1、Rotational Position Optimization (RPO) Disk SchedulingWalter A. BurkhardA3John D. PalmerA3Gemini Storage Systems LaboratoryAlmaden Research CenterDepartment of Computer Science and Engineering IBM Research DivisionUniversity of California, San Diego 650 Harry RoadLa Jolla, CA 92093-0114 USA San Jose
2、, CA 95120-6099 USAJuly 16, 2001submitted to the First Conference on File and Storage Technologies (FAST02), Monterey, California, January 28-29,2002.AbstractRotational position optimization disk scheduling algorithms utilize seek distance versus rotational distance informa-tion implemented as rpo t
3、ables (arrays) which are stored in flashmemory within each disk drive. We consider a novelrepresentation scheme for this information reducing the required flashmemory by a factor of more than thirty therebyreducing the manufacturing cost per drive. We present simulation results showing the throughpu
4、t for conservativeand aggressive versions of the scheme as well as comparative results with the standard production drives not usingthese results.1 IntroductionDisk drive scheduling algorithms have been proposed and studied over the past 35 years in an attempt to improveperformance. These algorithms
5、 utilize a stream of operation requests as input and arrange them as output. Manyalgorithms proposed to achieve better performance utilize disk internal state information; these algorithms are brieflypresented in the first section. We consider the implementation of a good disk scheduling algorithm;
6、our goal is toprovide less costly disk drives by reducing the internal flash memory within a disk thereby reducing fabrication costs.We study the throughput achievable using a disk drive simulation model together with random uniformly distributedoperations. We briefly overview various previous algor
7、ithms and then present our approach.The paper is organized in seven sections as follows. We overview the state based disk scheduling algorithms,present our disk model and the IBM Ultrastar 18LZX command scheduling algorithm. The fifth section follows witha description of our approach reducing the ro
8、tational positioning algorithm tables. The sixth section contains anoverview of the simulation as well as our results. Finally, we draw conclusions in section 7.2 Classic Scheduling AlgorithmsNumerous studies within the literature have considered command selection strategies such as First Come First
9、 Served(FCFS), Shortest Seek Time First (SSTF), and the SCAN scheduling algorithms 4, 3, 6, 11, 8, 2. The SSTF approachreduces the average response time compared to FCFS over a wide range of workloads. The SCAN policies, includingLOOK and C-SCAN, lower the variance in the response times; very recent
10、ly, Worthington et al. combined LOOKTechnical Report CS01-xxx, CSE, UCSD, xxxx xx, 2001and C-SCAN and provide evidence of excellent performance for current disk drives 14. Geist and Daniel proposeda continuum of algorithms between SSTF and LOOK that parametrically adjusts the propensity of the algor
11、ithm tochange direction across the disk platter 5.With the evolution of disk drives, standard disk form factors have shrunk and the full-stroke seek time has dimin-ished considerably. Within modern disk drives, the full-stroke seek time is approximately twice the spindle full rotationtime. This obse
12、rvation demands scheduling algorithms depending upon platter position as well as arm position.Several studies within the literature have considered algorithms combining both the seek and rotational latencies.Jacobson and Wilkes consider the Shortest Access Time First (SATF) 10, Seltzer, Chen and Ous
13、terhout considerShortest Time First (STF) 13, Worthington, Ganger and Patt consider the Shortest Positioning Time First (SPTF)14, and Heath, Pruett and Nguyen 7 consider an implementation of the these approaches.More recently, Andrews, Bender and Quang consider the complexity of off-line disk schedu
14、ling which they showto be NP-complete. Moreover, they consider non-greedy on-line disk scheduling algorithms and claim to have contra-dicted a conjecture that the greedy algorithms mentioned above are optimal 1.3 Disk ModelingA disk drive is composed of several concentric annular platters mounted on
15、 a spindle motor. Platters are divided intoconcentric circular tracks;acylinder is composed of the set of equal-radius tracks. The smallest unit that can be reador written to the disk is a sector which typically consists of 512 bytes of user data; individual sectors reside on a singletrack. Data is
16、transferred to and from the disk via the set of read/write heads (one per platter surface.) The heads aremounted on ends of the actuator arms. The actuator moves all arms together and the heads will reside on the tracks ofa cylinder.D7CTD6DAD3 CXCSCTD2D8CXACCTD6D7CRDDD0CXD2CSCTD6D1D3D8D3D6CPCRD8D9CP
17、D8D3D6 D7D4CXD2CSD0CTCPD6D1D7D7CTCRD8D3D6D4D0CPD8D8CTD6CWCTCPCSD7Figure 1. Disk drive internalsThe servo identifier (sid) wedges consist of a unique synchronization pattern together with information identifying thecylinder and sector as well as centering information to position the head on the track
18、; they are evenly spaced aroundthe platter independent of the recording zone. All arm positioning as well as sector access is ultimately done via sids.When the disk accesses a sector for reading or writing, the actuator must move the arms to the proper cylinder;then the desired sector must rotate un
19、der the head. A high-level pictorial description of a disk drive with two plattersand four arms is presented in figure 1; table 1 contains typical times and disk drive architectural parameters circa 1999for the IBM Ultrastar 18LZX drive 9.2form factor 3.5 inchcapacity 18.3 GBplatters 5heads 10rotati
20、on rate 10,000 rpmservo identifiers per platter 90average seek 4.9 msnumber of cylinders 11,712number of zones 15media data rate 23.3.44.3 MB/sTable 1. IBM Ultrastar 18LZX Specifications4 Rotational Position Optimization Command SchedulingThe IBM Ultrastar 18LZX command selection scheme, referred to
21、 as the rotational position optimization algorithm,is a greedy algorithm based upon the access time which depends upon both the seek and rotational latencies requiredto bring the desired physical block under the head. During the selection process, the access time for each commandwithin the queue is
22、determined and the command with the smallest time is selected.Figure 2 presents the reachable area portion of the platter within the gray area; the disk rotates in the clockwisedirection in the figure. Data in the reachable portion of the platter is accessible in one rotation from the currentcommand
23、 and actuator position. The remaining data of the platter requires an additional rotation.CRD9D6D6CTD2D8 D4D3D7CXD8CXD3D2D6D3D8CPD8CXD3D2CSCXD6CTCRD8CXD3D2Figure 2. Platter reachable areaIt is difficult in practice to determine precisely the boundary of the reachable area and a robust strategy for d
24、eterminingthe relative location of the border is essential for access time calculation. The cost of making the incorrect decision willbe an extra rotation, referred to as a miss, and such performance can be even worse than picking the next commandat random. A conservative strategy is to consider onl
25、y those commands far removed from the border; but, beingtoo conservative reduces the benefits of the scheduling algorithm. However, if the strategy is too aggressive, theperformance will also suffer from the additional misses.Since the reachable area border is fuzzy around the edge, the IBM Ultrasta
26、r 18LZX drives use probabilistic data3regarding the edges of the reachable area. Rather than determining the access time for each command within the queue,the expected access time (EAT) is determined for each. The expected access time is the time necessary to perform aparticular seek on the average.
27、 We discuss the calculation of a typical expected access time together with the internaltabular representation of the necessary data. Time is expressed in sids; each sid represents 6/90 ms = 44.44 AMs as notedin table 1. Figure 3 presents the non-miss probability curve for a particular seek distance
28、 where the x-axis representsthe rotational latency in sids from the current position and the y-axis represents the probability of reaching the desiredcylinder within the rotational latency without a miss; these probabilities are referred to as non-miss probabilities.BCBCBABEBCBABGBCBABIBCBABKBDBABAB
29、AD2D3D2B9D1CXD7D7D4D6D3CQCPCQCXD0CXD8DDD0D3DB CWCXCVCW D6D3D8CPD8CXD3D2CPD0 D0CPD8CTD2CRDDFigure 3. Typical non-miss probability curvefor a particular seek distanceFor a given seek distance CS, there are two integral values lowCSand highCSwhich specify a portion of one edge ofthe reachable area. As
30、shown in figure 3, for any rotational latency D6D0 at least as large as highCS, the probability of anon-miss is one and for D6D0 less than lowCS, the probability is zero. For each rotational latency D6D0, from lowCSto highCS,atypical table will contain the expected access time which has been evaluat
31、ed asEAT BP B4BDA0D4B5B4D6D0 B7BLBCB5 B7 D4 A1 D6D0where D4 is the non-miss probability of reaching the desired cylinder within D6D0 sids. The expected access time data forrotational latencies is stored within a table; these tables are referred to as the rotational position optimization (rpo)tables.
