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Sufficient conditions for existence of a fixed point in stochastic reward net-based iterative models

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2 Author(s)
V. Mainkar ; AT&T Bell Labs., Holmdel, NJ, USA ; K. S. Trivedi

Stochastic Petri net models of large systems that are solved by generating the underlying Markov chain pose the problem of largeness of the state-space of the Markov chain. Hierarchical and iterative models of systems have been used extensively to solve this problem. A problem with models which use fixed-point iteration is the theoretical proof of the existence, uniqueness and convergence of the fixed-point equations, which still remains an “art”. In this paper, we establish conditions, in terms of the net structure and the characteristics of the iterated variables, under which existence of a solution is guaranteed when fixed-point iteration is used in stochastic Petri nets. We use these conditions to establish the existence of a fixed point for a model of a priority scheduling system, at which tasks may arrive according to a Poisson process or due to spawning or conditional branching of other tasks in the system

Published in:

IEEE Transactions on Software Engineering  (Volume:22 ,  Issue: 9 )