Disk Scheduling with Dynamic Request Priorities. Yongcheng Li See-Mong Tan Zhigang Chen Roy H. Campbell. Department of Computer Science

Transcription

1 Disk Scheduling with Dynamic Request Priorities Yongcheng Li See-Mong Tan Zhigang Chen Roy H. Campbell Department of Computer Science University of Illinois at Urbana-Champaign Digital Computer Laboratory 134 W. Springeld Urbana, IL 6181 High performance servers in client/server distributed systems must manage and multiplex disk I/O resources eciently and fairly between multiple clients. In digital multimedia systems, clients may make requests of varying urgencies. The traditional approach to this problem thus assigns priorities to disk requests. High priority requests are scheduled rst, with low priority requests served only when the high priority queue is empty. While this approach permits priority optimization, it ignores seek optimization. When the length of the high priority queue is short compared to the low priority queue, disk utilization is very low. In this paper, we present a priority inversion disk scheduling algorithm where both priority and seek optimization are considered. The algorithm is evaluated through detailed simulation and its performance is compared with traditional scheduling algorithms. We then identied the conditions when our algorithm performs better. The simulation results show that under these conditions, we achieve close to 5% reduction in total system response time. Based on this, an adaptive disk scheduling algorithm was constructed which consistenly outperforms the traditional approach. 1

2 1 Introduction High performance servers in client/server distributed systems must manage and multiplex disk I/O resources eciently and fairly between multiple clients. The high number of requests in very large scale distributed information systems, such as World Wide Web servers for popular sites, or other digital library systems, impose a heavy load on the storage and I/O subsystems. The load condition also varies considerably over time. In addition, busy multimedia servers of the future must handle requests of dierent priorities. File requests which need disk I/O access require appropriate disk scheduling algorithms in order to maximize system performance. Existing algorithms for ecient disk scheduling include [1, 11, 22, 8, 12]. The goals of disk scheduling are to minimize seek time (system-oriented), response time (individual I/O request-oriented), and variance in response time. Scheduling algorithms that have been proposed include First Come First Served (FCFS), Shortest Seek Time First (SSTF), SCAN, and LOOK. However, these algorithms operate on only the requested track number. Emerging applications involving multimedia data impose additional constraints on disk requests, such as nish deadlines or relative priorities. For example, temporal constraints on isochronous multimedia data necessitate deadlines by which the data must be fetched. Careful consideration of these factors is required for consistent and ecient management of disk resources. A class of new disk scheduling algorithms were developed to deal with these additional constraints[18, 25, 19, 7, 3, 14, 6]. A common feature of these new scheduling algorithms is that the additional constraints are satised rst. Seek optimization is considered secondary and performed whenever possible. While these scheduling algorithms work well in some cases, disk utilization can be very low as seek optimization is always secondary. In this paper, we present a disk scheduling algorithm with dynamic request priorities where a disk request increases its priority if it has not been served for a long time. While satisfying the priority order of disk requests, we also consider the seek optimization. Our algorithm may serve some low priority requests before high priority requests. Priority inversions may thus occur in some 2

3 cases. However, the overall system performance is improved. Simulations done to test the performance of our algorithm under dierent load conditions and dierent parameter settings show that the total system response time can be reduced to half its original value. The remainder of the paper is organized as follows: section 2 discusses related work to disk scheduling. Section 3 describes our our scheduling algorithm. Section 4 presents our simulation model. Detailed simulation results are discussed in section 5. Lastly, we summarize our paper in section 6. 2 Related Work The rst group of traditional disk scheduling algorithms[22, 2, 8, 24, 4, 1]. do not use additional information in making disk request scheduling decisions. Seek optimization is done with the use of track information only. The second group of new algorithms make use of additional information such as request deadline or priority. 2.1 Traditional Disk Scheduling Algorithms FCFS This is a policy which has a random seek pattern. It does not take advantage of positional relationships between I/O requests in the current queue or of the current cylinder position of the read/write heads. In general, FCFS is acceptable when disk load is light. FCFS under heavy load gives poor throughput. SSTF The shortest-seek-time-rst policy improves throughput by servicing the request that results in the shortest seek distance. SSTF has fast mean response, but the algorithm gives rise to large variances in response time. SCAN With SCAN the disk arm acts as a shuttle as it sweeps back and forth across all the cylinders servicing requests. SCAN was proposed as an alternative to SSTF because it does not discriminate between individual requests. SCAN reduces the variance of response time without sacricing too much in terms of increasing the mean response time. 3

