Abstract:
A method for data distribution, including distributing logical addresses among an initial set of devices so as provide balanced access, and transferring the data to the devices in accordance with the logical addresses. If a device is added to the initial set, forming an extended set, the logical addresses are redistributed among the extended set so as to cause some logical addresses to be transferred from the devices in the initial set to the additional device. There is substantially no transfer of the logical addresses among the initial set. If a surplus device is removed from the initial set, forming a depleted set, the logical addresses of the surplus device are redistributed among the depleted set. There is substantially no transfer of the logical addresses among the depleted set. In both cases the balanced access is maintained.

Description:
CROSS-REFERENCE TO RELATED APPLICATION  
       [0001]     This application is divisional of U.S. patent application Ser. No. 10/620,080 filed Jul. 15, 2003, the content of which is incorporated herein by reference. 
     
    
     FIELD OF THE INVENTION  
       [0002]     The present invention relates generally to data storage, and specifically to data storage in distributed data storage entities.  
       BACKGROUND OF THE INVENTION  
       [0003]     A distributed data storage system typically comprises cache memories that are coupled to a number of disks wherein the data is permanently stored. The disks may be in the same general location, or be in completely different locations. Similarly, the caches may be localized or distributed. The storage system is normally used by one or more hosts external to the system.  
         [0004]     Using more than one cache and more than one disk leads to a number of very practical advantages, such as protection against complete system failure if one of the caches or one of the disks malfunctions. Redundancy may be incorporated into a multiple cache or multiple disk system, so that failure of a cache or a disk in the distributed storage system is not apparent to one of the external hosts, and has little effect on the functioning of the system.  
         [0005]     While distribution of the storage elements has undoubted advantages, the fact of the distribution typically leads to increased overhead compared to a local system having a single cache and a single disk. Inter alia, the increased overhead is required to manage the increased number of system components, to equalize or attempt to equalize usage of the components, to maintain redundancy among the components, to operate a backup system in the case of a failure of one of the components, and to manage addition of components to, or removal of components from, the system. A reduction in the required overhead for a distributed storage system is desirable.  
         [0006]     An article titled “Consistent Hashing and Random Trees: Distributed Caching Protocols for Relieving Hot Spots on the World Wide Web,” by Karger et al., in the  Proceedings of the  29 th ACM Symposium on Theory of Computing , pages 654-663, (May 1997), whose disclosure is incorporated herein by reference, describes caching protocols for relieving “hot spots” in distributed networks. The article describes a hashing technique of consistent hashing, and the use of a consistent hashing function. Such a function allocates objects to devices so as to spread the objects evenly over the devices, so that there is a minimal redistribution of objects if there is a change in the devices, and so that the allocation is consistent, i.e., is reproducible. The article applies a consistent hashing function to read-only cache systems, i.e., systems where a client may only read data from the cache system, not write data to the system, in order to distribute input/output requests to the systems. A read-only cache system is used in much of the World Wide Web, where a typical user is only able to read from sites on the Web having such a system, not write to such sites.  
         [0007]     An article titled “Differentiated Object Placement and Location for Self-Organizing Storage Clusters,” by Tang et al., in  Technical Report  2002-32 of the University of California, Santa Barbara (November, 2002), whose disclosure is incorporated herein by reference, describes a protocol for managing a storage system where components are added or removed from the system. The protocol uses a consistent hashing scheme for placement of small objects in the system. Large objects are placed in the system according to a usage-based policy.  
         [0008]     An article titled “Compact, Adaptive Placement Schemes for Non-Uniform Capacities,” by Brinkmann et al., in the August, 2002 , Proceedings of the  14 th    ACM Symposium on Parallel Algorithms and Architecures  ( SPAA ), whose disclosure is incorporated herein by reference, describes two strategies for distributing objects among a heterogeneous set of servers. Both strategies are based on hashing systems.  
         [0009]     U.S. Pat. No. 5,875,481 to Ashton, et al., whose disclosure is incorporated herein by reference, describes a method for dynamic reconfiguration of data storage devices. The method assigns a selected number of the data storage devices as input devices and a selected number of the data storage devices as output devices in a predetermined input/output ratio, so as to improve data transfer efficiency of the storage devices.  
         [0010]     U.S. Pat. No. 6,317,815 to Mayer, et al., whose disclosure is incorporated herein by reference, describes a method and apparatus for reformatting a main storage device of a computer system. The main storage device is reformatted by making use of a secondary storage device on which is stored a copy of the data stored on the main device.  
         [0011]     U.S. Pat. No. 6,434,666 to Takahashi, et al., whose disclosure is incorporated herein by reference, describes a memory control apparatus. The apparatus is interposed between a central processing unit (CPU) and a memory device that stores data. The apparatus has a plurality of cache memories to temporarily store data which is transferred between the CPU and the memory device, and a cache memory control unit which selects the cache memory used to store the data being transferred.  
