approximately the same within some specified tolerance or difference. For example, in the matrix  510 , values of entries in the matrix range from 19-21, inclusively. Element  520  provides a visualization of the values in the matrix  510  whereby the  520  illustrates a relatively flat or even distribution. 
     Referring to  FIG. 7 , shown is an example  600  illustrating a bad or undesired distribution of values in the in the neighborhood matrix in an embodiment in accordance with techniques herein. Element  610  illustrates the matrix have values in entries which are not relatively close to one another, such as not approximately the same within some specified tolerance or difference. For example, in the matrix  610 , values of entries in the matrix have q wide and varying range with some values being zero which means that some PDs never neighbor each other. Therefore, in this case, if one PD fails, some PDs would not participate in the rebuilding procedure. Element  620  provides a visualization of the values in the matrix  610  whereby the  620  does not illustrate a relatively flat or even distribution (e.g., as may be contrasted with  520  of  FIG. 6 ). 
     What will now be described in more detail is one way in which an embodiment in accordance with techniques herein may perform selection of disk extents for use in formation of a mapped RAID extent. This may also be referred to as a RAID extent selection algorithm that may be performed in at least one embodiment in accordance with techniques herein. For convenience and consistent with other discussion herein, assume the number of PDs in the pool is N and the RAID extent width is M. So there should be C n   m  possible ways to combine or select disk extents in connection with forming a single mapped RAID extent. As an example and continuing with a RAID-5 configuration with a RAID extent width of 5, 4D+1P (e.g., 4 data members and 1 parity member) mapped onto a pool including 16 PDs (e.g., N=16) 16 disks, in this case, there are totally C 16   5 =4368 ways to allocate a mapped RAID extent from the 16 PDs of the pool (e.g., select 5 disk extents from 5 PDs from a pool of 16 PDs). 
     After allocating a mapped RAID extent, the neighborhood matrix may be updated accordingly as described herein. While allocating disk extents for the mapped RAID extent formation, we could try all the possible disk extent combinations, and select the one which would make the matrix more “flat”. In other words, processing may be performed to select the particular set or combination of disk extents which would make numbers in the matrix much closer to each other. For example, an embodiment may use a suitable metric, measurement or statistic, such as variance. For example, an embodiment may use the variance of all values in matrix entries as the indicator or measurement of “flatness” (e.g., indicator or measurement of even ness of the distribution of neighborhood matrix entries). 
     For each mapped RAID extent allocation, an embodiment may loop over all the possible choices or combination of disk extents, and select the “best” one, which will make the matrix more “flat” (e.g. select the 5 disk extents for the mapped RAID extent from the 5 PDs which results in the minimum or smallest variance with respect to the neighborhood matrix entries). In such an embodiment, eventually when all the mapped RAID extents are allocated, we expect the final matrix is also “flat”, or approximately so, which is close to global optimization solution. 
     However, when N, the number of PDs in the pool is large, the number of all possible choices or combinations may be unacceptably large whereby considering each such combination as described above becomes computationally unacceptable and/or impractical in implementation (e.g., does not scale as N increases). For example, consider the case where N is 100 and M is 5, whereby C 100   5 =75287520. For each mapped RAID extent allocation in this example, evaluating all the possible choices is extremely time consuming. Thus, as a variation in at least one embodiment in accordance with techniques herein, processing may be performed to randomly select a subset of all possible choices or combination for evaluation/consideration, and for each mapped RAID extent allocation, processing may be performed which only considers/evaluates the small subset (from which one combination is selected for the single mapped RAID extent allocation). For example, in the above case, when N is 100 and M is 5, an embodiment may randomly select and use 3000 distinct combinations as included in the small subset. In at least one embodiment when selecting a subset of all possible combinations evaluated or under consideration, a rule may be imposed whereby, for the subset of combinations, all PDs of the pool should be covered by the subset. For example, assume the subset is 3000 where 3000 possible combinations of 5 PDs are randomly selected from the possible total number of 75287520 combinations. In addition, the 3000 combinations of the subset selected for further evaluation and consideration may further be required to cover or include combinations which span, collectively, across all 100 PDs (e.g., cannot select 3000 combinations for the subset where one of the PDs does not appear in any one of the 3000 combinations; in other words each of the 100 PDs must be included in at least one of the 3000 combinations of the randomly selected subset). 
