# Multi-disk scheduling for time-constrained requests in RAID-0 devices

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6 242 S.-W. Lo et al. / The Journal of Systems and Software 76 (25) numbers are listed in Table 3. Fig. 6a shows the disk queues sorted according to SSTF. The response times of the obs are listed in Table 4. The average response time of the requests is 9.58 ms. Suppose LRSF is adopted at the RAID- controller to synchronize the scheduling of the disks connected to the controller. Let the threshold TH be.75. Since ob 1,1 belonging to r 3 has the least remaining size, and it is the 1st ob in the queue, ob 1,1 is scheduled for service in the first disk. In the second disk, since ob 2,2 has the least remaining size in the second disk and pf 2;2 4:4 ms ¼ ¼ 1 is larger than the threshold.75, ob pf 2;1 4:4 ms 2,2 is scheduled for service in the second disk although ob 2,1 is the first ob in the second disk queue. In the third disk, because pf 3;2 3:93 ms ¼ ¼ :933 is larger than pf 3;1 4:22 ms the threshold.75, ob 3,2 is scheduled for service in the third disk. The response times of the obs using LRSF- SSTF is listed in Table 5. The disk queues sorted according to LRSF-SSTF are shown in Fig. 6b. The average response time of all the requests is 8.79 ms. It is about 8% better than the average response time, compared with the case without LRSF. Algorithm 1. (Least Request Size First (LRSF)) 1: input: a sorted ob set J x of disk x which contains n x obs x,1,..., x,nx. Each ob x,y in J x has a profit pf x,y and a remaining size rs x,y. TH is a threshold. 2: output: a ob from disk x 3: 4: /** The following steps collect the obs which may not degrade the disk throughput too much into the set T 1.Please note that x,1 is the ob having the highest profit.*/ Table 3 Job parameters Job Request number Cylinder number Seek distance Profit (1/seek time) Disk number J 1,3 r / J 3,3 r / J 2,1 r /4.4 2 J 3,2 r / J 1,1 r / J 1,2 r /4.3 1 J 2,3 r / J 3,1 r / J 2,2 r /4.4 2 Job 1.1 Job2.1 Job 3.1 Job1.1 Job 2.2 Job3.2 Job1.2 Job 2.2 Job 3.2 Job1.2 Job 2.1 Job3.1 Job1.3 Job2.3 Job 3.3 Job1.3 Job2.3 Job 3.3 (a) SSTF (b) LRSF-SSTF Fig. 6. SSTF schedules with/without LRSF. Table 4 Response times of the obs using SSTF Jobs in disk 1 Response time (ms) Jobs in disk 2 Response time (ms) Jobs in disk 3 Response time (ms) J 1, J 2,1 4.4 J 3, J 1,2 9.9 J 2, J 3, J 1, J 2, J 3, Table 5 Response times of the obs using LRSF-SSTF Jobs in disk 1 Response time (ms) Jobs in disk 2 Response time (ms) Jobs in disk 3 Response time (ms) J 1, J 2,2 4.4 J 3, J 1, J 2, J 3, J 1, J 2, J 3,