4 N-STEP SCAN A variant of SCAN is N-step SCAN which oers good performance in throughput and mean response time. N-step SCAN behaves like SCAN except that it services only those requests waiting when the particular sweep begins. Requests arriving during sweep are grouped together and ordered for optimum service during the return sweep. LOOK A variant of SCAN where the disk arm does not reach the inner or outer most track. The arm switches it direction as long as there are no more outstanding requests in that direction. LOOK performs better than SCAN under low load conditions and is nearly equivalent to SCAN when the load is high. V-SCAN A scheduling strategy that may be tuned to SSTF or SCAN by an adjustable parameter, permitting the dynamic adaptation of the algorithm to changing system conditions[9, 12]. Under heavy load it tends toward SCAN, and under light toward SSTF. From simulation results, V-SCAN is superior to either SCAN or SSTF. 2.2 New Disk Scheduling Algorithms The additional requirements introduced by applications, such as digital multimedia and database systems, make traditional disk scheduling algorithms described above inappropriate. Many new scheduling algorithms have been developed[3, 17, 2, 14, 6, 21] Multimedia-Specic Algorithms EDF The Earliest-Deadline-First algorithm is an analog of FCFS. Disk requests are ordered according to deadlines and the request with the earliest deadline is serviced rst. EDF has similar expected seek time as FCFS, since no positional information is used to make scheduling decisions. SCAN-EDF This strategy is a combination of the SCAN and EDF mechanisms. The request with the earliest deadline is always serviced rst; among requests with the same deadline, the specic one that is rst according to the scan direction is served rst. Since seek optimization is only applied to requests with the same deadline, its eciency depends on how often it can be applied. 4

5 2.2.2 Database-Specic Algorithms Priority-based schemes have been proposed for managing DBMS resources more eciently, These include processor scheduling, disk scheduling, and buer management [6]. The SCAN algorithm was modied to support prioritized requests. Disk requests are grouped on the basis of their priority, and within each group the SCAN algorithm is used. The highest priority group is always serviced rst. The lower priority groups are serviced only when higher priority groups are empty. These new scheduling policies work well in some situations. However, these algorithms treat deadlines/priorities and seek optimization separately. Seek optimization is considered only when the additional requirement is satised. The overall system performance may thus suer in in some cases. We give two examples where this is so. request q1 q2 q4 q3 track distance deadline current head position Figure 1: An example where considering seek time secondary may not provide the best system service. Example 1 The goal of (soft) real-time disk scheduling is to satisfy the deadline of as many disk requests as possible. Thus EDF and EDF-SCAN always service the disk request with the earliest deadline. Figure 1 illustrates an example of a schedule in which these algorithms are inappropriate. According to EDF or EDF-SCAN, disk request q1 with deadline 1 will be serviced rst. To service q1, the disk head needs to move a long distance. After q1 is served, q2, q3, and q4 can no longer be serviced by their deadline due to the large seek time required for the disk arm to move backwards along its seek path. However, if we service q2, q3, and q4 rst, then only q1 misses its deadline. Considering seek time and deadline together can further improve the system performance. 5

6 Example 2 Another example for disk scheduling with priorities is when the higher priority queue is always non-empty and short. In such a situation, the lower priority requests do not get serviced as the system is always busy servicing the high priority requests. Disk utilization can be very low especially if the higher priority requests are spaced far apart. Disk utilization can be increased by promoting the priority level of low priority requests after some interval. In this paper, we present our disk scheduling policy with dynamic request priorities. We will show the benet of our algorithm and the conditions under which it applies. 3 The Priority Inversion Disk Scheduling Algorithm We model the problem with disk requests of two kinds: high priority and low priority requests. The algorithm is easily generalized to multiple priority levels. We are interested in the waiting time of high priority requests. We are not concerned with the waiting time of low priority requests. A low priority request in the low priority queue is promoted to the high priority queue if it does not get serviced for a certain amount of time. An example of this problem can be found in[16, 15]. Naive Algorithm A solution to this problem is to always schedule the high priority requests at the expense of the low priority requests. The low priority requests are serviced only when high priority queue is empty. The total waiting time is thus the sum of the waiting time of all high priority requests. The LOOK scheduling algorithm is used to service requests in each queue. The algorithm is shown in Figure 2. Priority Inversion Algorithm As we described earlier, the problem with the algorithm is that when the high priority queue is always non-empty and short, the disk utilization is low. One way to improve the disk performance in this case is to serve some low priority requests when high priority queue is always short. The disadvantage of this policy is that priority inversions may occur when low priority requests are serviced while high priority requests are 6