     In at least one embodiment, a mapped RAID select algorithm may be performed as described below. As described above, N denotes the number of PDs in the pool; M denotes the width of the mapped RAID extent (e.g. number of disk extents in each mapped RAID extent); and E may denote the number of mapped RAID extents to be formed or allocated from the pool. The following steps may be performed in an embodiment in accordance with techniques herein with reference to  FIG. 8 . 
     In a first step  701 , initialize each cell or entry of the N*N neighborhood matrix to 0. In a second step  702 , randomly generate a distinct subset of RAID extent layouts from all C n   m  possible combinations. The foregoing subset may be distinct in that each member of the subset denotes a different combination of PDs selected from the possible N PDs. Denote the number of combinations in the subset as R. For a current mapped RAID extent being allocated (for which M disk extents are being selected), processing may be performed in step  704 . In step  704 , processing may be performed to loop over the subset of distinct RAID extent layout combinations to find the optimal combination which will results in the lowest variance of matrix numbers (e.g., select one combination from the subset which has the smallest or minimum variance with respect to the neighborhood matrix entries. Consistent with other discussion herein, the diagonal entries of the matrix are excluded from the variance calculation). In step  705 , the current mapped RAID extent may be allocated according to the optimal combination found in step  704 . Step  705  may also include accordingly updating the neighborhood matrix. At step  706 , a determination may be made as to whether all E mapped RAID extents have been allocated. If step  706  evaluates to yes, processing stops. If step  706  evaluates to no, control proceeds/returns to step  704  to continue processing and allocate the next mapped RAID extent. 
     Variance and other suitable calculations and statistics are known in the art. Variance may be calculated, for example, by determining the mean or average value with respect to all entries, excluding the diagonal entries of the matrix. For each entry of the matrix, a difference between the value in the entry and the mean may be determined, and the difference may then be squared (e.g. power of two). The variance is the sum of the foregoing squared differences as determined for each matrix entry (excluding matrix diagonal entries). 
     It should be noted that in step  702  above, processing is performed to generate a subset of distinct combinations. Generally, any suitable technique, process or algorithm may be used to generate such a subset. From a computational and implementation perspective, the subset of combinations may be generated and then the subset may be saved or described for use in other processing steps. 
     In connection with generating and saving a subset of all combinations, processing includes selecting M number from N numbers where there are a total of C n   m  combinations possible. In at least one embodiment, step  702  processing may include sorting all possible combinations in ascending order (e.g., indexed and sorted by PD numbers for the combination). The index of each combination in the sorted list may range from 0 to C n   m −1. In such an embodiment, the task of randomly generating a subset of all combinations may be accomplished by randomly generating/selecting a subset of index number from the foregoing index range, 0 to C n   m −1. In other words, an embodiment may use R distinct index numbers of the range to represent the R different combinations selected and included in the subset. When we want to use one combination, the index number may be mapped to its corresponding combination (e.g., set of PDs of the combination). 
     An embodiment may generate R distinct random numbers using any suitable technique known in the art to denote the selection/generation of the R distinct combinations. In at least one embodiment, a random number from 1 to R, inclusively, may be selected. If the number has already been generated, then retry until a non-repeated number is generated. The foregoing may be repeated until R distinct random numbers are generated. An embodiment may use, for example, a random number generator to randomly generate or select R numbers from the possible total number or range of 0 to C n   m −1. 
     At least one embodiment may use the following method as denoted in  FIG. 9  to translate or map a number “k” to its corresponding k-th combination from list “1”. Referring to  FIG. 9 , shown is a pseudo-code description of steps that may be performed to get the k-th combination. In the example  800 , line 1 denotes the routine or function kthCombination which takes parameters or arguments k, l, and r. “k” denotes the number mapped to its corresponding kth combination that is returned by the function kth combination. “r” denotes R as described above; and “l” is the list of all possible C n   r  combinations. The routine or function kthCombination returns the kth combination of all the possible combinations when selecting r elements from list 1. In line 7 of the pseudocode of 800, nCr returns the value of C n   r . 