         [0012]     U.S. Pat. No. 6,453,404 to Bereznyi, et al., whose disclosure is incorporated herein by reference, describes a cache system that allocates memory for storage of data items by defining a series of small blocks that are uniform in size. The cache system, rather than an operating system, assigns one or more blocks for storage of a data item.  
       SUMMARY OF THE INVENTION  
       [0013]     It is an object of some aspects of the present invention to provide a system for distributed data allocation.  
         [0014]     In preferred embodiments of the present invention, a data distribution system comprises a plurality of data storage devices wherein data blocks may be stored. The data blocks are stored at logical addresses that are assigned to the data storage devices according to a procedure which allocates the addresses among the devices in a manner that reduces the overhead incurred when a device is added to or removed from the system, and so as to provide a balanced access to the devices. The procedure typically distributes the addresses evenly among the devices, regardless of the number of devices in the system. If a storage device is added to or removed from the system, the procedure reallocates the logical addresses between the new numbers of devices so that the balanced access is maintained. If a device has been added, the procedure only transfers addresses to the added storage device. If a device has been removed, the procedure only transfers addresses from the removed storage device. In both cases, the only transfers of data that occur are of data blocks stored at the transferred addresses. The procedure thus minimizes data transfer and associated management overhead when the number of storage devices is changed, or when the device configuration is changed, while maintaining the balanced access.  
         [0015]     In some preferred embodiments of the present invention, the procedure comprises a consistent hashing function. The function is used to allocate logical addresses for data block storage to the storage devices at initialization of the storage system. The same function is used to consistently reallocate the logical addresses and data blocks stored therein when the number of devices in the system changes. Alternatively, the procedure comprises allocating the logical addresses between the devices according to a randomizing process at initialization. The randomizing process generates a table giving a correspondence between specific logical addresses and the devices. The same randomizing process is used to reallocate the logical addresses and their stored data blocks on a change of storage devices.  
         [0016]     In some preferred embodiments of the present invention, the procedure comprises allocating two copies of a logical address to two separate storage devices, the two devices being used to store copies of a data block, so that the data block is protected against device failure. The procedure spreads the data block copies uniformly across all the storage devices. On failure of any one of the devices, copies of data blocks of the failed device are still spread uniformly across the remaining devices, and are immediately available to the system. Consequently, device failure has a minimal effect on the performance of the distribution system.  
         [0017]     There is therefore provided, according to a preferred embodiment of the present invention, a method for data distribution, including:  
         [0018]     distributing logical addresses among an initial set of storage devices so as provide a balanced access to the devices;  
         [0019]     transferring the data to the storage devices in accordance with the logical addresses;  
         [0020]     adding an additional storage device to the initial set, thus forming an extended set of the storage devices consisting of the initial set and the additional storage device; and  
         [0021]     redistributing the logical addresses among the storage devices in the extended set so as to cause a portion of the logical addresses to be transferred from the storage devices in the initial set to the additional storage device, while maintaining the balanced access and without requiring a substantial transfer of the logical addresses among the storage devices in the initial set.  
         [0022]     Preferably, redistributing the logical addresses consists of no transfer of the logical addresses between the storage devices in the initial set.  
         [0023]     Preferably, distributing the logical addresses includes applying a consistent hashing function to the initial set of storage devices so as to determine respective initial locations of the logical addresses among the initial set, and redistributing the logical addresses consists of applying the consistent hashing function to the extended set of storage devices so as to determine respective subsequent locations of the logical addresses among the extended set.  
         [0024]     Alternatively, distributing the logical addresses includes applying a randomizing function to the initial set of storage devices so as to determine respective initial locations of the logical addresses among the initial set, and redistributing the logical addresses consists of applying the randomizing function to the extended set of storage devices so as to determine respective subsequent locations of the logical addresses among the extended set.  
         [0025]     At least one of the storage devices preferably includes a fast access time memory; alternatively or additionally, at least one of the storage devices preferably includes a slow access time mass storage device.  
         [0026]     Preferably, the storage devices have substantially equal capacities, and distributing the logical addresses includes distributing the logical addresses substantially evenly among the initial set, and redistributing the logical addresses consists of redistributing the logical addresses substantially evenly among the extended set.  
         [0027]     Alternatively, a first storage device of the storage devices has a first capacity different from a second capacity of a second storage device of the storage devices, and distributing the logical addresses includes distributing the logical addresses substantially according to a ratio of the first capacity to the second capacity, and redistributing the logical addresses includes redistributing the logical addresses substantially according to the ratio.  
