Abstract:
A system and method that utilize a scheduling algorithm to reorder queued I/O commands in rotating disk drives. The reordering is implemented by selecting commands based on a probabilistic approach that minimizes the expected next command access time. Thus, the scheduling algorithm allows data to be accessed in the shortest possible expected time, and maximizes the throughput of the drive. The scheduling algorithm improves the I/O average access time by estimating the expected access time (EAT) for the queued commands, and by reordering these commands so that the command with the least expected access time (LEAT) is executed first. The scheduling algorithm weights the possible access times of commands stored in the scheduling queue, and accounts for the probability of executing a command during a first possible revolution or cycle, as well as the probability of executing the command in the second possible revolution. Both of these probabilities are taken into consideration in reaching a final determination as to the queue order of the commands. This allows for taking calculated risks in scheduling commands so as to minimize long-term average latency.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application relates to co-pending patent application Ser. No. 09/481,233, titled “System and Method for Profiling Access to Disk Drive Commands Based on a Dual Servo Mode Model”, and to co-pending patent application Ser. No. 09/481,231, titled “System and Method for Grouping Disk Access Commands in a Queue According to Proximate Disk Positions”, which are filed by the same assignee as this application on even date herewith, and are incorporated herein by reference in their entirety. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to the field of data storage and particularly to a system and method for sorting I/O commands operations in rotating disk drives. More specifically, this invention relates to a computer program product for selecting the next command in an optimal way. Such selection is based on a probabilistic disk drive scheduling algorithm that reduces drive latency and improves its throughput. 
     BACKGROUND OF THE INVENTION 
     Computer systems or other accessories, collectively referred to as “computer systems”, generally include data storage devices, such as hard disk drives. A hard disk drive is an electromechanical or an optical-mechanical device that reads from and writes to a hard disk that includes one or more disk platens. The main components of a disk drive are a spindle on which the platens are mounted, a drive motor for spinning the platens, one or more read/write heads, a seek mechanism for positioning the heads over the platens, and a controller which synchronizes read/write commands and transfers information to and from other components of the computer system. 
     In operation, the computer system provides logical instructions to its disk drive, to read or write data into storage locations on the disk. Although the instructions typically include a logical address for the data, the data is not stored in logical format; rather, the data is stored in a physical address location. The controller typically translates the logical address into a physical address. Once the translation occurs, the controller directs the heads to the physical address location at which the desired data is stored or read. 
     The amount of time from the start of the movement of the heads arm until the start of the read or write phase of an I/O command is referred to as the “access time”. Access time is comprised of two components. The first component the seek and settling time, which is the time required to move a disk drive&#39;s read/write head to a specific track or cylinder on a disk and settling it on the target track. The second component is the rotational latency time, which corresponds to the additional time required for the disk to rotate so that the desired physical address location is located underneath the properly positioned head. 
     The available rotational time of a command is calculated based on the rotational position of the command and the current position of the head. If there is no chance that the command could be accessed at that time because of the radial distance, this rotational time is repeatedly incremented by one revolution time, until there is a positive probability of a successful access. 
     Each disk typically includes a plurality of concentric tracks, on one or both surfaces, from which information is read, or onto which information is written by a read/write element. In addition, each track is further divided into a plurality of sectors. A cylinder is formed by a plurality of tracks with the same radial coordinate on the stack of disks. In a disk drive, a disk rotates at a high speed while the read/write element “flies” over the surface of the rotating disk. The read/write element is positioned over specific areas or sectors of the disk in accordance with commands received from the computer system. The numerous commands of the computer system usually exceed the drive&#39;s ability to execute the commands immediately upon receipt, in which case a queue is formed. The set of commands available for execution by the disk drive is referred to as the “command queue”. 
     Traditionally, controllers have been developed to reorder the command queue according to a positional sequence. Examples include reducing the number of changes in the direction of the movement of the head, ordering according to the shortest calculated head movement regardless of direction, and more commonly ordering according to the shortest overall access time between successive commands. 
