Abstract:
A computer-implemented scheduling method and apparatus for scheduling operations relating to a predetermined activity. The activity includes scheduling operations of network-attached storage devices, or other computer-related operations, or non-computer related operations, such as manufacturing plant operations. Operational data is received that is indicative of the operations. Attributes regarding the received operational data are identified. A linear ordering of the attributes is imposed via a predetermined curve. The curve is an aggregation of at least substantially continuous functions from intervals so as to form a substantially repetitive pattern. Operations are scheduled based upon the imposed linear ordering. With such an approach, the overall performance aspects of the system is significantly improved.

Description:
BACKGROUND AND SUMMARY OF THE INVENTION 
     The present invention relates generally to computer-implemented schedulers, and more particularly to computer-implemented schedulers for computer operations and for other systems. 
     Scheduling which operations precede other operations is an omnipresent problem. This problem is encountered in determining which computer files are to be retrieved before other files from a computer storage device. This problem is also encountered in what computer threads are to be processed before other threads. Outside of the computer domain, this problem is encountered in manufacturing systems where it must be determined which manufacturing operations are to be performed before others. These are non-limiting examples of where scheduling problems arise. 
     A more detailed non-limiting example is provided within the context of computer information storage scheduling. The computer information storage scheduling problem is multi-dimensional in the sense that it involves many parameters and system components. With the high dimensionality of the scheduling space, it is difficult to implement a Network-Attached Storage Device (NASD) scheduling algorithm that takes into consideration such measures of goodness as disk scheduling performance aspects, network scheduling performance aspects, and real-time disk request deadlines. Previous storage scheduling approaches are not well suited for optimizing the NASD performance with respect to all of these measures of goodness. Accordingly, present scheduling approaches lack a viable global scheduling strategy for NASDs that simultaneously optimizes performance with respect to multiple measures of goodness. 
     The present invention overcomes this disadvantage as well as other disadvantages. In accordance with the teachings of the present invention, a computer-implemented scheduling method and apparatus is provided for scheduling operations relating to a predetermined activity. The activity includes scheduling operations of network-attached storage devices, or other computer-related operations, or non-computer related operations, such as manufacturing plant operations. Operational data is received that is indicative of the operations. Attributes regarding the received operational data are identified. A linear ordering of the attributes is imposed via a predetermined curve. The curve is an aggregation of at least substantially continuous functions from intervals so as to form a substantially repetitive pattern. Operations are scheduled based upon the imposed linear ordering. With such an approach, the overall performance aspects of the system is significantly improved. 
     For a more complete understanding of the invention, its objects and advantages, reference should be made to the following specification and to the accompanying drawings. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a block diagram depicting the networked system employing the present invention; 
     FIG. 2 is a schematic diagram depicting the preferred internal components for an NASD; 
     FIG. 3 is a block diagram depicting the functions and data utilized by the present invention; 
     FIG. 4 is an x-y-z graph depicting an exemplary arrangement in three-dimensional space for attributes considered by the present invention in scheduling requests; 
     FIGS. 5 a-   5   f  are depictions of various exemplary space filling curves; 
     FIG. 6 is a graph diagram depicting a duplication of a space-filling curve across the unbounded dimension; 
     FIG. 7 is a graph diagram depicting an example of how requests are scheduled in reverse order in an embodiment of the present invention; 
     FIG. 8 is a graph diagram depicting an example of how a sweep space-filling curve orders points in one direction while addressing jumps; and 
     FIG. 9 is a block diagram depicting the functions and data utilized by the present invention in handling other exemplary applications. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     FIG. 1 depicts a network  20  with multiple clients ( 22 ,  24 ,  26 ) that request multimedia streams, and also depicts several network-attached storage devices (NASDs) ( 30 ,  32 ,  34 ) that are attached to network  20 . Clients ( 22 ,  24 ,  26 ) request specific disk pages from NASDs ( 30 ,  32 ,  34 ), which are in turn, shipped through network  20  from the NASD containing the requested page to the client that requested the page. 
     The NASD System 
     With reference to FIG. 2, an NASD  34  of the present invention preferably includes a disk  50 , a request queue  52 , a central processing unit  54 , a buffer area  56  to store the pages read from disk, and a network connection via network interfaces  58  and  60 . NASD  34  is a disk storage device that is directly connected to the network (not shown). NASD  34  has network interfaces  58  and  60  to receive requests for disk pages from the network and to send back the resulting data page(s) to the requestor client. 
     Once a request is received, it is queued into the disk queue  52 . According to the present invention&#39;s scheduling algorithm that is executed by NASD CPU  54 , the requests are ordered and processed by CPU  54  in that order. If the request is a read request, the data is retrieved from the disk and is preferably placed in disk buffer  56 , waiting to be sent to the requestor. CPU  54  also schedules the order in which the pages in buffer  56  are sent over the network. In the preferred embodiment, this is done through network interfaces  58  and  60 . 
     NASD Request Characterization 
     With reference to FIG. 3, a client&#39;s disk page request r to a NASD can be characterized by the following parameters  70 : 
     1. c: the disk cylinder number in which the disk page resides inside the NASD, 
     2. t: the request&#39;s real-time deadline, and 
     3. d: the request&#39;s network destination. The disk cylinder number determines the amount of disk seek time needed to retrieve the requested disk page. The request&#39;s real-time deadline is the time after which the request becomes effectively useless, and the request would be considered lost and/or unfulfilled. The request&#39;s network destination is where the requested data from the disk is to be sent. The network destination determines the propagation delay time it takes the requested data to reach its destination in the network. Therefore, a page request to a NASD can be modeled by the three-tuple: &lt;c,t,d&gt; which the present invention uses to determine a processing order for the page request. 
     NASD Request Processing 
     Based on the processing order as determined by the present invention, the NASD processes a request with the parameters &lt;c,t,d&gt;. Based on the cylinder location of the disk head and the request&#39;s location c, a certain amount of seek time (t c ) is spent until the disk head reaches cylinder c. A page p is retrieved from the disk and is placed in the NASD buffer pool  56  until p is submitted to its destination in the network. The NASD buffer pool  56  is an important resource as it isolates the effect of network delays from the rest of the system. 
     In order to send a page p across the network, p is removed from the NASD buffer pool  56 , and given to network interface hardware  60 . Preferably, network interface  60  uses the following protocol to send p to its destination in the network: 
     1. setting up the network connection with the destination 
     2. dividing p into packets 
     3. for each packet p i : 
     (a) sending p i  over the network 
     (b) waiting for an acknowledgement that p i  is received 
     4. closing the connection with the destination 
     In a non-limiting exemplary implementation, there are m clients  27  connected to a network that has several NASDs. Data is distributed in units of blocks to the NASDs in a random fashion. For a given NASD, a set of data read requests are queued. Each request is parameterized by a tuple &lt;c,t,d&gt;. The present invention orders these requests so as to enhance the overall system performance according to certain measures of goodness. 
     Measures of Goodness 
     Based on the characterization of the NASD requests according to the tuple &lt;c,t,d&gt;, the following four measures of goodness  72  are the preferred aspects utilized to concurrently optimize disk scheduling, network scheduling, and deadline scheduling aspects. 
     1. The request deadline misses: The requests that are not served before their deadline expires are said to be missed by the system. The target is to minimize the number of deadline misses. 
     2. The overall NASD bandwidth: This indicates the number of bytes per second that are shipped out of the NASD to their destination in the network. The target is to maximize the NASD bandwidth so that it is as close as possible to the network bandwidth. 
     3. The disk bandwidth: This is affected by the order in which the disk-requests are processed. If the requests are ordered in such a way that the seek time is minimized, then the disk bandwidth would be maximized. The target is to maximize the disk bandwidth. 
     4. The NASD buffer pool occupancy: This determines the size of the buffer pool necessary to accommodate the data pages before sending them to the network. The target is to minimize the occupancy of the buffer pool, so that the NASD does not get congested. 
     While the first two measures of goodness reflect the system overall behavior, the last two measures of goodness analyze why certain scheduling plans are better or worse than the others. 