7 Loop { } If (High Priority Queue!= Empty) Schedule High Priority Queue Else Schedule Low Priority Queue Figure 2: The disk scheduling algorithm. waiting in the queue. However, higher disk utilization is possible. Loop { } If (High Priority Queue!= Empty) Schedule High Priority Queue Else Schedule Low Priority Queue If (The Length of High Priority Queue <= Threshold) Select The Oldest Request From The Low Priority Queue And Put It In The High Priority Queue Figure 3: A greedy priority inversion disk scheduling algorithm. Figure 3 shows a greedy priority inversion disk scheduling algorithm. In this algorithm, the high priority queue is served rst. If the high priority queue is empty, the low priority queue is serviced. The length of high priority queue is checked. If the length of high priority queue is less than or equal to some T hreshold, we move a disk request from the low priority queue to the high priority queue. Disk utilization is thus increased, however, we incur some amount of priority inversion. For the low-to-high promotion policy, the earliest request is chosen since it will be the rst one to change its priority. We call the previous priority inversion algorithm a greedy algorithm. This is because whenever the length of the high priority queue is less than the T hreshold, a request from the low priority queue is moved up to the high priority queue. This algorithm may not perform well when there are few high priority requests. In 7

8 Loop { } If (High Priority Queue!= Empty) Schedule High Priority Queue Else Schedule Low Priority Queue If (The Length of High Priority Queue <= Threshold) If (The Number of High Priority Requests >= Low_Limit) Select The Oldest Request From The Low Priority Queue And Put It In The High Priority Queue Figure 4: A conservative priority inversion disk scheduling algorithm. such a situation, many low priority requests are put in the high priority queue and the priority inversion may adversely impact the improvement gained by higher disk utilization. In order to handle this situation, the conservative priority inversion algorithm (shown in Figure 4) can be used. In the conservative algorithm, when the length of the high priority queue is less than the T hreshold, the number of high priority requests in the high priority queue is tested. Only when this number is greater than a Low Limit do we move a request from the low priority queue to the high priority queue. None of these algorithms will t in all situations. It is intuitively clear that: the algorithm works well when the disk load is low, the greedy priority inversion algorithm might outperform others when the disk load is high and there are many high priority requests, and the conservative priority inversion algorithm suits the situation in an in-between state. We performed simulations to test these algorithms and the results are discussed in the following sections. 8

9 Parameter Meaning Value T racks Number of tracks on disk 1 SeekF actor Seek time scaling factor.6ms DiskConstant Rotational Latency + Transfer Time 15.ms Table 1: The parameters of the disk device. Parameter Request Interval HP P ercentage P Change Duration Meaning Request arrival interval Percentage of high priority request Priority change duration 4 Simulation Model 4.1 Disk Model Table 2: The parameters of the disk workload. A simulation was built to model the I/O requests in a system with a single data disk[13]. The program models a single-head disk device at the track level. We do not model sectors within tracks since none of the algorithms under study perform rotational optimization. The parameters that control the I/O system conguration are shown in Table 1. The access time for a disk request n tracks away from the current head position is expressed by the following equation: Access(n) = Seek(n) + Rotational Latency + T ransfer T ime In our model, rotational latency and transfer time are grouped together in the single parameter, DiskConstant. Since seek time is non-linear with respect to seek distance in current disk technology[5], we use the following function to calculate the access time: Access(n) = SeekF actor p n + DiskConstant 4.2 Workload Model The parameters that control the workload characteristics are shown in Table 2. Requests for I/O service 9

