Skip to main content
SpringerLink
Log in

Communication Delays and Multiprocessor Tasks

  • Chapter
Scheduling Computer and Manufacturing Processes

  • 55 Accesses

Abstract

One of the assumptions imposed in Chapter 3 was that each task is processed on at most one processor at a time. However, in recent years, with the rapid development of manufacturing as well as microprocessor and especially multi-microprocessor systems, the above assumption has ceased to be justified in some important applications. There are, for example, self-testing multi-microprocessor systems in which one processor is used to test others, or diagnostic systems in which testing signals stimulate the tested elements and their corresponding outputs are simultaneously analyzed [Avi78, DD81]. When formulating scheduling problems in such systems, one must take into account the fact that some tasks have to be processed on more than one processor at a time. On the other hand, communication issues must be also taken into account in systems where tasks (e. g. program modules) are assigned to different processors and exchange information between each other.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. F. D. Anger, J. Hwang, Y. Chow, Scheduling with sufficiently loosely coupled processors, J. Parallel Distributed Comput. 9, 87–92, 1990.

    Article  Google Scholar 

  2. A. V. Aho, J. E. Hopcroft, J. D. Ullman, The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, Mass., 1974.

    Google Scholar 

  3. A. Avizienis, Fault tolerance: the survival attribute of digital systems, Proc. IEEE 66, 1978, 1109–1125.

    Article  Google Scholar 

  4. M. Ahuja, Y. Zhu, An O(logn) feasibility algorithm for preemptive scheduling of n independent jobs on a hypercube, Inform. Process. Lett. 35, 1990, 7–11.

    Article  Google Scholar 

  5. L. Bianco, J. Błażewicz, M. Drozdowski, P. dell’Olmo, Scheduling preemptive multiprocessor tasks on dedicated processors, Performance Evaluation 20, 1994, 361–371.

    Article  Google Scholar 

  6. L. Bianco, J. Błażewicz, M. Drozdowski, P. dell’Olmo, Scheduling multiprocessor tasks on a dynamic configuration of dedicated processors, Ann. Oper. Res. 58, 1995, 493–517

    Article  Google Scholar 

  7. L. Bianco, J. Błażewicz, M. Drozdowski, P. dell’Olmo, Linear algorithms for preemptive scheduling of multiprocessor tasks subject to minimal lateness, Discrete Appl. Math. 1996, to appear.

    Google Scholar 

  8. L. Bianco, J. Błażewicz, M. Drozdowski, P. dell’Olmo, Preemptive multiprocessor task scheduling with release times and time windows, Ann. Oper. Res., 1996, to appear.

    Google Scholar 

  9. J. Błażewicz, P. Bouvry, F. Guinand, D. Trystram, Scheduling complete in-trees on two uniform processors with communication delays, Inform. Process. Lett., 1996, to appear.

    Google Scholar 

  10. J. Błażewicz, M. Drozdowski, Scheduling jobs on hybercubes, Parallel Computing 21, 1995, 1946–1956.

    Google Scholar 

  11. J. Błażewicz, M. Drozdowski, The performance limits of a two dimensional network of load-sharing processors, Foundations Comput. Dec. Sci., 1996, to appear.

    Google Scholar 

  12. J. Błażewicz, M. Drozdowski, Distributed processing of divisible jobs with communication startup costs, Discrete Appl. Math., 1996, to appear.

    Google Scholar 

  13. J. Błażewicz, M. Drozdowski, F. Guinand, D. Trystram, Scheduling under architectural constraints, Tech.Report RA-003/95, Institut of Computing Science, Poznan University of Technology, 1995.

    Google Scholar 

  14. J. Błażewicz, M. Drozdowski, P. dell’Olmo, M. G. Speranza, Scheduling multiprocessor tasks on three dedicated processors, Inform. Process. Lett. 41, 1992, 275–280. Corrigendum: Inform. Process. Lett. 49, 1994, 269–270.

    Article  Google Scholar 

  15. J. Błażewicz, M. Drozdowski, G. Schmidt, D. de Werra, Scheduling independent two processor tasks on a uniform duo-processor system, Discrete Appl. Math. 28, 1990, 11–20.

