This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
General Schedulers for the Pinwheel Problem Based on Double-Integer Reduction
June 1992 (vol. 41 no. 6)
pp. 755-768

The pinwheel is a hard-real-time scheduling problem for scheduling satellite ground stations to service a number of satellites without data loss. Given a multiset of positive integers (instance) A=(a/sub 1/, . . . a/sub n/), the problem is to find an infinite sequence (schedule) of symbols from (1,2, . . . n) such that there is at least one symbol i within any interval of a/sub i/ symbols (slots). Not all instances A can be scheduled; for example, no 'successful' schedule exists for instances whose density is larger than 1. It has been shown that any instance whose density is less than 2/3 can always be scheduled. Two new schedulers are proposed which improve this 2/3 result to a new 0.7 density threshold. These two schedulers can be viewed as a generalization of the previously known schedulers, i.e. they can handle a larger class of pinwheel instances including all instances schedulable by the previously known techniques.

[1] M. Y. Chan and F. Chin, "Schedulers for larger classes of pinwheel instances,"Algorithmica, to be published.
[2] S. K. Dhall and C. L. Liu, "On a real-time scheduling problem,"Oper. Res., vol. 26, no. 1, pp. 127-140, 1978.
[3] J. Du, "On a graph representation of cyclic schedules in pinwheel scheduling," Dep. Comput. Sci., Hong Kong Univ. of Sci. and Technol., Hong Kong, manuscript, 1991.
[4] R. Holte, A. Mok, L. Rosier, I. Tulchinsky, and D. Varvel, "The pinwheel: A real-time scheduling problem," inProc. 22nd Hawaii Int. Conf. Syst. Sci., Jan. 1989, pp. 693-702.
[5] R. Holte, L. Rosier, I. Tulchinsky, and D. Varvel, "Pinwheel scheduling with two distinct numbers,"Theoret. Comput. Sci., to be published.
[6] D. E. Knuth,The Art of Computer Programming, Vol. 1. Reading, MA: Addison-Wesley, 1973.
[7] E. L. Lawler and C. U. Martel, "Scheduling periodically occurring tasks on multiple processors,"Inform. Processing Lett., vol. 12, no. 1, pp. 9-12, 1981.
[8] J.Y-T. Leung, "A new algorithm for scheduling periodic, real-time tasks,"Algorithmica, vol. 4, pp. 209-219, 1989.
[9] J.Y-T. Leung and M. L. Merrill, "A note on preemptive scheduling of periodic, real-time tasks,"Inform. Processing Lett., vol. 11, pp. 115-118, 1980.
[10] J.Y-T. Leung and J. Whitehead, "On the complexity of fixed-priority scheduling of periodic, real-time tasks,"Perform. Eval., vol. 2, pp. 237-250, 1982.
[11] C. L. Liu and J. W. Layland, "Scheduling algorithms for multiprogramming in a hard real-time environment,"J. ACM, vol. 20, no. 1, pp. 46-61, Jan. 1973.
[12] A. K. Mok, "Fundamental design problems of distributed systems for the hard-real-time environment," Ph.D. dissertation, M.I.T. Lab. for Comput. Sci., May 1983.
[13] W. D. Wei and C. L. Liu, "On a periodic maintenance problem,"Oper. Res. Lett., vol. 2, no. 2, pp. 90-93, 1983.

Index Terms:
pinwheel problem; double-integer reduction; scheduling problem; satellite ground stations; satellite ground stations; scheduling.
Citation:
M.Y. Chan, F.Y.L. Chin, "General Schedulers for the Pinwheel Problem Based on Double-Integer Reduction," IEEE Transactions on Computers, vol. 41, no. 6, pp. 755-768, June 1992, doi:10.1109/12.144627
Usage of this product signifies your acceptance of the Terms of Use.