     Lines 2-3 of the example  800  indicate that if r=0, null is returned. Lines 4-5 of the example  800  indicate that if r is equal to the length of “1,” then “1” is returned. If the conditions at lines 2 and 4 evaluate to false, control flows through to line 6. At line 7, “i” is assigned the value of C n   r  for current values of “N” and R. At line 8, a determination is made as to whether k&lt;i. If so, line 9 is performed where the value returned is the sum of l[0:1] from the list “l” and the kth combination (k, l[1:], r−1). Otherwise, if line 8 evaluates to false, line 11 is performed. It should be noted that lines 9 and 11 implement recursive calls to the routine or function kthCombination. 
     In connection with techniques herein, following are some examples of different parameter values of M, N, R and E that may be used in an embodiment in accordance with techniques herein. In a first embodiment in accordance with techniques herein, the number of PDs in the pool, N, may be 16; the RAID extent width, M, may be 5 (e.g., for a RAID-5 group having 4 data members and 1 parity member); the extent count E may be 250 and the size of the subset of randomly selected distinct combinations, R, may be 300. The foregoing first embodiment may be characterized as a moderately sized configuration. (e.g., 250 mapped RAID extents are allocated).  FIG. 10A  illustrates the distribution of values of the neighborhood matrix entries obtained by the inventors in connection with an implementation of techniques herein in this first embodiment. As can be seen in the example  900 , the distribution is relatively flat. The example  900  and also examples  920  and  940  described below are illustrations of the resulting distribution of entries of the neighborhood matrix similar to that as described herein, for example with respect to element  520  of  FIG. 6 . 
     In a second embodiment in accordance with techniques herein, the number of PDs in the pool, N, may be 50; the RAID extent width, M, may be 8 (e.g., for a RAID-6 group having 6 data members and 2 parity members); the extent count E may be 2000 and the size of the subset of randomly selected distinct combinations, R, may be 3000. The foregoing second embodiment may be characterized as a large configuration (e.g., 2000 mapped RAID extents are allocated).  FIG. 10B  illustrates the distribution of values of the neighborhood matrix entries obtained by the inventors in connection with an implementation of techniques herein in this second embodiment. As can be seen in the example  9020 , the distribution is relatively flat. 
     In a third embodiment in accordance with techniques herein, the number of PDs in the pool, N, may be 16; the RAID extent width, M, may be 85 (e.g., for a RAID-5 group having 64 data members and 1 parity member); the extent count E may be 20 and the size of the subset of randomly selected distinct combinations, R, may be 1000. The foregoing third embodiment may be characterized as a small configuration (e.g., 20 mapped RAID extents are allocated).  FIG. 10C  illustrates the distribution of values of the neighborhood matrix entries obtained by the inventors in connection with an implementation of techniques herein in this third embodiment. As can be seen in the example  920 , the distribution may be characterized as relatively flat but not as flat as other distributions illustrated in  FIGS. 10A and 10B . 
     Described above are techniques that may be used to layout mapped RAID extents with a goal of distributing disk extents forming such mapped RAID extents evenly across all PDs of the pool. With such techniques described herein, when PD of the pool fails, all the other PDs are involved in the entire rebuilding procedure (e.g., used to rebuild or reconstruct the data of the failed PD). Therefore, the rebuilding performance is improved over performance typical or expected with existing traditional RAID groups. As described above, techniques herein may use a neighborhood matrix to evaluate whether the mapped RAID extents are evenly distributed across PDs of the pool. In at least one embodiment, a small subset of combinations may be selected for evaluation and consideration rather than the entire set of combinations in efforts to reduce the computing complexity and associated computation time and resources utilized. 
     The techniques herein may be performed by executing code which is stored on any one or more different forms of computer-readable media. Computer-readable media may include different forms of volatile (e.g., RAM) and non-volatile (e.g., ROM, flash memory, magnetic or optical disks, or tape) storage which may be removable or non-removable. 
     While the invention has been disclosed in connection with preferred embodiments shown and described in detail, their modifications and improvements thereon will become readily apparent to those skilled in the art. Accordingly, the spirit and scope of the present invention should be limited only by the following claims.