    Article  Google Scholar 

  16. J. Błażewicz, M. Drozdowski, G. Schmidt, D.de Werra, Scheduling independent multiprocessor tasks on a uniform k-processor system, Parallel Computing 20, 1994, 15–28.

    Article  Google Scholar 

  17. J. Błażewicz, M. Drabowski, J. Węglarz, Scheduling independent 2-processor tasks to minimize schedule length, Inform. Process. Lett. 18, 1984, 267–273.

    Article  Google Scholar 

  18. J. Błażewicz, M. Drabowski, J. Węglarz, Scheduling multiprocessor tasks to minimize schedule length, IEEE Trans. Comput. C-35, 1986, 389–393.

    Article  Google Scholar 

  19. J. Błażewicz, M. Drozdowski, D. de Werra, J. Węglarz, Deadline scheduling of multiprocessor tasks, Discrete Appl. Math. 65, 1996, 81–96.

    Article  Google Scholar 

  20. J. Błażewicz, K. Ecker, A linear time algorithm for restricted bin packing and scheduling problems, Oper. Res. Lett. 2, 1983, 80–83.

    Article  Google Scholar 

  21. V. E. Benes, Permutation groups, complexes, and rearrangeable connecting networks, Bell Syst. Tech. J. 43, 1964, 1619–1640.

    Google Scholar 

  22. E. Bampis, A. Giannokos, J.-C. König, On the complexity of scheduling with large communication delays, European J. Oper. Res., 1996, to appear.

    Google Scholar 

  23. V. Bharadwaj, D. Ghose, V. Mani, A study of optimality conditions for load distribution in tree networks with communication delays, Tech.Report 423/GI/02–92, Dept. of Aerospace Engineering, Indian Institute of Science, Bangalore, 1992.

    Google Scholar 

  24. V. Bharadwaj, D. Ghose, V. Mani, Optimal sequencing and arrangement in distributed single-level tree networks with communication delays, IEEE Trans. Parallel Distrib. Syst. 5, 1994, 968–976.

    Article  Google Scholar 

  25. J. Błażewicz, Z. Liu, Scheduling multiprocessor tasks with chain constraints, European J. Oper. Res., 1996, to appear.

    Google Scholar 

  26. J. Błażewicz, J. K. Lenstra, A. H. G. Rinnoy Kan, Scheduling subject to resource constraints: classification and complexity, Discrete Appl. Math. 5, 1983, 11–24

    Article  Google Scholar 

  27. S. H. Bokhari, On the mapping problem, IEEE Trans. Comput. C-30, 1981, 207–214.

    Article  Google Scholar 

  28. L. Bianco, P. dell’Olmo, M. G. Speranza, Nonpreemptive scheduling of independent tasks with dedicated resources, Report, IASI, Roma, 1991

    Google Scholar 

  29. S. Bataineh, T. G. Robertazzi, Bus oriented load sharing for a network of sensor driven processors, IEEE Trans. Syst. Man. Cybernet. 21, 1991, 1202–1205.

    Article  Google Scholar 

  30. N. G. de Bruijn, A combinatorial problem, Koninklijke Netherlands: Academie van Wetenschappen, Proc. 49, 1946, 758–764.

    Google Scholar 

  31. P. Brucker, Scheduling Algorithms, Springer, Berlin, 1995.

    Book  Google Scholar 

  32. D. Bertsekas, J. Tsitsiklis, Parallel and Distributed Computation, Prentice Hall, Englewood Cliffs, N.J., 1989.

    Google Scholar 

  33. Y. L. Chen, Y. H. Chin, Scheduling unit-time jobs on processors with different capabilities, Comput. Oper. Res. 16, 1989, 409–417.

    Article  Google Scholar 

  34. I. Y. Colin, P. Chretienne, C.P.M. scheduling with small communication delays and task duplication, Oper. Res. 39, 1991, 680–684.

    Article  Google Scholar 

  35. E. G. Coffman, Jr., M. R. Garey, D. S. Johnson, A. S. La Paugh, Scheduling file transfers, SIAM J. Comput. 14, 1985, 744–780.