         [0028]     Preferably, distributing the logical addresses includes allocating a specific logical address to a first storage device and to a second storage device, the first and second storage devices being different storage devices, and storing the data consists of storing a first copy of the data on the first storage device and a second copy of the data on the second storage device.  
         [0029]     The method preferably includes writing the data from a host external to the storage devices, and reading the data to the external host from the storage devices.  
         [0030]     There is further provided, according to a preferred embodiment of the present invention, an alternative method for distributing data, including:  
         [0031]     distributing logical addresses among an initial set of storage devices so as provide a balanced access to the devices;  
         [0032]     transferring the data to the storage devices in accordance with the logical addresses;  
         [0033]     removing a surplus device from the initial set, thus forming a depleted set of the storage devices comprising the initial storage devices less the surplus storage device; and  
         [0034]     redistributing the logical addresses among the storage devices in the depleted set so as to cause logical addresses of the surplus device to be transferred to the depleted set, while maintaining the balanced access and without requiring a substantial transfer of logical addresses among the storage devices in the depleted set.  
         [0035]     Preferably, redistributing the logical addresses consists of no transfer of the logical addresses to the storage devices in the depleted set apart from the logical addresses of the surplus device.  
         [0036]     Distributing the logical addresses preferably consists of applying a consistent hashing function to the initial set of storage devices so as to determine respective initial locations of the logical addresses among the initial set, and redistributing the logical addresses preferably includes applying the consistent hashing function to the depleted set of storage devices so as to determine respective subsequent locations of the logical addresses among the depleted set.  
         [0037]     Alternatively, distributing the logical addresses consists of applying a randomizing function to the initial set of storage devices so as to determine respective initial locations of the logical addresses among the initial set, and redistributing the logical addresses includes applying the randomizing function to the depleted set of storage devices so as to determine respective subsequent locations of the logical addresses among the depleted set.  
         [0038]     The storage devices preferably have substantially equal capacities, and distributing the logical addresses consists of distributing the logical addresses substantially evenly among the initial set, and redistributing the logical addresses includes redistributing the logical addresses substantially evenly among the depleted set.  
         [0039]     There is further provided, according to a preferred embodiment of the present invention, a method for distributing data among a set of storage devices, including:  
         [0040]     applying a consistent hashing function to the set so as to allocate logical addresses to respective primary storage devices of the set and so as to provide a balanced access to the devices;  
         [0041]     forming subsets of the storage devices by subtracting the respective primary storage devices from the set;  
         [0042]     applying the consistent hashing function to the subsets so as to allocate the logical addresses to respective secondary storage devices of the subsets while maintaining the balanced access to the devices; and  
         [0043]     storing the data on the respective primary storage devices and a copy of the data on the respective secondary storage devices in accordance with the logical addresses.  
         [0044]     There is further provided, according to a preferred embodiment of the present invention, a method for distributing data among a set of storage devices, including:  
         [0045]     applying a randomizing function to the set so as to allocate logical addresses to respective primary storage devices of the set and so as to provide a balanced access to the devices;  
         [0046]     forming subsets of the storage devices by subtracting the respective primary storage devices from the set;  
         [0047]     applying the randomizing function to the subsets so as to allocate the logical addresses to respective secondary storage devices of the subsets while maintaining the balanced access to the devices; and  
         [0048]     storing the data on the respective primary storage devices and a copy of the data on the respective secondary storage devices in accordance with the logical addresses.  
         [0049]     There is further provided, according to a preferred embodiment of the present invention, a data distribution system, including:  
         [0050]     an initial set of storage devices among which are distributed logical addresses so as provide a balanced access to the devices, and wherein data is stored in accordance with the logical addresses; and  
         [0051]     an additional storage device to the initial set, thus forming an extended set of the storage devices comprising the initial set and the additional storage device, the logical addresses being redistributed among the storage devices in the extended set so as to cause a portion of the logical addresses to be transferred from the storage devices in the initial set to the additional storage device, while maintaining the balanced access and without requiring a substantial transfer of the logical addresses among the storage devices in the initial set.  
         [0052]     There is further provided, according to a preferred embodiment of the present invention, a data distribution system, including:  
         [0053]     an initial set of storage devices among which are distributed logical addresses so as provide a balanced access to the devices, and wherein data is stored in accordance with the logical addresses; and  
         [0054]     a depleted set of storage devices, formed by subtracting a surplus storage device from the initial set, the logical addresses being redistributed among the storage devices in the depleted set so as to cause logical addresses of the surplus device to be transferred to the depleted set, while maintaining the balanced access and without requiring a substantial transfer of the logical addresses among the storage devices in the depleted set.  
         [0055]     Preferably, redistributing the logical addresses comprises no transfer of the logical addresses to the storage devices in the depleted set apart from the logical addresses of the surplus device.  
