Fluid Model Checking of Timed Properties

Luca Bortolussi; Roberta Lanciani

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arXiv · 1506.05909

Fluid Model Checking of Timed Properties

Luca Bortolussi·Roberta Lanciani

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Abstract

We address the problem of verifying timed properties of Markovian models of large populations of interacting agents, modelled as finite state automata. In particular, we focus on time-bounded properties of (random) individual agents specified by Deterministic Timed Automata (DTA) endowed with a single clock. Exploiting ideas from fluid approximation, we estimate the satisfaction probability of the DTA properties by reducing it to the computation of the transient probability of a subclass of Time-Inhomogeneous Markov Renewal Processes with exponentially and deterministically-timed transitions, and a small state space. For this subclass of models, we show how to derive a set of Delay Differential Equations (DDE), whose numerical solution provides a fast and accurate estimate of the satisfaction probability. In the paper, we also prove the asymptotic convergence of the approach, and exemplify the method on a simple epidemic spreading model. Finally, we also show how to construct a system of DDEs to efficiently approximate the average number of agents that satisfy the DTA specification.

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Luca Bortolussi, Roberta Lanciani. 2015-06-19. Fluid Model Checking of Timed Properties. https://arxiv.org/abs/1506.05909

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