     Part of the responsibility of scheduler  74  in NASD CPU is to schedule the requests. The overall goal is to enhance the system performance parameters  72  which center upon the following three scheduling activities  77 : 
     1. disk scheduling 
     2. network scheduling 
     3. deadline scheduling The target of disk scheduling is to enhance the performance of the disk by reducing the amount of time wasted in disk head movements. On the other hand, the target of network scheduling is to enhance the output network throughput of the NASD. Finally, the target of deadline scheduling is to reduce the number of client requests that miss their deadlines. 
     Instead of scheduling each NASD scheduler separately and/or independently of the other NASD schedulers that are on the network, the present invention provides an overall scheduling approach that meets the target of each scheduler without preferably favoring any of the schedulers over the others. In other words, scheduler  74  is typically “fair” to the NASD measures of goodness  72 , and tries to meet the target of the other NASD schedulers. 
     Scheduler  74  includes a mapper  80  that maps disk request parameters/attributes (e.g., tuple &lt;c,t,d&gt;)  70  preferably onto an n-dimensional space. The mapped parameters for a disk request constitute a point in the n-dimensional space. Given a collection of these points, module  82  linearly orders the points so that the requests are processed in that order. Module  82  utilizes space-filling curves  84  in order to perform the linear ordering of the points. A space-filling curve acts like a thread that passes through every point in the n-dimensional space so that every point is visited only once. In this way, the use of the space-filling curves reduces the dimensionality of a disk request from an n-dimensional problem space to a single-dimension problem space. A single-dimension problem space is a reduction of the problem so as to provide for a linear ordering of points. 
     Different space filling curves  84  are used based upon the application at hand. A space-filling curve selector module  86  selects from a library of space filling curves the space-filling curve best suited for the application at hand. In the preferred embodiment, space-filling curve selector module  86  selects a space-filling curve to order the points based upon the following characteristics: whether a space-filling curve is pre-disposed towards an axis being bounded or unbounded in the n-dimensional space; whether a space filling curve is biased towards one of the axes; whether a space-filling curve exhibits reverse ordering in any/all of its dimensions; and whether a space-filling curve exhibits “jumps” in any of its dimensions. 
     Module  82  utilizes a geometric data determinator  87  in order to determine how the space-filling curve should intersect with the points. For a two-dimensional space, geometric data determinator  87  examines the geometric coordinates (i.e., x, y coordinates) of the mapped attributes to determine where they fall on the space-filling curve. For a three-dimensional space, geometric data determinator  87  examines the x, y, z geometric coordinates of each mapped point to determine where on the space-filling curve the points fall. The space-filling curve technique utilizes a curve with a predetermined shape which visits each point. 
     The space-filling curve technique is discussed in more detail after the discussion of the mapping onto the n-dimensional space technique. 
     Inserting a New Request 
     With reference to FIG. 4, assume that a three-dimensional space  98  is utilized where the first dimension  100  (the x-axis) represents the disk cylinder number, the second dimension  102  (the y-axis) represents the request&#39;s deadline, and the third dimension  104  (the z-axis) represents the network destination of the request. 
     The disk has a constant number of cylinders, numbered from 0 to x max . Therefore, the x-axis  100  will have a maximum value of x max  and all the clients&#39; requests to the NASD will reside in the range [0, x max ], inclusive. 
     The real-time deadline can be an absolute deadline or a relative one. The decision to choose the deadline as relative or absolute may affect the range of values in the y-axis  102 . In the case of having a relative real-time deadline, the values of the y-coordinate can vary from 0 up to the maximum possible relative delay y max . In the case of having an absolute real-time deadline, the preferred embodiment does not include a maximum value for the y-coordinate, and hence the values of the y-coordinate are unbounded. 
     The z-axis  104  represents the network destination of the request, i.e., the client&#39;s location in the network where the result of the request (usually a disk page) will be shipped by the NASD. For example, assume that there are four network destinations A, B, C, and D. Each of the possible network destinations is mapped to one point in the z-axis  104 . With this approach, the network destinations can be sorted based on their known average network delay. In this case, the destinations with less network delay are placed closer to the origin. Since the network delay may vary over time, the function that maps from the network destination into a corresponding location in the z-axis  104  may dynamically vary as time goes. 
