A holonomic systems approach to special functions identities
Journal of Computational and Applied Mathematics
Solving linear integral equations in Maple
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
Theoretical Computer Science
Markov regenerative stochastic Petri nets
Performance '93 Proceedings of the 16th IFIP Working Group 7.3 international symposium on Computer performance modeling measurement and evaluation
Model-checking continuous-time Markov chains
ACM Transactions on Computational Logic (TOCL)
Performance Analysis of Communication Systems with Non-Markovian Stochastic Petri Nets
Performance Analysis of Communication Systems with Non-Markovian Stochastic Petri Nets
Performance of Computer Communication Systems: A Model-Based Approach
Performance of Computer Communication Systems: A Model-Based Approach
International Workshop on Timed Petri Nets
Model-Checking for Probabilistic Real-Time Systems (Extended Abstract)
ICALP '91 Proceedings of the 18th International Colloquium on Automata, Languages and Programming
Model checking for probability and time: from theory to practice
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
Bounded model checking for GSMP models of stochastic real-time systems
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Fixed-delay events in generalized semi-Markov processes revisited
CONCUR'11 Proceedings of the 22nd international conference on Concurrency theory
Performance evaluation of schedulers in a probabilistic setting
FORMATS'11 Proceedings of the 9th international conference on Formal modeling and analysis of timed systems
A maximal entropy stochastic process for a timed automaton,
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
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We consider the problem of verifying reachability properties of stochastic real-time systems modeled as generalized semi-Markov processes (GSMPs). The standard simulation-based techniques for GSMPs are not adequate for solving verification problems, and existing symbolic techniques either require memoryless distributions for firing times, or approximate the problem using discrete time or bounded horizon. In this paper, we present a symbolic solution for the case where firing times are random variables over a rich class of distributions, but only one event is allowed to retain its firing time when a discrete change occurs. The solution allows us to compute the probability that such a GSMP satisfies a property of the form "can the system reach a target, while staying within a set of safe states". We report on illustrative examples and their analysis using our procedure.