10 arrive with exponentially distributed inter-arrival times with arrival interval denoted by Request I nterval. The number of high priority requests are controlled by the parameter HP P ercentage. This percentage dictated the mix of high and low priority requests. Thus a HP P ercentage of 3% indicates a mix of 3% high priority and 7% low priority requests. Each request accesses a single track that is chosen uniformly from the range [1; T racks]. When a low priority request waits in the low priority queue for more than P Change Duration seconds, it is moved to the high priority queue. 4.3 Performance Metrics In the following sections we discuss some of the results from the experiments that we performed. For each experiment we ran the simulation using at least 4 dierent random seeds to obtain a 9% condence interval. Each run lasted about 64 seconds where approximately 3 I/O requests were processed, with the Request Interval around 2ms. The primary metric used to measure performance is total response time. Recall that waiting time is collected for only high priority requests. The goal was to schedule I/O requests in order to achieve the lowest possible total response time. Other interesting metrics are average seek time and the total number of priority inversions. These metrics are helpful in analyzing the characteristics of the dierent algorithms. 5 Experimental Results Experiments were done to test the performance of dierent algorithms under dierent workload and parameter settings. First, we chose the Request Interval as 19ms and P Change Duration as 5s. The performance of the greedy priority inversion algorithm was collected with dierent T hreshold and HP P ercentage. Second, we ran these experiments with dierent workloads. Finally, the eect of Request Interval is tested. Based on the experimental results, an adaptive disk scheduling algorithm is presented to deal with dierent situations. 1

11 5.1 Experiment 1: Request Interval=19ms, P Change Duration=5s As discussed in previous section, the greedy priority inversion algorithm might outperform the algorithm when the disk load is high. Thus in our rst experiment, a heavy workload was chosen. The Request Interval is selected as 19ms, which corresponds to 52 arrivals/second. The P Change Duration is set at 5 seconds greedy navie Threshold Priority Inversion Number greedy Threshold Average Seeking Time (ms) greedy Threshold (a) Total Waiting Time (b) Priority Inversion Number (c) Average Seeking Time Figure 5: Request Interval=19ms, P Change Duration=5s, and HP P ercentage= greedy Threshold Priority Inversion Number greedy Threshold Average Seeking Time (ms) greedy Threshold (a) Total Waiting Time (b) Priority Inversion Number (c) Average Seeking Time Figure 6: Request Interval=19ms, P Change Duration=5s, and HP P ercentage=.7. First we compare these two algorithms with HP P ercentage equal to.3, ie. 3% of the requests are high priority, 7% are low priority. The experimental results are plotted in Figure 5. From Figure 5(a), we can see that the greedy priority inversion algorithm has small total waiting time when the T hreshold is greater than 5, and it reaches its maximum reduction of total waiting time to 6% of the algorithm's value when the T hreshold is near 8 or 9. Since the greedy algorithm serves the low priority requests while high priority requests are waiting, it has a large priority inversion number and the priority inversion number increases as the T hreshold becomes large, as we expected (Figure 5(b)). The average seek time of the greedy 11

12 algorithm decreases as the T hreshold increases (Figure 5(c)). This is because when the high priority queue is short, it is lled with low priority requests, resulting in an increase in disk utilization. The performance of the greedy algorithm is worse than the algorithm when the T hreshold is small. The reason is that when the T hreshold is small, and there are few high priority requests, the low priority requests are promoted to the high priority queue. The length of high priority queue is kept around the T hreshold which is a small value and the disk utilization is thus very low. However, as the T hreshold increases, the eect of the greedy algorithm becomes smaller. The large number of priority inversions reduce the potential benet gained by the greedy algorithm. In another experiment, we changed the parameter HP P ercentage to 7% in order to study the situation with more high priority requests. The experimental results are shown in Figure 6. Figure 6 has similar curves to that of Figure 5. From both of the two gures, we can see that the greedy algorithm performs best when T hreshold is near 8 or 9. This is reasonable since when there are 8 or 9 requests in the high priority queue, the disk utilization will not be low; on the other hand, there will also not be too many priority inversions. In the following experiments, we chose 8 as the T hreshold for the greedy algorithm. Total Waiting Time(s) Threshold = Probability of High Priority Request Priority Inversion Number Threshold = Probability of High Priority Request Average Seeking Time (ms) Threshold = Probability of High Priority Request (a) Total Waiting Time (b) Priority Inversion Number (c) Average Seeking Time Figure 7: Request Interval=19ms, P Change Duration=5s. The greedy algorithm and the algorithm are compared with dierent HP P ercentages (from.1 to.9). The results are shown in Figure 7. The greedy algorithm outperforms the algorithm when HP P ercentage is greater than.2. The greedy algorithm reaches its maximum total waiting time reduction of 48% when HP P ercentage is around.5. When the HP P ercentage is very small, low priority requests are served most of the time. Using the algorithm, the low priority queue is serviced when the queue 12

13 length is large. It thus performs better than the greedy algorithm when the high priority queue, which is lled with low priority requests, is serviced with its length at 8. When HP P ercentage is large, the high priority queue is always long, causing the greedy algorithm to have less chance to take eect. Therefore the greedy algorithm performs best when HP P ercentage is around.5. In any case, the greedy algorithm outperforms the algorithm when HP P ercentage is larger than Experiment 2: Vary Workload In this experiment, we compare the algorithm and the greedy algorithm under dierent load conditions. We vary the disk request arrival intervals from 15ms to 5ms. The results are shown in Figure 8, 9, and 1 where the HP P ercentage is.3,.5, and.7 respectively. Due to the range dierence, each gure is partitioned into two parts where the performance dierence is shown more clearly Average Arrival Interval (ms) (a) Request Interval in [15ms, 18ms] Average Arrival Interval (ms) (b) Request Interval in [19ms, 5ms] Figure 8: HP P ercentage=.3, P Change Duration=5s. We observed that the greedy algorithm performs better when the load is high (Figure 8(a), 9(a), 1(a)), i.e. with the request arrival interval between 15ms and 19ms. However, the algorithm has a smaller total waiting time when the arrival interval is larger than 22ms. When the arrival interval is in between 19ms and 22ms, the better algorithm depends on the percentage of high priority requests. The more high priority requests, the better performance the greedy algorithm (Figure 8(b), 9(b), 1(b)). One observes that the algorithm is very sensitive to the load condition when the arrival interval is between 19ms and 22ms (call this the sensitive zone). Its performance changes dramatically compared to the greedy algorithm at points in the sensitive zone. When the load condition can not be predicted precisely, 13

14 Average Arrival Interval (ms) (a) Request Interval in [15ms, 18ms] Average Arrival Interval (ms) (b) Request Interval in [19ms, 5ms] Figure 9: HP P ercentage.5, P Change Duration=5s Average Arrival Interval (ms) (a) Request Interval in [15ms, 18ms] Average Arrival Interval (ms) (b) Request Interval in [19ms, 5ms] Figure 1: HP P ercentage=.7, P Change Duration=5s. it is dicult to decide which algorithm to use in the sensitive zone. In this situation, the greedy algorithm is \too greedy." The greedy algorithm performs poorly in this case as it moves low priority requests to high priority queue too aggressively. Thus a good candidate algorithm in the sensitive zone might be the conservative algorithm. As discussed earlier, the Low Limit is one important parameter in the conservative algorithm. Figure 11 shows the result of the conservative algorithm compared with the and greedy algorithms in the sensitive zone. The conservative algorithm performance is in between that of the greedy algorithm and the algorithm. When the arrival interval is near 19ms, the conservative algorithm performs better than the algorithm but has less performance improvement than the greedy algorithm. However, the conservative algorithm still performs better than or comparably with the algorithm when the load is 14

15 greedy Low_Limit= greedy Low_Limit=3 Low_Limit= greedy Low_Limit=3 Low_Limit= Average Arrival Interval (ms) Average Arrival Interval (ms) Average Arrival Interval (ms) (a) HP P ercentage=.3 (b) HP P ercentage=.5 (c) HP P ercentage=.7 Figure 11: P Change Duration=5s. light in the sensitive zone. A good scheduling algorithm is thus an adaptive composition of the three algorithms that customizes itself based on the changing load. According to our simulation results, we can use the following adaptive disk scheduling algorithm: IF (HP_Percentage <=.3) { IF (Request_Interval < 19) Use the greedy algorithm (); IF (Request_Interval = 19) Use the conservative algorithm (Low_Limit = 5); IF (Request_Interval > 19) Use the algorithm; } ELSE { IF (Request_Interval <= 19) Use the greedy algorithm (); IF (Request_Interval = 2) Use the conservative algorithm (Low_Limit = 4); IF (Request_Interval = 21) Use the conservative algorithm (Low_Limit = 3); 15

16 IF (Request_Interval >= 22) Use the algorithm; } The adaptive algorithm always performs better than the algorithm. The adaptive algorithm is also robust. By this we mean that the algorithm is stable in the presence of errors in load condition measurement within the sensitive zone. For example, if the load condition is 2ms and the measurement is 22ms, the adaptive algorithm still performs better or comparably with the algorithm. The more accurately the load condition is measured, the better the adaptive algorithm performs. It is easy to nd the performance crossover point of the greedy and algorithms. When the disk serves faster than the request arrival rate, the priority inversion caused by the greedy algorithm will degrade overall system performance. On the other hand, when the disk is overloaded, the low priority requests rarely have any chance to be serviced. Increasing disk utilization by servicing some low priority requests helps improve the overall I/O system performance. From experiment 1, we know that the average seek time is around 4 to 5 ms. The DiskConstant is 15ms. Thus the total disk access time is about 2ms. That is why a sensitive zone is formed when the Request Interval is between 19ms to 22ms. The adaptive algorithm is useful in situations when the disk load is low, the algorithm works ne and the clients are rewarded with small waiting times, and in situations when the server is overloaded overloaded, applying the greedy algorithm results in an up to% reduction in total waiting time. More clients are served compared to using the algorithm. 5.3 Experiment 3: Vary P Change Duration An important parameter not tested so far is P Change Duration, which species how long a low priority request waits before it is promoted. Figure 12 compares the greedy and algorithms with a Request Interval of 19ms. Three HP P ercentage,.3,.5, and.7 are used in the experiments. We vary the P Change Duration from to 16 seconds. The greedy algorithm performs better when P Change Duration is small. When HP P ercentage is small (Figure refexp31(a)), the algorithm works better as the P Change Duration becomes large. However, the more high priority requests (Figure refexp31(a), (b)) we 16

17 have, the better the greedy algorithm performs. Note that the total time we run in the previous experiment is 64 seconds and the greedy algorithm will not take eect during the rst and last P Change Duration seconds of the experiment. When P Change Duration is large, e.g. greater than 8 seconds, the eective time of the greedy algorithm is very short compared to the running time. A longer experiment was run and the results are shown in Figure 13. We can see from the gure that the greedy algorithm outperforms the algorithm for all the P Change Duration values ranging from to 16 seconds. The larger the HP P ercentage is, the more benet is achieved from the greedy algorithm Priority Changing Duration (s) Priority Changing Duration (s) Priority Changing Duration (s) (a) HP P ercentage=.3 (b) HP P ercentage=.5 (c) HP P ercentage=.7 Figure 12: Request Interval=19ms, run time=64s Priority Changing Duration (s) Priority Changing Duration (s) Priority Changing Duration (s) (a) HP P ercentage=.3 (b) HP P ercentage=.5 (c) HP P ercentage=.7 Figure 13: Request Interval=19ms, run time=3s. 17

18 6 Conclusion High performance servers must manage their I/O resources eciently and consistently. Heavily loaded systems, such as World Wide Web servers or future digital library systems, place very large loads on the systems' storage and I/O subsystems. In digital multimedia systems, disk requests are assigned priorities corresponding to the varying urgencies of client requests. Disk scheduling algorithms fundamentally determine how fast I/O requests are processed, as well as how consistent and low response times may be achieved. In this paper, a new greedy priority inversion disk scheduling algorithm is presented and detailed simulations done to evaluate and compare the new algorithm with a algorithm. Our experimental results show that when the disk load is light, the algorithm performs commendably. When the disk load is high with many high priority requests, the new algorithm outperforms the algorithm with a maximum total response time reduction of up to 5%. In situations where the demands placed on server I/O subsystems are heavy, the new algorithm is appropriate. A conservative algorithm reduces sensitivity to load changes around the crossover point from to greedy and vice versa. We also present an adaptive disk scheduling algorithm where the I/O subsystem can select the proper scheduling algorithm according to dierent load conditions and the percentage of high priority requests. The adaptive algorithm performs consistently better than any single scheduling algorithm. The adaptive system is also relatively insensitive to changes in the load around the sensitive zone when arrivals in disk requests just match the service capacity of the disk. References [1] J. Abate and H. Dubner. Optimizing the performance of a drum-like storage. IEEE Trans. Comput., 18(11):992{997, November [2] R.K. Abbott and H. Garcia-Molina. Scheduling real-time transactions with disk resident data. In Proc. of the 15th International Conference on Very Large Data Bases, Amsterdam,

19 [3] R.K. Abbott and H. Garcia-Molina. Scheduling I/O requests with deadlines: a performance evaluation. In Proc. of the 11th Real-Time Systems Symposium, pages 113{124, 199. [4] D. Bitton. Arm scheduling in shadowed disks. In Digest of Papers, COMPCON Spring'89, Thirty-Fourth IEEE Computer Society International Conference: Intellectual Leverage, pages 132{136, [5] D. Bitton and J. Gray. Disk shadowing. In Proc. of the 14th VLDB Conference, pages 331{338, [6] M.J. Carey, R. Jauhari, and M. Livny. Priority in DBMS resource scheduling. In Proc. of the 15th International Conference on Very Large Data Bases, Amsterdam, [7] M.S. Chen, D.D. Kandlur, and P.S. Yu. Optimization of the group sweeping scheduling (GSS) with heterogeneous multimedia streams. In Proc. of the First ACM International Conference on Multimedia, pages 235{241, Anaheim, CA, [8] E.G. Coman and M. Hofri. On the expected performance of scanning disks. SIAM J. Comput., 11(1):6{7, February [9] S. Daniel and R. Geist. V-SCAN: an adaptive disk scheduling algorithm. In Proc. of the IEEE International Symposium on Computer System Organization, [1] P.J. Denning. Eects of scheduling on le memory operations. Proc. AFIPS 1967 SJCC, 3:9{21. [11] H. Frank. Analysis and optimization of disk storage devices for time-sharing systems. J. ACM, 16(4):62{62, October [12] R. Geist and S. Daniel. A continuum of disk scheduling algorithms. ACM Transactions on Computer Systems, 5(1):77{92, February [13] R. Jain. The art of computer systems performance analysis: techniques for experiment design, measurement, simulation, and modeling. John Wiley & Songs, Inc., New York, [14] W. Kim and J. Srivastava. Enhancing real-time DBMS performance with multiversion data and priority based disk scheduling. In Proc. of the 12th Real-Time Systems Symposium, pages 222{231,

20 [15] Y. Li and R. Campbell. A dynamic priority-based scheduling method in distributed systems. In Proceedings of the International Conference on Parallel and Distributed Processing Techniques and Applications (PDPTA'95), pages 177{186, November [16] Y. Li, V. Puvvada, and R. Campbell. Dynamic retrieval of remote digital object. In Proc. of ACM Fourth International Conference on Information and Knowledge Management (CIKM'95), pages 182{ 187, Maryland, November [17] T. Lin and W. Tarng. Scheduling periodic and aperiodic tasks in hard real-time computing systems. In Proc. SIGMETRICS, ACM Press, New York, pages 31{38, [18] P. Lougher and D. Shepherd. The design of a storage services for continuous media. The Computer Journal, 36(1):32{42, [19] R. Rowe. Interactive music system. MIT Press, Cambridge, MA, [2] M.M. Salem, A.O. El-Gwad, H.M. Harb, and O.A. Zahran. Computers operating systems: V-SSTF dynamic disk scheduling technique. In Proc. of the Third International Conference on Software Engineering for Real Time System, pages 254{259, London, UK, [21] R. Steinmetz and K. Nahrstedt. Multimedia: computing, communications, and applications. Prentice Hall PTR, [22] T.J. Teorey and T.B. Pinkerton. A comparative analysis of disk scheduling policies. Communications of the ACM, 15(3):177{184, March [23] Thomas T. Kwan and Robert E. McGrath and Daniel A. Reed. NCSA's World Wide Web server: Design and performance. IEEE Computer, pages 68{74, November [24] N.C. Wilhelm. An anomaly in disk scheduling: a comparison of FCFS and SSTF seek scheduling using an empirical model for disk accesses. Communications of the ACM, 19(1):13{17, January [25] J. Yee and P.V. Vatarya. Disk scheduling policies for real-time multimedia applications. Technical report, University of California, Berkeley, CA, August