     For example, by using a window over time, the average network delay is computed for every destination during the window period. The mapping function (from a network destination to a location in the z-axis)  104  is modified by the end of the window interval, if the delays happen to be significantly different. To avoid reshuffling the requests that are already scheduled, once the mapping function changes, only the newly arriving requests preferably are reshuffled and not the ones already inserted into the system. 
     Given a request r=&lt;c,t,d&gt; from a client to the NASD, the processor of the NASD inserts r as a point in the three-dimensional space  98 . 
     Request Ordering via Space-Filling Curves 
     NASD requests are modeled as points in the three-dimensional space  98 . Given a collection of these points, the points are linearly ordered so that the requests are processed in that order. The present invention utilizes space-filling curves in order to perform the linear ordering of the points. 
     One way of performing the mapping of the n-dimensional space into the one-dimensional space is by using space filling curves, e.g., the Peano curve, or the Hilbert curve These curves are generally discussed respectively in: G. Peano. Sur une courbe qui remplit toute une aire plaine. Mathematische Annalen, 36:157-160, 1890 (which translates into “G. Peano. On One Curve That Fills All of a Space Plane. Mathematical Annals, 1890); and D. Hilbert. Ueber stetige abbildung einer linie auf ein flashenstuck. Mathematische Annalen, 38:459-460, 1891 (which translates into D. Hilbert. On Steady Formation of a Line on a Bottle Head. Mathematical Annals, 1891). 
     Space-Filling Curves 
     A space-filling curve acts like a thread that passes through every cell element (or pixel) in the n-dimensional space so that every cell is visited only once. Thus, a space filling curve (SFC) imposes a linear order of the cells in the n-dimensional space. FIGS. 5 a-   5   f  illustrate in a non-limiting way several space-filling curves for the two-dimensional space. The passing of the curve through the points acts to reduce the problem space to a single dimension. A space-filling curve is an aggregation of a continuous functions from intervals so as to form a substantially repetitive pattern. The connection points between the intervals are non-differentiable. 
     FIG. 5 a  is a snake space-filling curve; FIG. 5 b  is a sweep space-filling curve; FIG. 5 c  is a spiral space-filling curve; FIG. 5 d  is a zig-zag space-filling curve; FIG. 5 e  is a Peano space-filling curve; and FIG. 5 f  is an Hilbert space-filling curve. 
     Each space-filling curve has its own advantages and disadvantages which are discussed in greater detail below. However, it is to be understood that the present invention is not limited to only these space-filling curves, but includes, any space-filling curve that is suitable for the task at hand, as well as space filling curves which can handle additional dimensions in space (i.e., more than two dimensions). 
     Axis-Parameter Assignment and Bias 
     A difficulty with using SFCs for scheduling is the axis-parameter assignment problem. This problem can be described in the following way. Given that requests to be scheduled are characterized by three parameters (as is the case in the NASD scheduling problem), in order to use a space-filling curve, each one of the three parameters should be assigned to one of the axes of the underlying three-dimensional space. However, it may be the case that the space-filling curve does not treat the axes uniformly. In other words, a space filling curve may be biased towards one of the axes. 
     For example, the snake and the sweep space-filling curves (FIGS. 5 a  and  5   b , respectively) are more biased towards the horizontal dimension (the x-axis  120 ). The reason is that both curves tend to schedule all the points in the x-direction first. In other words, these types of SFCs perform only one step in the y (vertical) direction  122  after performing seven contiguous steps in the x (horizontal) direction  120 . The other space-filling curves shown in FIGS. 5 c-   5   f  tend to be less biased towards any of the dimensions. Therefore, when using the snake or the sweep space-filling curves of FIGS. 5 a  and  5   b , the present invention considers these curve&#39;s aspects in assigning parameters to dimensions, as this affects the system performance due to the existing bias. 
     Unbounded Vs. Bounded Parameters 
     Some system parameters, e.g., the disk cylinder number, have an upper-bound, which is the maximum cylinder number. On the other hand, some parameters (e.g., absolute deadline) continually increase and do not typically have an upper-bound. 
