New algorithms for the disk scheduling problem

Processor speed and memory capacity are increasing several times faster than disk speed. This disparity suggests that disk I/O performance will become an important bottleneck. Methods are needed for using disks more efficiently. Past analysis of disk scheduling algorithms has largely been experimental and little attempt has been made to develop algorithms with provable performance guarantees. We consider the following disk scheduling problem. Given a set of requests on a computer disk and a convex reachability function which determines how fast the disk head travels between tracks, our goal is to schedule the disk head so that it services all the requests in the shortest time possible. We present a 3/2-approximation algorithm (with a constant additive term). For the special case in which the reachability function is linear we present an optimal polynomial-time solution. The disk scheduling problem is related to the special case of the asymmetric Traveling Salesman Problem with the triangle inequality (ATSP-/spl Delta/) in which all distances are either 0 or some constant /spl alpha/. We show how to find the optimal tour in polynomial time and describe how this gives another approximation algorithm for the disk scheduling problem. Finally we consider the on-line version of the problem in which uniformly-distributed requests arrive over time. We present an algorithm (related to the above ATSP-/spl Delta/) that appears to give higher throughput than previously existing head scheduling algorithms.

[1]  John Wilkes,et al.  An introduction to disk drive modeling , 1994, Computer.

[2]  Ján Plesník,et al.  The NP-Completeness of the Hamiltonian Cycle Problem in Planar Digraphs with Degree Bound Two , 1979, Inf. Process. Lett..

[3]  Neil C. Wilhelm.  An anomaly in disk scheduling: a comparison of FCFS and SSTF seek scheduling using an empirical model for disk accesses , 1976, CACM.

[4]  Calvin C. Gotlieb,et al.  Performance of Movable-Head Disk Storage Devices , 1973, JACM.

[5]  Federico Malucelli,et al.  HAMILTONIAN PATHS ALGORITHMS FOR DISK SCHEDULING , 1994 .

[6]  Robert Geist,et al.  A continuum of disk scheduling algorithms , 1987, TOCS.

[7]  Walter C. Oney.  Queueing Analysis of the Scan Policy for Moving-Head Disks , 1975, JACM.

[8]  David Kotz,et al.  A Detailed Simulation Model of the HP 97560 Disk Drive , 1994 .

[9]  Alan M. Frieze,et al.  On the worst-case performance of some algorithms for the asymmetric traveling salesman problem , 1982, Networks.

[10]  R. P. Dilworth,et al.  A DECOMPOSITION THEOREM FOR PARTIALLY ORDERED SETS , 1950 .

[11]  Toby J. Teorey,et al.  A comparative analysis of disk scheduling policies , 1972, CACM.

[12]  Micha Hofri.  Disk scheduling: FCFS vs.SSTF revisited , 1980, CACM.

[13]  Mary Baker,et al.  Non-volatile memory for fast, reliable file systems , 1992, ASPLOS V.

[14]  Yale N. Patt,et al.  Scheduling algorithms for modern disk drives , 1994, SIGMETRICS 1994.

[15]  John Wilkes,et al.  UNIX Disk Access Patterns , 1993, USENIX Winter.

[16]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[17]  John Wilkes,et al.  Disk scheduling algorithms based on rotational position , 1991 .

[18]  Kenneth Steiglitz,et al.  Combinatorial Optimization: Algorithms and Complexity , 1981 .

[19]  Margo I. Seltzer,et al.  Disk Scheduling Revisited , 1990 .

[20]  H. Kuhn.  The Hungarian method for the assignment problem , 1955 .

[21]  Yale N. Patt,et al.  On-line extraction of SCSI disk drive parameters , 1995, SIGMETRICS '95/PERFORMANCE '95.

[22]  James Lau,et al.  File System Design for an NFS File Server Appliance , 1994, USENIX Winter.

[23]  Edward G. Coffman,et al.  Analysis of Scanning Policies for Reducing Disk Seek Times , 1972, SIAM J. Comput..

[24]  Kenneth P. Bogart,et al.  Introductory Combinatorics , 1977 .