     Numerous methods of drive scheduling have been devised to minimize the average access time. The conventional rule used by scheduling algorithms has been to choose the next read/write command from its local queue by essentially executing the earliest executable command. There is, however, some uncertainty with regard to the actual time it would take from the end of the currently active command, that is the command being currently executed, until the onset of execution of the next command. In part, this uncertainty is due to the fact that the seek and settling times are not absolutely deterministic. In some cases, due to the variance of the seek and settling time, the head will not be ready to start executing even though the correct rotational position has been attained. Another problem is that even if there were no uncertainty, once the start and end positions are taken into account, still there would not be sufficient time to calculate the precise access time while the scheduling algorithm is scanning the queue of commands. 
     In the event the actual access time is underestimated, a complete revolution may be lost. A common solution has been to add a “safety” margin (sometimes called a “fudge” factor) to the seek and settling time and establish a safe estimate of the time at which execution can start for certain. By adding this safety margin, the scheduling algorithm sometimes bypasses or delays a command if this command is not certain to be executed during the first revolution. Such approach could significantly and adversely affect the throughput of the disk drive. 
     Another disk scheduling method is illustrated in U.S. Pat. No. 5,570,332 to Heath et al that describes a method to reduce rotational latency in a disk drive by dividing the disk into discrete angular regions. The command queue is then sorted according to commands addressing cylinders or tracks within the angular region having the shortest rotational latency. The sorting algorithm searches the queue for commands addressing physical addresses beginning with those in neighboring angular regions. With each repositioning of the read/write head, the rotational latency of the angular regions from the new head location is reevaluated. However, the time estimates are based on adding safety margins and hence are biased. 
     Yet another disk scheduling method is exemplified in U.S. Pat. No. 5,664,143 to Olbrich, that describes a method for the rotational position queue to be initially ordered. A first command is chosen and assigned the physical address of its last requested block. Each remaining command in the queue is assigned the physical address of its first requested block. The address differences between each remaining command and the first command are converted into a time difference. The time required for the head to be positioned, the seek time, is subtracted from each time difference. For subtractions resulting in times less than zero an additional amount of time corresponding to a full revolution of latency is added. The commands are then sorted by the smallest time difference, such that the command with the shortest time difference becoming the next command. After the execution of the first command, the command with the shortest time difference is removed from the queue and the next command becomes the first command. The ordering algorithm is then repeated to determine a new next command. Though this scheduling algorithm may have met its objectives, there is nonetheless room for further optimization of expected access seek time by using probabilistic criteria to evaluate commands in the disk scheduling queue. 
     Still another disk scheduling method is illustrated in U.S. Pat. No. 5,854,941 to Ballard et al., that describes a disk scheduling queue for sorting pending disk I/O commands according to an estimated access time. The estimated access time is calculated from first and second rotational times that are derived from a rotational time table based on logical address and head movement time. Once the command is executed, the rotational positioning algorithm is repeated and the queue is resorted. However, the estimate results in a deterministic value rather than a weighted average that takes into account the probabilities of the possible values. 
     It is therefore clear that the ability of the head to be placed at the desired track has heretofore been either assumed to be a deterministic factor, or the rotational latency is assumed to provide a sufficient time for certain success of executing the command at the estimated time. Thus, there is still an unsatisfied need for a scheduling algorithm that selects commands based on an unbiased probabilistic approach, for reducing the disk drive latency and improving its throughput. 
     SUMMARY OF THE INVENTION 
     In accordance with the present invention, a computer program product is provided as a scheduling algorithm for use in disk drives to place I/O commands in a queue. The scheduling strategy is implemented by selecting commands based on a probabilistic approach that minimizes the expected next command access time. Thus, the present scheduling algorithm allows data to be accessed in the shortest expected amount of time possible, maximizes the throughput of the drive and improves the overall performance of the computer system. 