32、 For each seek distance CS, the values highCSand lowCSare stored together with the expected access times forrotational latencies between lowCSand highCS. Since the platter is continuously rotating, the current location typicallyis the location at the termination of the current command. Determining t
33、he non-miss probabilities is an interestingquestion but beyond our immediate study; however we return to this topic within the our conclusion.Accordingly, the expected access time rpo tabular data is pre-computed for the Ultrastar 18LZX drive family; it isstored on each disk drive in flash memory. O
34、ur approach ultimately will reduce the size of the necessary flash memorywhile maintaining acceptable throughput performance. Multiple tables are used, each describing a particular modeof operation, e.g. inward moving read operation. There are a number of factors impacting edge determination suchas
35、operation type: read or write, absolute head location whether near the inner or outer portions of the platter, seekdirection: inward or outward, etc.The general expected access time EAT calculation is approximated within the following expression where table is4an internal table. For seek distance CS
36、 and rotational latency D6D0 from the end of the current command first to the desiredcommandEATB4D6D0BN CSB5BPBKBOBMD6D0 B7BLBC D6D0 BO lowCSD6D0 D6D0 BQ highCStableCJD6D0 A0 D0D3DBCSCL otherwiseThe precise description of the EAT calculation follows the next paragraph where cylinder groups are intro
37、duced.Each high, low, and EAT value can be made smaller than 256 and will reside within a byte. Accordingly asdescribed, a table with 11712 slots will require approximately 350KB of flash memory. It is, however, not necessaryto have a slot for each seek distance (in cylinders) because the time inter
38、vals being measured (sid intervals) arerelatively coarse. It is only necessary to include enough slots to differentiate times over 2.5 revolutions of interestwhich is approximately 235 slots. Now each slot will correspond to a contiguous sequence of seek distances; eachsuch sequence is referred to a
39、s a cylinder group. The ensemble of cylinder groups is non-overlapping and covers the11712 seek distances. The first cylinder groups, corresponding to seeks where the actuator is moving very slowly,contain very few seek distances. The latter cylinder groups, corresponding to seeks where the actuator
40、 is movingrapidly at a constant rate, contain many more seek distances. The IBM Ultrastar 18LZX implements rpo tables eachwith 227 slots; accordingly, each table requires approximately 6.9KB of flash memory.The expected access time for logical block (sector) address (LBA) N is calculated as follows:
41、1. Calculate the physical block cylinder, track and sid for N.2. The absolute difference between the current cylinder and the desired cylinderspecifies the cylinder group CS which determines the table slot entry.3. The difference between the sid of N and the current sid yields EAT.If EAT BO 0, then
42、EAT := EAT + 90 .4. if EAT BO minimum operation time, then EAT := EAT + 90 .5. high := table d .high low := table d .low6. if EAT BO low, then EAT := EAT + 907. if EAT BO high and EAT AL low, then EAT := table d .eat EAT low return EATStep 1 requires knowledge of the zoned recording data layout. The
43、 seek distance CS, referred to as the cylinder group,is determined next as is the seek direction. Then, in step 3, the diference in sid between N and the (termination ofthe) current operation is our first approximation to the expected access time. Since the platter rotates in one direction,EAT must
44、be positive. One rotation corresponds to 90 sids as noted in table 1. Moveover, if EAT is less than a fixedoperation dependent minimum, 16 sids for read and 24 sids for write, which corresponds to operation initialization,EAT is incremented by one rotation. Step 5, obtains the low and high values fo
45、r the desired cylinder group. Then ifEAT is less than low, EAT is incremented by 90. Finally, in step 7, the EAT value is obtained from the tabular datafor sids within the range low to high. Within steps 4 and 6, increasing EAT by 90 sids represents an extra rotation. Ofcourse within step 7, misses
46、will occur but the expected value calculation includes this.55 Our ApproachThe discussion thus far describes the IBM Ultrastar 18LZX rpo scheduling algorithm. Now we consider an approach tofurther reduce the flash memory size while maintaining acceptable performance; our discussion centers on dimini
47、shingthe data stored within an rpo table slot.BCBCBABEBCBABGBCBABIBCBABKBDBABABAD2D3D2B9D1CXD7D7D4D6D3CQCPCQCXD0CXD8DDD0D3DB CWCXCVCW D6D3D8CPD8CXD3D2CPD0 D0CPD8CTD2CRDDFigure 4. Typical non-miss probability curvefor a particular cylinder groupFor each cylinder group, the probability of a non-miss c
48、an be specified as in figure 4; these curves specify the non-miss probability as a function of the rotation latency in sids, relative to the termination sid of the current operation.Any rotational latency at least as big as high has probability one of non-miss access. Rather than storing all high lo
49、w values, we will consider storing only one value; the non-miss probability curve is represented as a step function.Either we have 100% chance of a miss or 0% chance within this approach. The reduction in space will be considerableand the throughput performance will remain acceptable.BCBCBABEBCBABGBCBABIBCBABKBDBABABACPD6CTCP BTCPD6CTCP BUD2D3D2B9D1CXD7D7D4D6D3CQCPCQCXD0CXD8DDD0D3DB CWCXCVCW D6D3D8CPD8CXD3D2CPD0 D0CPD8CTD2CRDDCZFigure 5. Typical non-miss probability curvefor a particular cylinder groupFigure 5 contains, for a particular table and cylinder gr