     Some space-filling curves (e.g., the spiral curve of FIG. 5 c ) assume that all dimensions have an upper-bound. Similarly, other space-filling curves (e.g., the snake and the sweep of FIGS. 5 a  and  5   b ) may only have the unbounded parameter as their y-axis. In the preferred embodiment, the present invention does not include the x-axis being the unbounded one as some requests would starve while waiting to be scheduled. However, it is to be understood that the present invention is not limited to this, but includes using in an alternate embodiment the x-axis as the unbounded one depending upon the application at hand. 
     In choosing a space-filling curve for ordering and scheduling requests, the present invention considers the boundedness/unboundedness of the scheduling parameters as well as the nature of the space-filling curve that is chosen by considering the following cases: 
     Case 1: the space-filling curve uses upper-bounds in all dimensions, and all the scheduling parameters are also bounded. 
     Case 2: the space-filling curve uses upper-bounds in all dimensions, and only one of the scheduling parameters has no upper-bound. 
     Case 3. the space-filling curve does not require upper-bounds in all its dimensions, and similarly, all the scheduling parameters have no upper bounds 
     Case 4: the space-filling curve does not require upper-bounds in all its dimensions, and any or all of the scheduling parameters are bounded. 
     In Cases 1 and 3, the space-filling curve is used directly without any changes. In Case 2, the space-filling curve along the unbounded dimension is duplicated/repeated (see FIG.  6 ). Finally, in Case 4, since the space-filling curve does not require upper-bounds (e.g., the Peano, Hilbert, and the zig-zag space-filling curves), whenever the upper-bounds of the parameters in any of the dimensions is reached, then the space-filling curve is truncated until all the space is filled out. Once this happens, the space-filling curve is restarted from the origin of the space. 
     Reverse Ordering 
     In reverse ordering of scheduling points, the order of visiting the points of the underlying space is examined. For example In FIG. 7 which contains a spiral space-filling curve, the order in which the horizontal stripes are visited is numbered 1-7. Observe that the order induced by this space filling curve alternates. At one time, the order of visiting the points is from smallest to largest in following path  200  forwards, and in the following time, the order of visiting the points is from largest to smallest in following path  202  in reverse. Similar behavior in the vertical direction is exhibited as well. Within the present invention, the visiting the points from largest to smallest is referred to as “reverse ordering”. 
     On the other hand and with reference to FIG. 8, consider the sweep space-filling curve. The points in the horizontal (x) axis  120  are visited in the order from smallest to largest. 
     Whether reverse ordering is unfavorable or not relates to the semantics of the sorted parameter. For example, consider the real-time deadline as such a parameter. Then, scheduling from largest to smallest, i.e., in reverse order, means that the points with a larger deadline are scheduled before the points with a smaller deadline. In this case, reverse ordering is typically considered unfavorable. 
     As another example, consider the case of disk-head scheduling. Based on the disk-head movement, alternating between forward and reverse ordering is favorable. Within the field of the present invention, this is referred to as a circular scan algorithm. However, scheduling in the forward direction only is considered less favorable (this is referred to within the field of the present invention as a scan algorithm). 
     Thus, the present invention considers in its scheduling approach whether a space-filling curve exhibits reverse ordering in any/all of its dimensions or not. This approach of the present invention benefits the performance of the system when assigning the scheduling parameters to the various dimensions/axes. 
     SFC Jumps and Their Relation to Scheduling 
     Another factor related to using space-filling curves in scheduling is “jumps”. Jumps in a space-filling curve reflect the locality of the consecutive points in the order implied by the space-filling curve. For example, consider the sweep space-filling curve of FIG. 5 b , in contrast to the snake space-filling curve of FIG. 5 a . Based on the discussion above, an advantage of the sweep over the snake curves is that the sweep scans the space without using reverse ordering, while the snake curve does. However, one advantage of the snake space-filling curve over the sweep space-filling curve is that the sweep space-filling curve does not exhibit jumps while the snake space-filling curve does. By the end of each horizontal sweep, the sweep space-filling curve jumps back to the beginning of the horizontal axis while advancing the vertical axis by one step as indicated by jump  124 . 
     Similar to reverse ordering, jumps may or may not be favorable according to the application. For example, in disk-head scheduling, jumps are considered disadvantageous, as they result in a longer seek time without retrieving any data. 
     Intentional Bias 
     Although being unbiased to any one of the dimensions of the scheduling space is typically considered a positive aspect of a space-filling curve, in an alternate embodiment, the present invention biases the NASD scheduler towards a certain aspect of performance. In this embodiment, the present invention, for example, has a higher goal of reducing the number of requests that lose their deadline, than increasing the disk or network bandwidth. In this embodiment, the present invention favors the real-time deadline dimension of the scheduling space. 
     The present invention achieves this intentional bias towards one of the dimensions through several techniques while still using space-filling curves. One technique is to scale down (reduce) the resolution of the dimension that is to be favored over the scale of the other dimensions. This way, the scheduler spends more time (or makes bigger jumps) in the scaled down axis, while being more detailed (or slower) in the other dimensions, and hence favoring the scaled down dimension over the other dimensions. 
     The Effect of Packet-Level Scheduling 
     In another alternate embodiment, instead of scheduling at the disk page-level granularity, the present invention schedules at the packet-level granularity. 
     With page-level scheduling, a page is copied from the buffer pool to the network interface hardware. The page is divided into packets and a packet is sent one at a time over the network. If the NASD experiences network delays, the network interface hardware usually has no other option but to send out the remaining packets of the same page. This results in additional delay that lowers the overall NASD bandwidth. 
     With packet-level scheduling in this alternate embodiment, once the network interface hardware determines that the packets of a page are experiencing significant network delays, it switches to shipping another page (or packet) from the NASD buffer pool instead of waiting to finish shipping all the packets of the current page. To assist in accomplishing this, the present invention keeps track of partial status of which packets of a page are sent out and which are still to be sent out. This results in better overall NASD bandwidth for the price of additional overhead for bookkeeping. 
     While the present invention has been described in its presently preferred form, it is to be understood that there are numerous applications and implementations for the present invention. For example, and as mentioned above, the present invention has applications in computer operations other than disk scheduling. For example, the present invention can be used to schedule computer threads  200 . Threads  200  need to be scheduled by scheduler  74  so as to optimize the time required for their functions to be achieved. Attributes  70  of the threads are mapped onto an n-dimensional space by mapper  80 . For sake of a non-limiting example, such thread attributes may include when the thread needs to have its processing completed, the priority/importance of the thread, the amount of time needed for the thread to complete its processing, the effect of missing a thread&#39;s deadline, etc. A space-filling curve is selected by selector  86  and used by module  82  to provide a linear ordering  204  of the points. 
     The present invention is not limited to computer operations, but also includes such other scheduling applications as scheduling operations  208  in a manufacturing plant. Attributes  70  of the plant operations are mapped onto an n-dimensional space by mapper  80 . For sake of a non-limiting example, such plant operation attributes may include when the plant operation needs to have its processing completed, the priority/importance of the operation, the amount of time needed for the operation to complete its processing, the effect of missing a plant operation&#39;s deadline, etc. A space-filling curve is selected by selector  86  and used by module  82  to provide a linear ordering  204  of the points. 
     Moreover, the present invention utilizes fractals  216  in order to provide a linear order to the points. Fractals are typically geometrical shapes whose structure is such that magnification by a given factor reproduces the original object. Fractals are generally discussed in the following reference: Peitgen et al., Chaos and Fractals, Chapter 2, Springer-Verlag, New York, 1992. A fractal can be selected based upon the following characteristics: whether a fractal is pre-disposed towards an axis being bounded or unbounded in the n-dimensional space; whether a fractal is biased towards one of the axes; whether a fractal exhibits reverse ordering in any/all of its dimensions; and whether a fractal exhibits “jumps” in any of its dimensions. In fact, fractals can be viewed as a subset of space-filling curves. 
     Accordingly, the invention is capable of modification and changes without departing from the spirit of the invention as set forth in the appended claims.