     The scheduling algorithm of the present invention improves the disk I/O average access time by estimating the expected access time (EAT) for the queued commands, and by selecting commands so that the command with the least EAT (LEAT) is executed first. 
     Whereas certain conventional scheduling algorithms rely on rotational latency or appended additional time to compensate for the uncertainty inherent in the seek and settling times, as described earlier, the probabilistic approach of the present invention does not postpone the execution of commands due to this uncertainty, but rather relies upon, and incorporates such uncertainty as a useful criterion in the comparison of commands. An exemplary criterion used in a preferred embodiment of the present invention is the least expected access time. 
     The least expected access time is a concept which is introduced herein, and which is derived by having the disk scheduling algorithm sort pending disk I/O commands into a disk scheduling queue according to the expected time necessary to reach the target positions on the disk. The probabilistic algorithm weights the possible access times of commands sorted in the disk scheduling queue, and accounts for the probability of the drive executing a command during the first possible revolution as well as the probability of the drive executing the command in the second possible revolution. Both of these probabilities are taken into consideration in reaching a final determination as to the queue order of the commands. This would eliminate the rigid deterministic approach followed by conventional scheduling algorithms and allow for taking calculated risks in scheduling commands so as to minimize the long-term average latency. 
     As an illustration, the scheduling algorithm assigns an Expected Access Time EAT(i) to an ith command as follows: 
     
       
           EAT ( i )=(1− p ( i )) s ( i )+ p ( i )( s ( i )+ r )= s ( i )+ rp ( i ), 
       
     
     where p(i) is the probability that a revolution will be missed, r is the one revolution time, and s(i) is the minimum time it would take to achieve the correct rotational position with nonzero probability of completing the seek and settling. The probability p(i) reflects various types of uncertainties, both intrinsic and resulting from the lack of computational resources. For simplicity purposes, the possibility of missing more than one revolution was neglected, though those skilled in the art could account for this factor without departing from the scope of the present invention. 
     According to one embodiment, the scheduling algorithm will assign an EAT to each of the commands in the queue. As a result, each of the queued commands will be provided with a single number rather than two numbers as explained above in connection with the conventional deterministic approach. The scheduling algorithm will then reorder the queue commands according to a desired LEAT scheme, for example according to-ascending expected access times, so that the command with the LEAT will be executed next. 
     According to an alternative embodiment, the probability p(i) does not have to be computed for every single command in the queue. Rather, depending on the current best candidate, if a command certainly cannot be accessed faster than the current best candidate, then this command will not be assigned an EAT. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The various features of the present invention and the manner of attaining them will be described in greater detail with reference to the following description, claims, and drawings, wherein reference numerals are reused, where appropriate, to indicate a correspondence between the referenced items, and wherein: 
     FIG. 1 is a schematic illustration of a disk drive that implements a scheduling algorithm according to the present invention; 
     FIG. 2 is a schematic, top plan view of the disk drive of FIG. 1 viewed from a different angle; 
     FIG. 3 is comprised of FIGS. 3A and 3B, and represents a flow chart that illustrates the operation of a preferred embodiment of the scheduling algorithm; 
     FIG. 4 is a graph that illustrates “mintime” versus the maximum seek length for a disk, and which is stored in tabular form in a processor of the disk drive of FIG.  1 . 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     FIGS. 1 and 2 illustrate a disk drive  10  comprised of a head stack assembly  12  and a stack of spaced apart magnetic, optical and/or MO data storage disks or media  14  that are rotatable about a common shaft  16 . The head stack assembly  12  includes a number of actuator arms  20  that extend into spacings between the disks  14 , with only one disk  14  and one actuator arm  20  being illustrated for simplicity of illustration. 
     The head stack assembly  12  also includes an E-shaped block  24  and a magnetic rotor  26  attached to the block  24  in a position diametrically opposite to the actuator arms  20 . The rotor  26  cooperates with a stator (not shown) for the actuator arms  20  to rotate in a substantially radial direction, along an arcuate path in the direction of an arrow A. Energizing a coil of the rotor  26  with a direct current in one polarity or the reverse polarity causes the head stack assembly  12 , including the actuator arms  20 , to rotate around axis P in a direction substantially radial to the disks  14 . 
     A transducer head  40  is mounted on the free end of each actuator arm  20  for pivotal movement around axis P. The magnetic rotor  26  controls the movement of the head  40  in a radial direction, in order to position the head  40  in registration with data information tracks or data cylinders  42  to be followed, and to access particular data sectors  44  on these tracks  42 . 
     Numerous tracks  42 , each at a specific radial location, are arrayed in a concentric pattern in a magnetic medium of each surface of data disks  14 . A data cylinder includes a set of corresponding data information tracks  42  for the data surfaces of the stacked disks  14 . Data information tracks  42  include a plurality of segments or data sectors  44 , each containing a predefined size of individual groups of data records that are saved for later retrieval and updates. The data information tracks  42  can be disposed at predetermined positions relative to a servo reference index. 
     The location of each sector  44  is identified by a sector identification (SID) read by the head  40  from the disk surface. Each command is stored as an object of a linked list (or a data structure) representing the queue, and is characterized by a physical location on the surface of the disk  14 , which occupies one or more data sectors  44 . Each data sector is identified by a radial coordinate and an angular coordinate (also referred to as rotational position). 
     The disk drive  10  further includes an interface processor  50  which is coupled to a command queue controller  55  that links the interface processor  50  to the head stack assembly  12 , via a servo processor  57 . The interface processor  50  implements a scheduling algorithm that sets a queue execution order of the pending commands when the current I/O command is being executed. During operation, the command queue controller  55  receives the logical addresses of the commands from the interface processor  50 , and translates them into physical addresses on the disks  14 . The command queue controller  55  then sends control signals to the servo processor  57  to move the heads  40 . In FIG. 1, the interface processor  50 , the command queue controller  55  and the servo processor  57  are shown to constitute part of the disk drive  10 . However, persons skilled in the art will recognize that these components may be provided as part of a separate host computer system. 
     Having described the general environment in which the present invention can be used, its operation will now be described with further reference to FIG. 3 (FIGS.  3 A and  3 B). The present scheduling algorithm is implemented by the command queue controller  55  for sorting and scheduling commands in a command queue, to substantially minimize the long-term average access time of commands. As it will be explained below, the algorithm identifies a candidate command from the command queue with the least expected access time (LEAT), and reorders the command queue accordingly, so that this candidate command is executed following the current command. Using the LEAT leads to an approximately minimum average access time in the long run. 
     The scheduling algorithm is represented by a method  100  and illustrated in FIGS. 3A and 3B. The scheduling algorithm starts at block or step  105  by marking the end of the execution of the current command by the head  40 . With reference to FIG. 2, an exemplary current command is denoted by the numeral reference  60 . At step  110 , the scheduling algorithm initializes “mintime”, by setting it to a predetermined large value. As used herein, “mintime” denotes a program variable which is gradually decreased until it reaches a final minimum value. 
     At step  115 , the scheduling algorithm acquires the first rotational time of a candidate command in the queue. With reference to FIG. 2, an exemplary candidate command is denoted by the numeral reference  65 . The rotational time of the candidate command  65  is measured by the angular difference between the candidate command  65  relative to the end of the current command  60 . In other terms, the rotational time of the candidate command  65  is the amount of time until the first time after the end of the current command that the rotational position of the candidate command will coincide with the rotational position of the head  40 . 
