Dirk Hauschildt and Rüdiger Valk.
Safe states in banker like resource allocation problems.
In Advances in Petri Nets 1985, volume 222 of Lecture
Notes in Computer Science, pages 253-277. Springer-Verlag, Berlin,
Heidelberg, New York, 1986.
Resumen: 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 represented 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.
@InCollection{Hauschildt+86, author = {Hauschildt, Dirk and Valk, R{\"u}diger}, title = {Safe states in Banker like resource allocation Problems}, booktitle = {Advances in Petri Nets 1985}, volume = 222, pages = {253--277}, year = 1986, series = LNCS, publisher = Springer, address = Springer.addr, ISSN = {0302-9743}, ISBN = {978-3-540-16480-7}, doi = {10.1007/BFb0016216}, 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 represented 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 material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.