    Article  Google Scholar 

  36. Chr89a P. Chretienne, A polynomial algorithm to optimally schedule tasks over an ideal distributed system under tree-like precedence constraints, European J. Oper. Res 2, 1981, 225–230.

    Google Scholar 

  37. Chr89b P. Chretienne, Task scheduling over distributed memory machines, in: Proceedings of the International Workshop on Parallel and Distributed Algorithms, North-Holland, Amsterdam, 1989.

    Google Scholar 

  38. P. Chretienne, Tree scheduling with communication delays, Discrete Appl. Math. 49, 1994, 129–141.

    Article  Google Scholar 

  39. G. I. Chen, T. H. Lai, Preemptive scheduling of independent jobs on a hypercube, Inform. Process. Lett. 28, 1988, 201–206.

    Article  Google Scholar 

  40. R. S. Chang, R. C. T. Lee, On a scheduling problem where a job can be executed only by a limited number of processors, Comput. Oper. Res. 15, 1988, 471–478

    Article  Google Scholar 

  41. P. Chretienne, C. Picouleau, The basic scheduling problem with interprocessor communication delays, MASI Report 91/6, Institut Blaise Pascal, Paris, 1991.

    Google Scholar 

  42. Y. C. Cheng, T. G. Robertazzi, Distributed computation with communication delays, IEEE Trans. Aerospace Electr. Syst. 24, 1988, 511–516

    Article  Google Scholar 

  43. Y. C. Cheng, T. G. Robertazzi, Distributed computation with communication delays, IEEE Trans. Aerospace Electr. Syst. 26, 1990, 511–516.

    Article  Google Scholar 

  44. M. Dal Cin, E. Dilger, On the diagnostability of self-testing multimicroprocessor systems, Microprocessing and Microprogramming 7, 1981, 177–184.

    Article  Google Scholar 

  45. M. Drozdowski, W. Kubiak, Scheduling parallel tasks with sequential heads and tails, Working paper, Memorial University of Newfoundland, St. John’s, 1995.

    Google Scholar 

  46. J. Du, J. Y-T. Leung, Complexity of scheduling parallel tasks systems, SIAM J. Discrete Math. 2, 1989, 473–487.

    Article  Google Scholar 

  47. Dro96a M. Drozdowski, Selected Problems of Scheduling Tasks in Multiprocessor Computer Systems, Poznań University of Technology Press, Poznań, 1996.

    Google Scholar 

  48. M. Drozdowski, Real-time scheduling of linear speedup parallel tasks, Inform. Process. Lett. 1996, to appear.

    Google Scholar 

  49. K. H. Ecker, R. Hirschberg, Scheduling communication demands in networks, Proc. of the Workschop onn Parallel and Distributed Real-Time Systems, Newport Beach, 1993.

    Google Scholar 

  50. K. H. Ecker, D. Hammer, Integrated scheduling for CIM systems. Proc. TIMS XXXII, Anchorage, 1994.

    Google Scholar 

  51. K. H. Ecker, H. Hodam, Heuristic algorithms for the task scheduling under consideration of communication delays, Report, T. U. Clausthal, 1996.

    Google Scholar 

  52. D. Ghose, V. Mani, Distributed computation in a linear network: Closed-form solutions and computational techniques, IEEE Trans. Aerospace Electr. Syst. 30, 1994, 471–483.

    Article  Google Scholar 

  53. M. Goemans, An approximation algorithm for scheduling on three dedicated processors, Discrete Appl. Math. 61, 1995, 49–60.

    Article  Google Scholar 

  54. R. L. Goke, Banyan networks for partitioning multiprocessor systems, Ph.D. Thesis, Univ. Florida, Gainesville, 1976.

    Google Scholar 

  55. F. Guinand, D. Trystram, Optimal scheduling of UECT trees on two processors, Report, Universite Joseph Fourier, Grenoble, 1993.

    Google Scholar 

  56. A. Gerasoulis, T. Yang, On the granularity and clustering of directed acyclic task graphs, Report TR-153, Dept. Comput. Sci., Rutgers University, 1992.

    Google Scholar 

  57. E. Haddad, Communication protocol for optimal redistribution of divisible load in distributed real-time systems, Proc. of the ISMM Internat. Conf. on Intelligent Information Management Systems, Washington, 1994, 39–42.