     At decision step  120 , the scheduling algorithm inquires whether the rotational time determined in step  115  is greater than a current “mintime”, which is the shortest expected time for the drive  10  to access a candidate command among those that the command queue controller  55  has scanned so far. If the scheduling algorithm determines that the rotational time is greater than or equal to the current “mintime”, which implies the existence of another command in the queue which is at least as appropriate for execution, then the scheduling algorithm bypasses the candidate command  65  and proceeds to the next command in the queue (step  125 ). 
     The scheduling algorithm then inquires, at decision step  130 , whether the end of the queue has been reached, that is whether the scheduling algorithm has completed the scanning of all the commands in the queue. If it has, then it proceeds to step  135  where it returns the best found result or command with the least expected access time (LEAT). If, on the other hand, the end of the queue has not been reached, the scheduling algorithm returns to the beginning of the loop and considers the next command in the queue. 
     Returning to decision step  120 , if the scheduling algorithm determines that the rotational time is less than the current “mintime”, which implies that the candidate command  65  might be better than any previously scanned command, the scheduling algorithm checks additional conditions that would confirm, with a higher degree of certainty, whether or not the candidate command  65  has the least expected access time (LEAT) among previously scanned commands. To this end, the scheduling algorithm proceeds to step  140  where it acquires various parameters specific to the candidate command  65 . These parameters include, for example, the cylinder difference, the read/write type, the direction of the movement of the head (inward or outward) and the head number. 
     Based on these parameters, the scheduling algorithm determines the maximum possible seek length within the current “mintime” at step  145 . It then proceeds to decision step  150  (FIG. 3B) where it compares the required seek time for the candidate command  65  (obtained at step  140 ) with the maximum possible seek length within the current “mintime” (obtained at step  145 ). This approach allows the scheduling algorithm to optimize the calculation of seek time in that the scheduling algorithm is no longer required to dedicate time referring to look-up tables stored in the interface processor  50  for each candidate command  65 . Rather, the scheduling algorithm checks only once the maximum seek time corresponding to the “mintime”, and then compares the required seek time for the candidate command  65  to the maximum possible seek length within the current “mintime”. 
     With reference to FIG. 4, it illustrates an exemplary graph  200  that charts the maximum possible seek length versus available rotational time which is stored as a look-up table in the memory of the interface processor  50 . The shaded area, defined by the coordinates of the available rotational time and the coordinate axes, represents the maximum seek length values (measured in cylinders) for candidate commands, that are less than the maximum possible seek length corresponding to the rotational time. 
     If at step  150  the required seek time for the candidate command  65  is greater than the maximum seek length that is possible within the current “mintime”, as exemplified by the value  220  that lies above the shaded area, the scheduling algorithm bypasses the candidate command  65  for not possessing the LEAT, i.e., the currently best known command is more appropriate than the candidate command. The scheduling algorithm then proceeds to step  125  (FIG. 3A) and runs the sequence of steps as described above. 
     If, however, at step  150  the required seek time for the candidate command  65  is found to be less than or equal to the maximum possible seek length within the current “mintime”, as exemplified by the value  210  that lies within the shaded area (FIG.  4 ), the scheduling algorithm proceeds to perform more refined calculations that would confirm, with an even higher degree of accuracy, whether or not the candidate command  65  has the least expected access time. 
     To this end, the scheduling algorithm consults a table stored in the memory of the interface processor  50 , and inquires at step  155  if, based on the parameters discovered so far, the candidate command may require an additional revolution to be added to the access time corresponding to the required seek length determined at step  140 . In one embodiment, the stored look-up table provides two or more (e.g. five) columns of numbers that provide the probability of a successful execution of the candidate command  65 . For example, one column provides the shortest seek length with the zero probability of success, and another column provides the length of the longest seek with unity probability of success. 
     At step  155 , the scheduling algorithm compares the seek length of the candidate command  65  to the column with zero probability of success, and, if it determines that the seek of the candidate command is longer than the seek length in that column, then the candidate command time is increased by one revolution at step  160 , and the scheduling algorithm proceeds to decision step  170 . If at step  155  the scheduling algorithm determines that the seek of the candidate command is shorter than the seek length in the column with the zero probability of success, it does not increase the candidate command time by a revolution, but proceeds to decision step  165 . 