11 S.-W. Lo et al. / The Journal of Systems and Software 76 (25) %.12 miss ratio 12.% 1.% 8.% 6.% 4.% 2.% FIFO FIFO/LRSF FIFO/LRSF-OTW response time (sec) FIFO FIFO/LRSF FIFO/LRSF-OTW.% (a) Miss Ratio (b) Response Time Fig. 9. Miss ratio and average response time of FIFO with/without LRSF and OTW. 5.%.35 miss ratio 4.% 3.% 2.% 1.% EDF EDF/LRSF EDF/LRSF-OTW response time (sec) EDF EDF/LRSF EDF/LRSF-OTW.% (a) Miss Ratio (b) Response Time Fig. 1. Miss ratio and average response time of EDF with/without LRSF and OTW. miss ratio 3.% 25.% 2.% 15.% 1.% 5.% C-LOOK C-LOOK/LRSF C-LOOK/LRSF-OTW response time (sec) C-LOOK C-LOOK/LRSF C-LOOK/LRSF-OTW.% (a) Miss Ratio (b) Response Time Fig. 11. Miss ratio and average response time of C-LOOK with/without LRSF and OTW. cant. OTW improves the performance significantly because OTW considers the optimization in rotation delay while C-LOOK only considers seek time. C-LOOK with LRSF and OTW gives the best performance especially when the workload is heavy comparing to C-LOOK only and C-LOOK with LRSF. If the workload is heavy, C-LOOK/LRSF-OTW can improve the average response time and the miss ratio of C-LOOK by around 25% and 15%, respectively. Fig. 12a and b show the miss ratio and the average response time of requests in SATF with/without LRSF and OTW, respectively. When the inter-arrival time of requests increases from 3 to 7 ms, the performance difference among SATF with LRSF and OTW (SATF/ LRSF-OTW), SATF with LRSF (SATF/LRSF), and SATF only (SATF) decreases gradually. It is because SATF is a very efficient disk scheduling algorithm, the improvement from LRSF and OTW is small when the workload is not heavy. Note that SATF was shown to be better than many traditional disk scheduling algorithms such as C-LOOK. In general, SATF/LRSF improves SATF by around 1% in average response time and by around 2% in miss ratio. Fig. 13a and b show the performance improvement of LRSF and OTW in SSEDV. SSEDV considers the reordering of disk obs according to the weighted sum of their seek times and deadlines. If the inter-arrival time is increased, the average response time of SSEDV decreases gradually. However, the miss ratio decreases dramatically when the inter-arrival time is decreased from.8 to.9. This phenomenon shows that SSEDV is a very good real-time disk scheduling

12 248 S.-W. Lo et al. / The Journal of Systems and Software 76 (25) miss ratio 35.% 3.% 25.% 2.% 15.% 1.% 5.% SATF SATF/LRSF SATF/LRSF-OTW response time (sec) SATF SATF/LRSF SATF/LRSF-OTW.% (a) Miss Ratio (b) Response Time Fig. 12. Miss ratio and average response time of SATF with/without LRSF and OTW. 5.%.35 miss ratio 4.% 3.% 2.% 1.% SSEDV SSEDV/LRSF SSEDV/LRSF-OTW response time (sec) SSEDV SSEDV/LRSF SSEDV/LRSF-OTW.% (a) Miss Ratio (b) Response Time Fig. 13. Miss ratio and average response time of SSEDV with/without LRSF and OTW. Table 8 The disk utilizations of the proposed algorithms Algorithms and inter-arrival time FCFS EDF CLOOK SATF SSEDV Disk algorithm only Disk algorithm/lrsf Disk algorithm/lrsf-otw algorithm if the system has sufficient disk bandwidth. SSEDV/LRSF-OTW still outperforms SSEDV by around 5% if the workload is light, e.g., inter-arrival time larger 9 ms, and the improvement is higher when the workload is heavier, i.e., inter-arrival time = 8 ms. Table 8 shows the disk utilization of different singledisk scheduling algorithms when LRSF, and LRSF- OTW are applied in the algorithms. In the table, we show the results of the algorithms when the workload is heavy for better comparison. As shown in the table, having LRSF in the scheduling algorithms (C-LOOK, SATF, SSEDV) increases the disk utilization. It is because since the service time of a ob is optimized by the adopted single-disk scheduling algorithm, the use of LRSF increases the average service time of the obs as LRSF may raise the priority of a ob waiting in the disk queue for service, instead of choosing the highest priority ob in the queue. If the disk serves the highest priority ob, the service time should be the smallest. For example, in SATF, the highest priority ob in the queue should be the one with the shortest access time. However, some algorithms (EDF, FCFS) do not consider the movement of the r/w heads of a disk. Using LRSF in these algorithms does not significantly increase the access time. Comparing LRSF with LRSF-OTW, we can see that the disk utilization of LRSF-OTW is lower since the problem of higher service time as a result from raising the priority of a ob in the disk queue is minimized by the OTW scheme WinBench98-based results for pre-fetching While the previous section explores the performance improvement from LRSF and OTW in an RAID- with different disk scheduling algorithms, the purpose of this section is to assess the performance improvement from the pre-fetching mechanism using realistic workloads when different disk algorithms are used in the RAID-. We consider an RAID- controller with eight disks. We simulate a disk drive having 4 MB internal caching space for pre-fetching, and the controller has

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