         [0056]     The distributed logical addresses are preferably determined by applying a consistent hashing function to the initial set of storage devices so as to determine respective initial locations of the logical addresses among the initial set, and redistributing the logical addresses preferably includes applying the consistent hashing function to the depleted set of storage devices so as to determine respective subsequent locations of the logical addresses among the depleted set.  
         [0057]     Alternatively, the distributed logical addresses are determined by applying a randomizing function to the initial set of storage devices so as to determine respective initial locations of the logical addresses among the initial set, and redistributing the logical addresses preferably includes applying the randomizing function to the depleted set of storage devices so as to determine respective subsequent locations of the logical addresses among the depleted set.  
         [0058]     The storage devices preferably have substantially equal capacities, and the distributed logical addresses are distributed substantially evenly among the initial set, and redistributing the logical addresses includes redistributing the logical addresses substantially evenly among the depleted set.  
         [0059]     Alternatively or additionally, a first storage device included in the storage devices has a first capacity different from a second capacity of a second storage device included in the storage devices, and the distributed logical addresses are distributed substantially according to a ratio of the first capacity to the second capacity, and redistributing the logical addresses includes redistributing the logical addresses substantially according to the ratio.  
         [0060]     Preferably, the distributed logical addresses include a specific logical address allocated to a first storage device and a second storage device, the first and second storage devices being different storage devices, and storing the data includes storing a first copy of the data on the first storage device and a second copy of the data on the second storage device.  
         [0061]     The system preferably includes a memory having a table wherein is stored a correspondence between a plurality of logical addresses and a specific storage device in the initial set, wherein the plurality of logical addresses are related to each other by a mathematical relation.  
         [0062]     There is further provided, according to a preferred embodiment of the present invention, a data distribution system, including:  
         [0063]     a set of data storage devices to which is applied a consistent hashing function so as to allocate logical addresses to respective primary storage devices of the set and so as to provide a balanced access to the devices; and  
         [0064]     subsets of the storage devices formed by subtracting the respective primary storage devices from the set, the consistent hashing function being applied to the subsets so as to allocate the logical addresses to respective secondary storage devices of the subsets while maintaining the balanced access to the devices, data being stored on the respective primary storage devices and a copy of the data being stored on the respective secondary storage devices in accordance with the logical addresses.  
         [0065]     There is further provided, according to a preferred embodiment of the present invention, a data distribution system, including:  
         [0066]     a set of data storage devices to which is applied a randomizing function so as to allocate logical addresses to respective primary storage devices of the set and so as to provide a balanced access to the devices; and  
         [0067]     subsets of the storage devices formed by subtracting the respective primary storage devices from the set, the randomizing function being applied to the subsets so as to allocate the logical addresses to respective secondary storage devices of the subsets while maintaining the balanced access to the devices, data being stored on the respective primary storage devices and a copy of the data being stored on the respective secondary storage devices in accordance with the logical addresses.  
         [0068]     The present invention will be more fully understood from the following detailed description of the preferred embodiments thereof, taken together with the drawings, a brief description of which is given below.  
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0069]      FIG. 1  illustrates distribution of data addresses among data storage devices, according to a preferred embodiment of the present invention;  
         [0070]      FIG. 2  is a flowchart describing a procedure for allocating addresses to the devices of  FIG. 1 , according to a preferred embodiment of the present invention;  
         [0071]      FIG. 3  is a flowchart describing an alternative procedure for allocating addresses to the devices of  FIG. 1 , according to a preferred embodiment of the present invention;  
         [0072]      FIG. 4  is a schematic diagram illustrating reallocation of addresses when a storage device is removed from the devices of  FIG. 1 , according to a preferred embodiment of the present invention;  
         [0073]      FIG. 5  is a schematic diagram illustrating reallocation of addresses when a storage device is added to the devices of  FIG. 1 , according to a preferred embodiment of the present invention;  
         [0074]      FIG. 6  is a flowchart describing a procedure that is a modification of the procedure of  FIG. 2 , according to a preferred embodiment of the present invention;  
         [0075]      FIG. 7  is a schematic diagram which illustrates a fully mirrored distribution of data for the devices of  FIG. 1 , according to a preferred embodiment of the present invention; and  
         [0076]      FIG. 8  is a flowchart describing a procedure for performing the distribution of  FIG. 7 , according to a preferred embodiments of the present invention.  