    Google Scholar 

  58. J.-J. Hwang, Y.-C. Chow, F. D. Anger, C.-Y. Lee, Scheduling precedence graphs in systems with interprocessor communication times, SIAM J. Comput. 18, 1989, 244–257.

    Article  Google Scholar 

  59. J. A. Hoogeveen, J. K. Lenstra, B. Veltman, Three, four, five, six or the complexity of scheduling with communication delays, Report BS-R9229, CWI, Amsterdam, 1992

    Google Scholar 

  60. C. P. M. van Hoesel, Preemptive scheduling on a hypercube, Report 8963/A, Econometric Institute, Erasmus University, Rotterdam, 1989.

    Google Scholar 

  61. J. A. Hoogeven, S. L. van de Velde, B. Veltman, Complexity of scheduling multiprocessor tasks with prespecified processor allocation, Discrete Appl. Math. 55, 1994, 259–272.

    Article  Google Scholar 

  62. D. S. Johnson, C. L. Monma, A scheduling problem with simultaneous machine requirement, Proc, TIMS XXVI, Copenhagen, 1984.

    Google Scholar 

  63. A. Jakoby, R. Reischuk, The complexity of scheduling problems with communication delays for trees, Proc. Scandinavian Workshop on Algorithmic Theory 3, 1992, 165–177.

    Google Scholar 

  64. H. J. Kim, G. I. Jee, J. G. Lee, Optimal load distribution for tree network processors, 1995, submitted for publication.

    Google Scholar 

  65. H. Krawczyk, M. Kubale, An approximation algorithm for diagnostic test scheduling in multicomputer systems, IEEE Trans. Comput. C-34, 1985, 869–872.

    Article  Google Scholar 

  66. G. A. P. Kindervater, J. K. Lenstra, Parallel computing in combinatorial optimization, Ann. Oper. Res. 14, 1988, 245–289.

    Article  Google Scholar 

  67. C. P. Kruskal, M. Snir, A unified theory of interconnection network structure, Preprint, 1986.

    Google Scholar 

  68. M. Kubale, The complexity of scheduling independent two-processor tasks on dedicated processors, Inform. Proc. Lett. 24, 1987, 141–147.

    Article  Google Scholar 

  69. M. Kubale, Preemptive scheduling of two-processor tasks on dedicated processors (in Polish), Zeszyty Naukowe Politechniki Ślaskiej, Automatyka 100, 1990, 145–153.

    Google Scholar 

  70. E. L. Lloyd, Concurrent task systems, Oper. Res. 29, 189–201.

    Google Scholar 

  71. S. Lam, R. Sethi, Worst case analysis of two scheduling algorithms, SIAM J. Comput. 6, 1977, 518–536.

    Article  Google Scholar 

  72. R. H. Möhring, Computationally tractable classes of ordered sets, I. Rival (ed.), Algorithms and Order, 105–193, Kluwer, Dordrecht, 1989.

    Chapter  Google Scholar 

  73. P. dell’Olmo, M. G. Speranza, Z. S. Tuza, Easy and hard cases of a scheduling problem on 3 dedicated processor, Report, LASI, Rome, 1995.

    Google Scholar 

  74. C. Picouleau, Two new NP-complete scheduling problems with communication delays and unlimited number of processors. Report RP91/24, MASI, Institut Blaise Pascal, Universite Paris VI, 1991.

    Google Scholar 

  75. C. Picouleau, Etude de problèmes d’ optimization dans les systèmes distributés, Ph.D. Thesis, Université Paris VI, 1992.

    Google Scholar 

  76. J. G. Peters, M. Syska, Circuit-switched broadcasting in torus networks, IEEE Trans. Parallel Distrib. Syst., 1996, to appear.

    Google Scholar 

  77. F. P. Preparata, J. Vuillemin, The cube-connected cycles: A versatile network for parallel computation, Commun. ACM, May 1981, 300–309.

    Google Scholar 

  78. C. H. Papadimitriou, M. Yannakakis, Towards an architecture-independent analysis of parallel algorithms, SIAM J. Comput. 19, 1990, 322–328.

