skip to main content
article
Free Access

On the execution of parallel programs on multiprocessor systems—a queuing theory approach

Published:01 April 1990Publication History
Skip Abstract Section

Abstract

The new class of queuing models, called Synchronized Queuing Networks, is proposed for evaluating the performance of multiprogrammed and multitasked multiprocessor systems, where workloads consists of parallel programs of similar structure and where the scheduling discipline is first-come-first-serve.

Pathwise evolution equations are established for these networks that capture the effects of competition for processors and the precedence constraints governing tasks executions.

A general expression is deduced for the stability condition of such queuing networks under general statistical assumptions (basically the stationarity and the ergodicity of input sequences), which yields the maximum program throughput of the multiprocessor system, or equivalently, the maximum rate at which programs can be executed or submitted. The proof is based on the ergodic theory of queues.

Basic integral equations are also derived for the stationary distribution of important performance criteria such as the workload of the queues and program response times. An iterative numerical schema that converges to this solution is proposed and various upper and lower bounds on moments are derived using stochastic ordering techniques.

References

  1. 1 ANDREWS, G. R., AND SCHNEIDER, F.B. Concepts and notations for concurrent programming. ACM Comput. Surv. 15, 1 (Mar. 1983), 3-43. Google ScholarGoogle Scholar
  2. 2 BACCELLI, F. Two parallel queues created by arrivals with two demands: The M/G/2 symmetrical case. INRIA Rapport de Recherche, No. 426. INRIA, Valbonne, France, July 1985.Google ScholarGoogle Scholar
  3. 3 BACCELLI, F., AND BRI~MAUD, P. Palm probabilities and stationary queues. In Lecture Notes in Statistics, No. 41. Springer-Verlag, New York, 1987.Google ScholarGoogle Scholar
  4. 4 BACCELLI, F., AND LIU, Z. On the stability condition of a precedence-based queueing discipline. Adv. Appl. Prob. 21 (1989), 883-887.Google ScholarGoogle Scholar
  5. 5 BACCELLI, F., AND LIU, Z. On a class of stochastic evolution equations. Ann. Prob., to appear.Google ScholarGoogle Scholar
  6. 6 BACCELLI, F., AND MAKOWSKI, A. Simple computable bounds for the fork-join queue. In Proceedings of the Conference for Information Science Systems. Johns Hopkins Univ., Baltimore, Md., March 1985, pp. 436-441.Google ScholarGoogle Scholar
  7. 7 BACCELLI, F., MAKOWSKI, A., AND SHWARTZ, A. Fork-join queue and related systems with synchronization constraints: Stochastic ordering, approximations and computable bounds. J. Adv. Prob. 21 (1989), 629-660.Google ScholarGoogle Scholar
  8. 8 BACCELLI, F., MASSEY, W. A., AND TOWSLEY, D. Acyclic fork-join queuing networks. 3. ACM 36, 3 (July 1989), 615-642. Google ScholarGoogle Scholar
  9. 9 BATTAREL, G. J., AND SAVARY, H.F. Interprocess communication system of the MT35 digital exchange. Comput. Commun. Rev. 13, 2 (1983), 197-203. Google ScholarGoogle Scholar
  10. 10 BARLOW, R., ANO PROSCHAN, F. Statistical Theory of Reliability and Life Testing. Holt, Rinehart and Winston, New York, 1975.Google ScholarGoogle Scholar
  11. 11 CHEN, W. K. Applied graph theory. In Applied Mathematics and Mechanics, H. A. Lauwerier and W. T. Koiter, eds. North-Holland, New York, I971.Google ScholarGoogle Scholar
  12. 12 CHU, W. W., AND LEUNO, K.K. Module replication and assignment for real-time distributed processing systems. Proc. IEEE 75, 5 (May 1987), 547-562.Google ScholarGoogle Scholar
  13. 13 COFFMAN, E. G., AND DENNINO, P.J. Operating Systems Theory. Prentice-Hall, New York, 1972. Google ScholarGoogle Scholar
  14. 14 COSNARD, M., AND ROBERT, Y. Algorithmique Parallble: Une E, tude de ComplexitY. Techniques et Sciences Informatiques, Paris, France, 1987.Google ScholarGoogle Scholar
  15. 15 DEVROVE, L.P. Inequalities for the completion times of stochastic PERT networks. Math. Oper. Res. 4 (1980), 441-447.Google ScholarGoogle Scholar
  16. 16 DODIN, B. Bounding the project completion time distribution in PERT networks. Oper. Res. 33, 4 (July-Aug. 1985), 862-881.Google ScholarGoogle Scholar
  17. 17 DUNCAN, T., AND HUEN, W.H. Software structure of no. 5 ESS-A distributed telephone switching system. IEEE Trans. Commun. COM-30, 6 (1982), 1379-1385.Google ScholarGoogle Scholar
  18. 18 ELMAGHRABY, S.E. On the expected duration of PERT type networks. Manage. Sci. 13 (1967), 469-481.Google ScholarGoogle Scholar
  19. 19 FLATTO, L., AND HAHN, S. Two parallel queues created by arrivals with two demands. SIAM J. AppL Math 44 (1984), 1041-1053.Google ScholarGoogle Scholar
  20. 20 GELENBE, E., AND LIU, Z. Performance analysis approximations for parallel processing on multiprocessor systems. In IFIP Working Conference on Parallel Processing (Pisa, Italy, Apr.) North-Holland, New York, 1988, pp. 363-375.Google ScholarGoogle Scholar
  21. 21 GELENBE, E., MONTAGNE, E., SUROS, R., AND WOODSIDE, C.M. A performance model of blockstructured parallel programs. In Proceedings of the International Workshop on Parallel Algorithms and Architectures, M. Cosnard, et al., eds. North-Holland, New York, 1986, pp. 127-138. Google ScholarGoogle Scholar
  22. 22 GELENBE, E., NELSON, P., PHILIPS, T., AND TANTAWI, A. The asymptotic processing time for a model of parallel processing. In Proceedings of the National Computer Conference (Las Vegas). 1986.Google ScholarGoogle Scholar
  23. 23 HOARE, C. A. R. Communicating sequential processes. Commun. ACM 21, 8 (Aug. 1978), 666-677. Google ScholarGoogle Scholar
  24. 24 HOLLIDAY, M. A., AND VERNON, M.K. Exact performance estimates for multiprocessor memory and bus interference. IEEE Trans. Comput. C-36, I (Jan. 1987), 76-85. Google ScholarGoogle Scholar
  25. 25 HUANG, J.P. Modeling of software partition for distributed real-time applications. IEEE Trans. Sofiw. Eng. SE-11, l0 (1985), lll3-1 I26. Google ScholarGoogle Scholar
  26. 26 JONES, A. K., AND SCHWARZ, P. Experience using multiprocessor systems~A status report. ACM Comput. Surv. 12, 2 ( June 1980), 121-165. Google ScholarGoogle Scholar
  27. 27 KINGMAN, J. F.C. The ergodic theory of subadditive stochastic processes. J. Roy. Statist. Soc. Set. B 30 (1968), 499-510.Google ScholarGoogle Scholar
  28. 28 KINGMAN, j. F.C. Subadditive ergodic theory. Ann. Prob 1 (1973), 883-909.Google ScholarGoogle Scholar
  29. 29 KINGMAN, J. F. C. Subadditive processes. In I~cole d'Et6 de Probabilit6 de Saint-Hour, P.-L. Hennequin, ed. Lecture Notes in Mathematics, vol. 539. Springer-Verlag, New York, 1976, 165-223.Google ScholarGoogle Scholar
  30. 30 LAMPORT, L. Time, clocks and the ordering of events in a distributed system. Commun. ACM 21, 7 (July 1978), 558-565. Google ScholarGoogle Scholar
  31. 31 LIU, Z. Evaluation des performances d~applications parallrles sur des systrmes multiprocesseurs. Rapport de DEA, Univ. of Paris-Sud, Paris, France, Sept. 1986.Google ScholarGoogle Scholar
  32. 32 LOYNES, R.M. The stability of queues with non independent inter-arrival and service times. Proc. Cambridge Ph. Soc. 58 (1962), 497-520.Google ScholarGoogle Scholar
  33. 33 MARSAN, M. A., BALBO, G., CONTE, G., AND GREGORETTI, F. Modeling bus contention and memory interference in a multiprocessor system. IEEE Trans. Comput. C-32, 1 (Jan. 1983), 60-71.Google ScholarGoogle Scholar
  34. 34 MARSAN, M. A., AND GREGORETTI, F. Memory interference models for a multiprocessor system with a shared bus and a single external common memory. Microproc. Microprog. 7 (1981), 124-133.Google ScholarGoogle Scholar
  35. 35 MILUTINOVI(;, V., FORTES, J. A. B., AND JAMIESON, L.H. A multimicroprocessor architecture for real-time computation of a class of DFT algorithms. IEEE Trans. ASSP ASSP-34, 5 (1986), 1301-1309.Google ScholarGoogle Scholar
  36. 36 NELSON, R., AND TANTAWI, A.N. Approximate analysis of fork/join synchronization in parallel queues. IEEE Trans. Comput. C-37, 6 (1988), 739-743. Google ScholarGoogle Scholar
  37. 37 PYLE, I.C. The Ada Programming Language. Prentice-Hall International, London, 1981. Google ScholarGoogle Scholar
  38. 38 SIGMAN, K. Regeneration in queues with regenerative input. Queue. Syst., to appear.Google ScholarGoogle Scholar
  39. 39 STAFYLOPATIS, A., AND GELENBE, E. Delay analysis of resequencing systems with partial ordering. In Proceedings of PERFORMANCE 87, P.-J. Courtois and G. Latouche, eds. North Holland, New York, Dec. 1987, pp. 433-446. Google ScholarGoogle Scholar
  40. 40 STOYAN, D. Comparison Methods for Queues and Other Stochastic Models (English translation), D. J. Daley, ed. Wiley, New York, 1984.Google ScholarGoogle Scholar
  41. 41 TALBOT, F. B., PATTERSON, J. H., AND GEHRLEIN, W.V. A comparative evaluation of heuristic line balancing techniques. Manage. Sci. 32, 4 (Apr. 1986), 430-454. Google ScholarGoogle Scholar
  42. 42 TOWSLEY, D., AND YU, S.P. Bounds for two server fork-join queueing systems. Tech. Rep. TR87- 123. Dept. of Comput. Inf. Sci., Univ. Mass., Amherst, Mass., Nov. 1987. Google ScholarGoogle Scholar
  43. 43 TSITSIKLIS, J. N., PAPADIMITRIOU, C. H., AND HUMBLET, P. The performance of a precedencebased queuing discipline. J. ACM 33, 3 (July 1986), 593-602. Google ScholarGoogle Scholar
  44. 44 YALAMANCHILI, S., AND AGGARWAL, J.K. A characterization and analysis of parallel processor interconnection networks. IEEE Trans. Comput. C-36, 6 (June 1987), 680-691. Google ScholarGoogle Scholar

Index Terms

  1. On the execution of parallel programs on multiprocessor systems—a queuing theory approach

                  Recommendations

                  Comments

                  Login options

                  Check if you have access through your login credentials or your institution to get full access on this article.

                  Sign in

                  Full Access

                  • Published in

                    cover image Journal of the ACM
                    Journal of the ACM  Volume 37, Issue 2
                    April 1990
                    244 pages
                    ISSN:0004-5411
                    EISSN:1557-735X
                    DOI:10.1145/77600
                    Issue’s Table of Contents

                    Copyright © 1990 ACM

                    Publisher

                    Association for Computing Machinery

                    New York, NY, United States

                    Publication History

                    • Published: 1 April 1990
                    Published in jacm Volume 37, Issue 2

                    Permissions

                    Request permissions about this article.

                    Request Permissions

                    Check for updates

                    Qualifiers

                    • article

                  PDF Format

                  View or Download as a PDF file.

                  PDF

                  eReader

                  View online with eReader.

                  eReader
                  About Cookies On This Site

                  We use cookies to ensure that we give you the best experience on our website.

                  Learn more

                  Got it!