     
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS  
       [0077]     Reference is now made to  FIG. 1 , which illustrates distribution of data addresses among data storage devices, according to a preferred embodiment of the present invention. A storage system  12  comprises a plurality of separate storage devices  14 ,  16 ,  18 ,  20 , and  22 , also respectively referred to herein as storage devices B 1 , B 2 , B 3 , B 4 , and B 5 , and collectively as devices B n . It will be understood that system  12  may comprise substantially any number of physically separate devices, and that the five devices B n  used herein are by way of example. Devices B n  comprise any components wherein data  34 , also herein termed data D, may be stored, processed, and/or serviced. Examples of devices B n  comprise random access memory (RAM) which has a fast access time and which are typically used as caches, disks which typically have a slow access time, or any combination of such components. A host  24  communicates with system  12  in order to read data from, or write data to, the system. A central processing unit (CPU)  26 , using a memory  28 , manages system  12 , and allocates data D to devices B n . The allocation of data D by CPU  26  to devices B n  is described in more detail below.  
         [0078]     Data D is processed in devices B n  at logical block addresses (LBAs) of the devices by being written to the devices from host  24  and/or read from the devices by host  24 . At initialization of system  12  CPU  26  distributes the LBAs of devices B n  among the devices using one of the pre-defined procedures described below. CPU  26  may then store data D at the LBAs.  
         [0079]     In the description of the procedures hereinbelow, devices B n  are assumed to have substantially equal capacities, where the capacity of a specific device is a function of the device type. For example, for devices that comprise mass data storage devices having slow access times, such as disks, the capacity is typically defined in terms of quantity of data the device may store. For devices that comprise fast access time memories, such as are used in caches, the capacity is typically defined in terms of throughput of the device. Those skilled in the art will be able to adapt the procedures when devices B n  have different capacities, in which case ratios of the capacities are typically used to determine the allocations. The procedures allocate the logical stripes to devices B n  so that balanced access to the devices is maintained, where balanced access assumes that taken over approximately 10,000×N transactions with devices B n , the fraction of capacities of devices B n  used are equal to within approximately 1%, where N is the number of devices B n , the values being based on a Bernoulli distribution.  
         [0080]      FIG. 2  is a flowchart describing a procedure  50  for allocating LBAs to devices B n , according to a preferred embodiment of the present invention. The LBAs are assumed to be grouped into k logical stripes/tracks, hereinbelow termed stripes  36  ( FIG. 1 ), which are numbered 1, . . . , k, where k is a whole number. Each logical stripe comprises one or more consecutive LBAs, and all the stripes have the same length. Procedure  50  uses a randomizing function to allocate a stripe s to devices B n  in system  12 . The allocations determined by procedure  50  are stored in a table  32  of memory  28 .  
         [0081]     In an initial step  52 , CPU  26  determines an initial value of s, the total number T d  of active devices B n  in system  12 , and assigns each device B n  a unique integral identity between 1 and T d . In a second step  54 , the CPU generates a random integer R between 1 and T d , and allocates stripe s to the device B n  corresponding to R. In a third step  56 , the allocation determined in step  54  is stored in table  32 . Procedure  50  continues, in a step  58 , by incrementing the value of s, until all stripes of devices B n  have been allocated, i.e., until s&gt;k, at which point procedure  50  terminates.  
         [0082]     Table I below is an example of an allocation table generated by procedure  50 , for system  12 , wherein T d =5. The identifying integers for each device B n , as determined by CPU  26  in step  52 , are assumed to be 1 for B 1 , 2 for B 2 , . . . , 5 for B 5 .  
                       TABLE I                           Random           Stripe s   Number R   Device B s                       1   3   B 3           2   5   B 5         . . .   . . .   . . .       6058   2   B 2         6059   2   B 2         6060   4   B 4         6061   5   B 5         6062   3   B 3         6063   5   B 5         6064   1   B 1         6065   3   B 3         6066   2   B 2         6067   3   B 3         6068   1   B 1         6069   2   B 2         6070   4   B 4         6071   5   B 5         6072   4   B 4         6073   1   B 1         6074   5   B 5         6075   3   B 3         6076   1   B 1         6077   2   B 2         6078   4   B 4         . . .   . . .   . . .                  
 
         [0083]      FIG. 3  is a flowchart showing steps of a procedure  70  using a consistent hashing function to allocate stripes to devices B n , according to an alternative preferred embodiment of the present invention. In an initial step  72 , CPU  26  determines a maximum number N of devices B n  for system  12 , and a number of points k for each device. The CPU then determines an integer M, such that M&gt;&gt;N·k.  
         [0084]     In a second step  74 , CPU  26  determines N sets J n  of k random values S ab , each set corresponding to a possible device B n , as given by equations (1): 
 
J 1 ={S 11 ,S 12 , . . . ,S 1k } for device B 1 ; 
 
J 2 ={S 21 ,S 22 , . . . ,S 2k } for device B 2 ; 
 
J N ={S N1 ,S N2 , . . . ,S Nk } for device B N .  (1) 
 
         [0085]     Each random value S ab  is chosen from {0, 1, 2, . . . , M-1}, and the value of each S ab  may not repeat, i.e., each value may only appear once in all the sets. The sets of random values are stored in memory  28 .  
         [0086]     In a third step  76 , for each stripe s CPU  26  determines a value of s mod(M) and then a value of F(s mod(M)), where F is a permutation function that reassigns the value of s mod(M) so that in a final step  78  consecutive stripes will generally be mapped to different devices B n .  
         [0087]     In final step  78 , the CPU finds, typically using an iterative search process, the random value chosen in step  74  that is closest to F(s mod(M)). CPU  26  then assigns the device B n  of the random value to stripe s, according to equations (1).  
         [0088]     It will be appreciated that procedure  70  illustrates one type of consistent hashing function, and that other such functions may be used by system  12  to allocate LBAs to devices operating in the system. All such consistent hashing functions are assumed to be comprised within the scope of the present invention.  
         [0089]     Procedure  70  may be incorporated into memory  28  of system  12  ( FIG. 1 ), and the procedure operated by CPU  26  when allocation of stripes s are required, such as when data is to be read from or written to system  12 . Alternatively, a table  30  of the results of applying procedure  70 , generally similar to the first and last columns of Table I, may be stored in memory  28 , and accessed by CPU  26  as required.  
         [0090]      FIG. 4  is a schematic diagram illustrating reallocation of stripes when a storage device is removed from storage system  12 , according to a preferred embodiment of the present invention. By way of example, device B 3  is assumed to be no longer active in system  12  at a time t=1, after initialization time t=0, and the stripes initially allocated to the device, and any data stored therein, are reallocated to the depleted set of devices B 1 , B 2 , B 4 , B 5  of the system. Device B 3  may be no longer active for a number of reasons known in the art, such as device failure, or the device becoming surplus to the system, and such a device is herein termed a surplus device. The reallocation is performed using procedure  50  or procedure  70 , preferably according to the procedure that was used at time t=0. As is illustrated in  FIG. 4 , and as is described below, stripes from device B 3  are substantially evenly redistributed among devices B 1 , B 2 , B 4 , B 5 .  
         [0091]     If procedure  50  ( FIG. 2 ) is applied at t=1, the procedure is applied to the stripes of device B 3 , so as to randomly assign the stripes to the remaining active devices of system  12 . In this case, at step  52  the total number of active devices T d =4, and identifying integers for each active device B n  are assumed to be 1 for B 1 , 2 for B 2 , 4 for B 4 , 3 for B 5 . CPU  26  generates a new table, corresponding to the first and last columns of Table II below for the stripes that were allocated to B 3  at t=0, and the stripes are reassigned according to the new table. Table II illustrates reallocation of stripes for device B 3  (from the allocation shown in Table I).  
                                   TABLE II                                           Random                   Device B s     Number R   Device B s             Stripe s   t = 0   t = 1   t = 1                             1   B 3     1   B 1               2   B 5         B 5             . . .   . . .   . . .   . . .           6058   B 2         B 2             6059   B 2         B 2             6060   B 4         B 4             6061   B 5         B 5             6062   B 3     3   B 5             6063   B 5         B 5             6064   B 1         B 1             6065   B 3     2   B 2             6066   B 2         B 2             6067   B 3     3   B 5             6068   B 1         B 1             6069   B 2         B 2             6070   B 4         B 4             6071   B 5         B 5             6072   B 4         B 4             6073   B 1         B 1             6074   B 5         B 5             6075   B 3     4   B 4             6076   B 1         B 1             6077   B 2         B 2             6078   B 4         B 4             . . .   . . .   . . .   . . .                      
 
         [0092]     It will be appreciated that procedure  50  only generates transfer of stripes from the device that is no longer active in system  12 , and that the procedure reallocates the stripes, and any data stored therein, substantially evenly over the remaining active devices of the system. No reallocation of stripes occurs in system  12  other than stripes that were initially allocated to the device that is no longer active. Similarly, no transfer of data occurs other than data that was initially in the device that is no longer active. Also, any such transfer of data may be performed by CPU  26  transferring the data directly from the inactive device to the reallocated device, with no intermediate device needing to be used.  
         [0093]     Similarly, by consideration of procedure  70  ( FIG. 3 ), it will be appreciated that procedure  70  only generates transfer of stripes, and reallocation of data stored therein, from the device that is no longer active in system  12 , i.e., device B 3 . Procedure  70  reallocates the stripes (and thus their data) from B 3  substantially evenly over the remaining devices B 1 , B 2 , B 4 , B 5  of the system, no reallocation of stripes or data occurs in system  12  other than stripes/data that were initially in B 3 , and such data transfer as may be necessary may be performed by direct transfer to the remaining active devices. It will also be understood that if B 3  is returned to system  12  at some future time, the allocation of stripes after procedure  70  is implemented is the same as the initial allocation generated by the procedure.  