     When appropriate, such as when the seek of the candidate command  65  is not longer than the seek length in the column with the zero probability of success, the scheduling algorithm determines at decision step  165  whether the command time suffices with certainty for the seek. To this end, the scheduling algorithm compares the seek of the candidate command with the seek length in the column time with unity probability of success, and if it determines that the candidate seek is shorter than, or equal to the seek length in that column, then the candidate command  65  is deemed to satisfy the condition of decision step  165 , and the scheduling algorithm proceeds to step  170 . 
     If, on the other hand, the scheduling algorithm determines that the required candidate time does not suffice with certainty, that is the candidate seek is longer than the seek time in the column, the scheduling algorithm proceeds to step  175 , where it adds the expected lost time from look-up tables stored in the memory of the interface processor  50 . This step is carried out as follows: Suppose the rotational time between the end of the current command  60  (FIG. 2) and the start of the candidate command is s. More precisely, it would take s time units for the rotational position of the head to change from that of the end of the current command  60  to that of the start of start of the candidate command. 
     From the point of view of the scheduling algorithm, the quantity s is a constant depending on the difference in rotational locations. On the other hand, it is sometimes not certain whether the next command could be executed at time s (measured from the completion of the current command) or rather at time s+r, where r is the (constant) time it takes to complete a full revolution. For simplicity purposes, the possibility of missing more than one revolution is neglected in this analysis, though it could be accounted for by persons skilled in the field. If the probability of the candidate command missing a revolution is denoted by p, then the expected access time (EAT) is expressed by the following formula: 
       EAT=s+rp.   
     The probability p reflects various uncertainties, both intrinsic and due to the lack of computational resources for a more accurate evaluation. As a result, if a command (i) in the queue has rotational time s(i) and probability of success p(i) during the first revolution, its expected access time (EAT), t(i), is expressed by the following equation: 
     
       
           t ( i ) =s ( i )+ rp ( i ). 
       
     
     The scheduling algorithm then proceeds to decision step  170 , where it inquires whether the expected access time for the candidate command  65  obtained in step  140  is less than the current “mintime”. If it is not, the scheduling algorithm bypasses the candidate command  65  and proceeds to the next command in the queue at step  125  as explained above. If, on the other hand, the expected access time for the candidate command  65  obtained in step  140  is less than the current “mintime”, the scheduling algorithm proceeds to step  180 , and updates the current “mintime” with the value of the current candidate command  65 . It also stores the identity of the current command as the currently best known command. 
     Thereafter, the scheduling algorithm returns to steps  125  and  130  (FIG.  3 A), as explained above, and terminates by selecting the command with the least expected access time (LEAT) or t(i) at step  135 . This choice approximately maximizes the expected throughput of the disk drive  10 , and avoids the bias introduced by safety margins. So, for example, if r=100, the scheduling algorithm would prefer a command (i) with a rotational time s(i)=20 and a missed revolution probability of p(i)=0.30 to a command (j) with a rotational time s(j)=55 and a miss probability of p(j)=0, even though the command (i) may miss the revolution with a probability of 30%, since 20+0.3(100)32 50&lt;55. As used herein, “throughput” means the average number of commands per unit of time. 
     The scheduling algorithm includes an efficient implementation of the LEAT criterion, namely, that the probability of a missed revolution p(i) does not have to be computed for every single command in the queue. Depending on the current best candidate, a command can be seen to have no chance of being the best candidate in the queue, regardless of its probability p(i) of a missed revolution. 
     It is to be understood that the specific embodiments of the invention that have been described are merely illustrative of certain application of the principles of the present invention. Numerous modifications may be made to the scheduling algorithm described herein without departing from the scope of the present invention.