This Article 
 Bibliographic References 
 Add to: 
Pfair Scheduling of Generalized Pinwheel Task Systems
July 1998 (vol. 47 no. 7)
pp. 812-816

Abstract—The scheduling of generalized pinwheel task systems is considered. It is shown that pinwheel scheduling is closely related to the fair scheduling of periodic task systems. This relationship is exploited to obtain new scheduling algorithms for generalized pinwheel task systems. When compared to traditional pinwheel scheduling algorithms, these new algorithms are both more efficient from a run-time complexity point of view, and have a higher density threshold, on a very large subclass of generalized pinwheel task systems.

[1] M. Ajtai, J. Aspnes, M. Naor, Y. Rabani, L. Schulman, and O. Waarts, "Fairness in Scheduling," Proc. Sixth Ann. ACM-SIAM Symp. Discrete Algorithms, pp. 477-485, Jan. 1995.
[2] A. Bar-Noy, A. Mayer, B. Schieber, and M. Sudan, "Guaranteeing Fair Service to Persistent Dependent Tasks," SIAM J. Computing, vol. 28, no. 4, pp. 1,168-1,189, Aug. 1998.
[3] S. Baruah, "Fairness in Periodic Real-Time Scheduling," Proc. 16th Real-Time Systems Symp., pp. 200-209,Pisa, Italy, 1995.
[4] S. Baruah and A. Bestavros, "Timely and Fault-Tolerant Data Access from Broadcast Disks: A Pinwheel-Based Approach," Proc. Workshop Databases: Active&Real-Time, pp. 45-49,Rockville, Md., Nov. 1996.
[5] S. Baruah, N. Cohen, G. Plaxton, and D. Varvel, "Proportionate Progress: A Notion of Fairness in Resource Allocation," Algorithmica, vol. 15, no. 6, pp. 600-625, June 1996. Extended Abstract in Proc. 1993 ACM Ann. Symp. Theory of Computing.
[6] S. Baruah, L. Rosier, and D. Varvel, "Static and Dynamic Scheduling of Sporadic Tasks for Single-Processor Systems," Proc. Third Euromicro Workshop Real-time Systems, June 1991.
[7] S. Baruah, J. Gehrke, and G. Plaxton, "Fast Scheduling of Periodic Tasks on Multiple Resources," Proc. Ninth Int'l Parallel Processing Symp., pp. 280-288. IEEE CS Press, Apr. 1995. Extended version available via anonymous ftp fromas Technical Report TR-95-02.
[8] M. Chan and F. Chin, Schedulers for the Pinwheel Problem Based on Double-Integer Reduction IEEE Trans. Computers, vol. 41, no. 6, pp. 755-768, June 1992.
[9] M.Y. Chan and F. Chin, "Schedulers for Larger Classes of Pinwheel Instances," Algorithmica, vol. 9, no. 5, pp. 425-462, 1993.
[10] M. Dertouzos, "Control Robotics: The Procedural Control of Physical Processors," Proc. IFIP Congress, pp. 807-813, 1974.
[11] L. Ford and D. Fulkerson, Flows in Networks.Princeton, N.J.: Princeton Univ. Press, 1962.
[12] C.-C. Han and K.-J. Lin, “Scheduling Distance-Contrained Real-Time Tasks,” Proc. IEEE 13th Real-Time Systems Symp., pp. 300-308, Dec. 1992.
[13] C.-C. Han and K.G. Shin, "A Polynomial-Time Optimal Synchronous Bandwidth Allocation Scheme for the Timed-Token MAC Protocol," Proc. IEEE INFOCOM '95,Boston, Apr. 1995.
[14] C.-C. Han and K.G. Shin, “Real-Time Communication in FieldBus Multiaccess Network,” Proc. IEEE Real-Time Technology and Applications Symp., pp. 86-95, May 1995.
[15] R. Holte, A. Mok, L. Rosier, I. Tulchinsky, and D. Varvel, The Pinwheel: A Real-Time Scheduling Problem Proc. 22nd Hawaii Int'l Conf. System Science, pp. 693-702, Jan. 1989.
[16] R. Holte, L. Rosier, I. Tulchinsky, and D. Varvel, "Pinwheel Scheduling with Two Distinct Numbers," Theoretical Computer Science, vol. 100, no. 1, pp. 105-135, June 1992.
[17] C.-W. Hsueh, K.-J. Lin, and N. Fan, “Distributed Pinwheel Scheduling with End-to-End Timing Constraints,” Proc. IEEE Real-Time Systems Symp., Dec. 1995.
[18] S.S. Lin and K.J. Lin, "A Pinwheel Scheduler for Three Distinct Numbers with a Tight Schedulability Bound," Algorithmica, vol. 19, no. 4, pp. 411-426, 1997.
[19] C. Liu, "Scheduling Algorithms for Multiprocessors in a Hard Real-Time Environment," JPL Space Programs Summary 37-60, vol. II, pp. 28-37, 1969.
[20] C.L. Liu and J.W. Layland, “Scheduling Algorithms for Multiprogramming in a Hard Real-Time Environment,” J. ACM, vol. 20, no. 1, pp. 40-61, 1973.
[21] A. Mok, "Task Management Techniques for Enforcing ED Scheduling on a Periodic Task Set," Proc. Fifth IEEE Workshop Real-Time Software and Operating Systems, pp. 42-46,Washington, D.C., May 1988.

Index Terms:
Generalized pinwheels, fairness, real-time scheduling, density threshold.
Sanjoy K. Baruah, Shun-Shii Lin, "Pfair Scheduling of Generalized Pinwheel Task Systems," IEEE Transactions on Computers, vol. 47, no. 7, pp. 812-816, July 1998, doi:10.1109/12.709381
Usage of this product signifies your acceptance of the Terms of Use.