         [0094]      FIG. 5  is a schematic diagram illustrating reallocation of stripes when a storage device is added to storage system  12 , according to a preferred embodiment of the present invention. By way of example, a device  23 , also herein termed device B 6 , is assumed to be active in system  12  at time t=2, after initialization time t=0, and some of the stripes initially allocated to an initial set of devices B 1 , B 2 , B 3 , B 4 , B 5 , and any data stored therein, are reallocated to device B 6 . The reallocation is performed using procedure  70  or a modification of procedure  50  (described in more detail below with reference to  FIG. 6 ), preferably according to the procedure that was used at time t=0. As is illustrated in  FIG. 5 , and as is described below, stripes from devices B 1 , B 2 , B 3 , B 4 , B 5  are substantially evenly removed from the devices and are transferred to device B 6 . B 1 , B 2 , B 3 , B 4 , B 5 , B 6  act as an extended set of the initial set.  
         [0095]      FIG. 6  is a flowchart describing a procedure  90  that is a modification of procedure  50  ( FIG. 2 ), according to an alternative preferred embodiment of the present invention. Apart from the differences described below, procedure  90  is generally similar to procedure  50 , so that steps indicated by the same reference numerals in both procedures are generally identical in implementation. As in procedure  50 , procedure  90  uses a randomizing function to allocate stripes s to devices B n  in system  12 , when a device is added to the system. The allocations determined by procedure  90  are stored in table  32  of memory  28 .  
         [0096]     Assuming procedure  50  is applied at t=2, at step  52  the total number of active devices T d =6, and identifying integers for each active device B n  are assumed to be 1 for B 1 , 2 for B 2 , 3 for B 3 , 4 for B 4 , 5 for B 5 , 6 for B 6 . In a step  91  CPU  26  determines a random integer between 1 and 6.  
         [0097]     In a step  92 , the CPU determines if the random number corresponds to one of the devices present at time t=0. If it does correspond, then CPU  26  returns to the beginning of procedure  90  by incrementing stripe s, via step  58 , and no reallocation of stripe s is made. If it does not correspond, i.e., the random number is 6, corresponding to device B 6 , the stripe is reallocated to device B 6 . In step  56 , the reallocated location is stored in table  32 . Procedure  90  then continues to step  58 . Table III below illustrates the results of applying procedure  90  to the allocation of stripes given in Table II.  
                                   TABLE III                                           Random                   Device B s     Number R   Device B s             Stripe s   t = 0   t = 2   t = 2                             1   B 3     6   B 6               2   B 5     4   B 5             . . .   . . .   . . .   . . .           6058   B 2     5   B 2             6059   B 2     3   B 2             6060   B 4     5   B 4             6061   B 5     6   B 6             6062   B 3     3   B 5             6063   B 5     1   B 5             6064   B 1     3   B 1             6065   B 3     1   B 2             6066   B 2     6   B 6             6067   B 3     4   B 5             6068   B 1     5   B 1             6069   B 2     2   B 2             6070   B 4     1   B 4             6071   B 5     5   B 5             6072   B 4     2   B 4             6073   B 1     4   B 1             6074   B 5     5   B 5             6075   B 3     1   B 4             6076   B 1     3   B 1             6077   B 2     6   B 6             6078   B 4     1   B 4             . . .   . . .   . . .   . . .                      
 
         [0098]     It will be appreciated that procedure  90  only generates transfer of stripes, and thus reallocation of data, to device B 6 . The procedure reallocates the stripes to B 6  by transferring stripes, substantially evenly, from devices B 1 , B 2 , B 3 , B 4 , B 5  of the system, and no transfer of stripes, or data stored therein, occurs in system  12  other than stripes/data transferred to B 6 . Any such data transfer may be made directly to device B 6 , without use of an intermediate device B n .  
         [0099]     It will also be appreciated that procedure  70  may be applied when device B 6  is added to system  12 . Consideration of procedure  70  shows that similar results to those of procedure  90  apply, i.e., that there is only reallocation of stripes, and data stored therein, to device B 6 . As for procedure  90 , procedure  70  generates substantially even reallocation of stripes/data from the other devices of the system.  
         [0100]      FIG. 7  is a schematic diagram which illustrates a fully mirrored distribution of data D in storage system  12  ( FIG. 1 ), and  FIG. 8  is a flowchart illustrating a procedure  100  for performing the distribution, according to preferred embodiments of the present invention. Procedure  100  allocates each specific stripe to a primary device B n1 , and a copy of the specific stripe to a secondary device B n2 , n 1 ≠n 2 , so that each stripe is mirrored. To implement the mirrored distribution, in a first step  102  of procedure  100 , CPU  26  determines primary device B n1  for locating a stripe using procedure  50  or procedure  70 . In a second step  104 , CPU  26  determines secondary device B n2  for the stripe using procedure  50  or procedure  70 , assuming that device B n1  is not available. In a third step  106 , CPU  26  allocates copies of the stripe to devices B n1  and B n2 , and writes the device identities to a table  34  in memory  28 , for future reference. CPU  26  implements procedure  100  for all stripes  36  in devices B n .  
         [0101]     Table IV below illustrates devices B n1  and B n2  determined for stripes 6058-6078 of Table I, where steps  102  and  104  use procedure  50 .  
                       TABLE IV                       Stripe   Device B n1     Device B n2                     6058   B 2     B 4         6059   B 2     B 5         6060   B 4     B 2         6061   B 5     B 4         6062   B 3     B 1         6063   B 5     B 4         6064   B 1     B 3         6065   B 3     B 4         6066   B 2     B 5         6067   B 3     B 1         6068   B 1     B 3         6069   B 2     B 5         6070   B 4     B 1         6071   B 5     B 3         6072   B 4     B 2         6073   B 1     B 3         6074   B 5     B 1         6075   B 3     B 5         6076   B 1     B 3         6077   B 2     B 4         6078   B 4     B 1                    
 
         [0102]     If any specific device B n  becomes unavailable, so that only one copy of the stripes on the device is available in system  12 , CPU  26  may implement a procedure similar to procedure  100  to generate a new second copy of the stripes that were on the unavailable device. For example, if after allocating stripes 6058-6078 according to Table IV, device B 3  becomes unavailable, copies of stripes 6062, 6065, 6067, and 6075, need to be allocated to new devices in system  12  to maintain full mirroring. Procedure  100  may be modified to find the new device of each stripe by assuming that the remaining device, as well as device B 3 , is unavailable. Thus, for stripe 6062, CPU  26  assumes that devices B 1  and B 3  are unavailable, and determines that instead of device B 3  the stripe should be written to device B 4 . Table V below shows the devices that the modified procedure  100  determines for stripes 6058, 6060, 6062, 6065, 6072, and 6078, when B 3  becomes unavailable.  
                       TABLE V                       Stripe s   Device B n1     Device B n2                     6062   B 1     B 2         6065   B 4     B 5         6067   B 1     B 4         6075   B 5     B 2                    
 
         [0103]     It will be appreciated that procedure  100  spreads locations for stripes  36  substantially evenly across all devices B n , while ensuring that each pair of copies of any particular stripe are on different devices, as is illustrated in  FIG. 7 . Furthermore, the even distribution of locations is maintained even when one of devices B n , becomes unavailable. Either copy, or both copies, of any particular stripe may be used when host  24  communicates with system  12 . It will also be appreciated that in the event of one of devices B n  becoming unavailable, procedure  100  regenerates secondary locations for copies of stripes  36  that are evenly distributed over devices B n .  
         [0104]     Referring back to  FIG. 1 , it will be understood that the sizes of tables  30 ,  32 , or  34  are a function of the number of stripes in system  12 , as well as the number of storage devices in the system. Some preferred embodiments of the present invention reduce the sizes of tables  30 ,  32 , or  34  by duplicating some of the entries of the tables, by relating different stripes mathematically. For example, if system  12  comprises 2,000,000 stripes, the same distribution may apply to every 500,000 stripes, as illustrated in Table VI below. Table VI is derived from Table I.  
                               TABLE VI                       Stripe s   Stripe s   Stripe s   Stripe s   Device B s                       1   500,001   1,000,001   1,500,001   B 3           2   500,002   1,000,002   1,500,002   B 5         . . .   . . .   . . .   . . .   . . .       6059   506,059   1,006,059   1,506,059   B 2         6060   506,060   1,006,060   1,506,060   B 4         . . .   . . .   . . .   . . .   . . .                  
 
         [0105]     It will be appreciated that procedures such as those described above may be applied substantially independently to different storage devices, or types of devices, of a storage system. For example, a storage system may comprise a distributed fast access cache coupled to a distributed slow access mass storage. Such a storage system is described in more detail in the U.S. Application titled “Distributed Independent Cache Memory,” filed on even date, and assigned to the assignee of the present invention. The fast access cache may be assigned addresses according to procedure  50  or modifications of procedure  50 , while the slow access mass storage may be assigned addresses according to procedure  70  or modifications of procedure  70 .  
         [0106]     It will thus be appreciated that the preferred embodiments described above are cited by way of example, and that the present invention is not limited to what has been particularly shown and described hereinabove. Rather, the scope of the present invention includes both combinations and subcombinations of the various features described hereinabove, as well as variations and modifications thereof which would occur to persons skilled in the art upon reading the foregoing description and which are not disclosed in the prior art.