An upper bound on the cycle time of a stochastic marked graph using incomplete information on the transition firing time distributions

Authors:
Gerrit K. Janssens;Kenneth SöRensen;Wout Dullaert
Affiliations:
Faculty of Applied Economics, Hasselt University-Campus Diepenbeek, Agoralaan - D building, 3590 Diepenbeek, Belgium;Center for Industrial Management, Catholic University of Louvain, Celestijnenlaan 300A, 3001 Leuven (Heverlee), Belgium;Institute for Transport and Maritime Management Antwerp, University of Antwerp, Keizerstraat 64, 2000 Antwerp, Belgium and Antwerp Maritime Academy, Noordkasteel Oost 6, 2030 Antwerpen, Belgium
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2009

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Abstract

Stochastic marked graphs, a special class of stochastic timed Petri nets, are used for modelling and analyzing decision-free dynamic systems with uncertainties in timing. The model allows evaluating the performance of such systems under a cyclic process. Given the probabilistic characteristics of the transition times, the cycle time of the system can be determined from the initial marking. In this contribution, we compute an upper bound on the cycle time of a stochastic marked graph in case the probabilistic characteristics of the transition times are not fully specified.