    Article  Google Scholar 

  79. T. G. Robertazzi, Processor equivalence for a linear daisy chain of load sharing processors, IEEE Trans. Aerospace Electr. Syst. 29, 1993, 1216–1221.

    Article  Google Scholar 

  80. Ray87a V. J. Rayward-Smith, UET scheduling with unit interprocessor communication delays, Discrete Appl. Math. 18, 1987, 55–71.

    Article  Google Scholar 

  81. Ray87b V. J. Rayward-Smith, The complexity of preemptive scheduling giveninter-processor communication delays, Inform. Process. Lett. 25, 1987, 123–125.

    Article  Google Scholar 

  82. T. H. Szymansky, V. C. Hamacher, On the universality of multipath multistage interconnection networks, J. Parallel Distributed Comput. 7, 1989, 541–569.

    Article  Google Scholar 

  83. X. Shen, E. M. Reingold, Scheduling on a hypercube, Inform. Process. Lett. 40, 1991, 323–328.

    Article  Google Scholar 

  84. J. Sohn, T. G. Robertazzi, A multi-job load sharing strategy for divisible jobs on bus networks, Tech.Report 697, SUNY at Stony Brook College of Eng. and Appl. Sci., 1994

    Google Scholar 

  85. S. Sohn, T. G. Robertazzi, An optimal load sharing strategy for divisible jobs with time-varying processor speed and channel speed, Proc. of the ISCA Inter-national Conf. on Parallel and Distributed Computing Systems, Orlando, 1995, 27–32.

    Google Scholar 

  86. J. Sohn, T. G. Robertazzi, Optimal divisible job load sharing for bus networks, IEEE Trans. Aerospace Electr. Syst. 32, 1996, to appear.

    Google Scholar 

  87. J. Sohn, T. G. Robertazzi, S. Luryi, Optimizing computing costs using divisible load analysis, Report CEAS 719, University at Stony Brook, 1995.

    Google Scholar 

  88. H. S. Stone, Parallel processing with the perfect shuffle, IEEE Trans. Comput. C-20, 1971, 153–161.

    Article  Google Scholar 

  89. B. Veltman, Multiprocessor Scheduling with Communication Delays, Ph.D. Thesis, CWI-Amsterdam, 1993.

    Google Scholar 

  90. B. Veltman, B. J. Lage weg, J. K. Lenstra, Multiprocessor scheduling with communication delays, Report BS — R9018, CWI, Amsterdam, 1990.

    Google Scholar 

  91. J. P. C. Verhoosel, L. R. Welch, D. K. Hammer, A. D. Stoyenko, A model for scheduling of object-based, distributed real-time systems, J. Real-Time Systems 8, 1995.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Instytut Informatyki, Politechnika Poznanska, ul. Piotrowo 3a, 60-965, Poznań, Poland

    Prof. Dr. Jacek Błażewicz & Prof. Dr. Jan Węglarz

  2. Institut für Informatik, Technische Universität Clausthal, Erzstraße 1, 38678, Clausthal-Zellerfeld, Germany

    Prof. Dr. Klaus H. Ecker

  3. Institut für Gesellschafts- und Wirtschaftswissenschaften, Universität Bonn, Adenauerallee 24-42, 53113, Bonn, Germany

    Prof. Dr. Erwin Pesch

  4. Betriebswirtschaftslehre, insbesondere Informations- und Technologiemanagement, Universität des Saarlandes, Postfach 151150, 66041, Saarbrücken, Germany

    Prof. Dr. Günter Schmidt (Lehrstuhl)

Authors
  1. Prof. Dr. Jacek Błażewicz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Prof. Dr. Klaus H. Ecker
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Prof. Dr. Erwin Pesch
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Prof. Dr. Günter Schmidt
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Prof. Dr. Jan Węglarz
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Błażewicz, J., Ecker, K.H., Pesch, E., Schmidt, G., Węglarz, J. (1996). Communication Delays and Multiprocessor Tasks. In: Scheduling Computer and Manufacturing Processes. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03217-6_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-03217-6_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-03219-0

  • Online ISBN: 978-3-662-03217-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation