Skip to main content
Springer Nature Link
Log in

Safe states in Banker like resource allocation Problems

  • Conference paper
  • First Online:
Advances in Petri Nets 1985 (APN 1985)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 222))

Included in the following conference series:

  • 173 Accesses

Abstract

The paper deals with representations of the safe states set in the Banker's problem. Using a Petri Net model we derive formulas for this set (SAFE) directly and for its (smaller) minimal elements set MIN. Moreover, we partition the set MIN into subclasses, so that two elements of the same subclass only differ by the permutation of their components. The set SORT, which contains only one representend of each subclass, is an even smaller representation of the safe states. We also derive estimates for the size of SORT. Finally we investigate, how our results can be translated to the multidimensional Banker's Problem, where credits in more than one currency can be given.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. George E. Andrews: The Theory of Partitions; Encyclopedia of Mathematics and its Applications; Addison-Wesley Publishing Company (1976)

    Google Scholar 

  2. P.Brinch Hansen: Operating System Principles; Prentice Hall, Englewood Cliffs (1973)

    Google Scholar 

  3. E.W. Dijkstra: Co-operating sequential processes; in F. Genuys (Ed.): Programming Languages Academic Press, London (1968), 43–112

    Google Scholar 

  4. Otto Forster: Analysis I; Grundkurs Mathematik; Vieweg Verlag (1978)

    Google Scholar 

  5. Dirk Hauschildt: Verklemmungsfreie Betriebsmittelzuteilung mit Hilfe von Residuen. Report: Bericht Fachbereich Informatik; Universität Hamburg (1985)

    Google Scholar 

  6. R.C. Holt: Some Deadlock Properties of Computer Systems; Computing Surveys 4(1972), 179–196

    Article  Google Scholar 

  7. R.C.Holt: On Deadlocks in Computer Systems. Ph.D.Thesis. Toronto Univ. Canada (1971)

    Google Scholar 

  8. Kurt Jensen: Coloured Nets and The Invariant Method. DAIMI PB-104. Aarhus University (1979)

    Google Scholar 

  9. R.Schroff: Vermeidung von totalen Verklemmungen in bewerteten Petrinetzen. Doktorarbeit. Technische Universität München (1974)

    Google Scholar 

  10. R. Schroff: Vermeidung von totalen Verklemmungen in bewerteten Petrinetzen. Lecture Notes on Computer Science 26 (1974), 316–325; Berlin-Heidelberg-New York: Springer (1975)

    Google Scholar 

  11. R. Valk, M. Jantzen: The Residue of Vector Sets with Application to Decidability Problems in Petri Nets; Acta Informatica 21 (1985), 643–674.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fachbereich Informatik, Universität Hamburg, Rothenbaumchaussee 67/69, D-2000, Hamburg 13

    Dirk Hauschildt & Rüdiger Valk

Authors
  1. Dirk Hauschildt
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rüdiger Valk
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

G. Rozenberg

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hauschildt, D., Valk, R. (1986). Safe states in Banker like resource allocation Problems. In: Rozenberg, G. (eds) Advances in Petri Nets 1985. APN 1985. Lecture Notes in Computer Science, vol 222. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0016216

Download citation

  • DOI: https://doi.org/10.1007/BFb0016216

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16480-7

  • Online ISBN: 978-3-540-39822-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics