This Article 
 Bibliographic References 
 Add to: 
Distance-Constrained Scheduling and Its Applications to Real-Time Systems
July 1996 (vol. 45 no. 7)
pp. 814-826

Abstract—In hard real-time systems, each task must not only be functionally correct but also meet its timing constraints. A common approach to characterizing hard real-time tasks with repetitive requests is the periodic task model [1]. In the periodic task model, every task needs to be executed once during each of its periods. The execution of a task in one period is independent of the execution of the same task in another period. Hence, the executions of the same task in two consecutive periods may be right next to each other, or at the far ends of the two periods. While the periodic task model can serve as a simple paradigm for scheduling tasks with repetitive requests, it may not be suitable for all real-time applications. For example, in some real-time systems, the temporal distance between the finishing times of any two consecutive executions of the same task must be less than or equal to a given value. In other words, each execution of a task has a deadline relative to the finishing time of the previous execution of the same task. Scheduling algorithms designed for the periodic task model may not provide efficient solutions for tasks with temporal distance constraints.

In this paper, we propose the (preemptive) distance-constrained task system model which can serve as a more intuitive and adequate scheduling model for "repetitive" task executions. We design an efficient scheduling scheme for the model, and derive a schedulability condition for the scheduling scheme. The schedulability condition is a measure for providing the fundamental predictability requirement in hard real-time applications. To show the usefulness of the distance-constrained task model and its scheduling scheme, we also discuss how to apply the scheduling scheme to real-time sporadic task scheduling and to real-time communications.

[1] 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.
[2] C.-C. Han and K.-J. Lin, "Scheduling Jobs with Temporal Consistency Constraints," Proc. Sixth IEEE Workshop Real-Time Operating Systems and Software, pp. 18-23,Pittsburgh, May 1989.
[3] C.-C. Han, K.-J. Lin, and J.W.-S. Liu, "Scheduling Jobs with Temporal Distance Constraints," SIAM J. Computing, vol. 24, pp. 1,104-1,121, Oct. 1995.
[4] A. Elsaadany, M. Singhal, and M. Liu, "Priority Communication Schemes on Local Area Networks for Multimedia Traffic," Proc. 19th Conf. Local Computer Networks, pp. 372-379, Oct. 1994.
[5] J. Boudec, “The Asynchronous Transfer Mode: A Tutorial,” Computer Networks and ISDN Systems, Vol. 24, 1992, pp. 279–309.
[6] M. Kawarasaki and B. Jabbari, “B-ISDN Architecture and Protocol,” IEEE J. Selected Areas in Communications, Vol. 9 No. 9 Dec. 1991, pp. 1405–1415.
[7] T. Ng and V. Patel, "Timely Failure Detection in a Large Distributed Real-Time System," Proc. Int'l Workshop Object Oriented Real-Time Dependable Systems,Dana Point, Calif., 1994.
[8] "Coding of Moving Pictures and Associated Audio," SC29/WG11 Committee (MPEG) Draft of Standard ISO-IEC/JTC1 SC29, Nov. 1991.
[9] 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.
[10] M.Y. Chan and F. Chin, "Schedulers for Larger Classes of Pinwheel Instances," Algorithmica, vol. 9, pp. 425-462, 1993.
[11] S. Cheng and J.A. Stankovic,“Scheduling algorithms for hard real-time systems-a brief survey,” Hard Real-Time Systems, IEEE Press, vol. 88, pp. 88-173.
[12] J. Lehoczky, L. Sha, and Y. Ding, The Rate Monotonic Scheduling Algorithm: Exact Characterization and Average Case Behavior Proc. IEEE Real-Time Systems Symp., pp. 166-171, 1989.
[13] D.W. Leinbaugh, "Guaranteed Response Time in a Hard Real-Time Environment," IEEE Trans. Software Eng., Jan. 1980.
[14] J.Y.-T. Leung and M.L. Merrill, "A Note on Preemptive Scheduling of Periodic, Real-Time Tasks," Information Processing Letters, vol. 11, pp. 115-118, Nov. 1980.
[15] J.Y.-T. Leung and J. Whitehead, "On the Complexity of Fixed-Priority Scheduling of Periodic, Real-Time Tasks," Performance Evaluation, vol. 2, pp. 237-250, 1982.
[16] 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.
[17] 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.
[18] C.-C. Han and K.-J. Lin, "Scheduling Real-Time Computations with Separation Constraints," Information Processing Letters, vol. 42, May 1992.
[19] C.M. Aras, J.F. Kurose, D.S. Reeves, and H. Schulzrinne, “Real-Time Communication in Packet-Switched Networks,” Proc. IEEE, vol. 82, no. 1, pp. 122-139, Jan. 1994.
[20] “IEEE Standards for Local and Metropolitan Area Networks: Distributed Queue Dual Bus (DQDB) Subnetwork of a Metropolitan Area Network (MAN),” IEEE802.6, July 1991.
[21] C.-C. Han, C.-J. Hou, and K.G. Shin, "On Slot Allocation for Time-Constrained Messages in DQDB Networks," Proc. IEEE INFOCOM '95, pp. 1,164-1,171,Boston, Apr. 1995.
[22] 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.

Index Terms:
Distance-constrained task systems, (temporal) distance constraints, periodic task systems, pinwheel problem, real-time scheduling/communication.
Ching-Chih Han, Kwei-Jay Lin, Chao-Ju Hou, "Distance-Constrained Scheduling and Its Applications to Real-Time Systems," IEEE Transactions on Computers, vol. 45, no. 7, pp. 814-826, July 1996, doi:10.1109/12.508320
Usage of this product signifies your acceptance of the Terms of Use.