HYPE with stochastic events

TL;DR

This paper extends the HYPE process algebra for hybrid systems by incorporating stochastic non-urgent actions governed by probability distributions, and provides a formal semantics using Transition-Driven Stochastic Hybrid Automata.

Contribution

It introduces a probabilistic extension to non-urgent actions in HYPE and formalizes its semantics with Transition-Driven Stochastic Hybrid Automata.

Findings

HYPE now models stochastic non-urgent actions.

Semantics is given via Transition-Driven Stochastic Hybrid Automata.

The approach links hybrid systems with Piecewise Deterministic Markov Processes.

Abstract

The process algebra HYPE was recently proposed as a fine-grained modelling approach for capturing the behaviour of hybrid systems. In the original proposal, each flow or influence affecting a variable is modelled separately and the overall behaviour of the system then emerges as the composition of these flows. The discrete behaviour of the system is captured by instantaneous actions which might be urgent, taking effect as soon as some activation condition is satisfied, or non-urgent meaning that they can tolerate some (unknown) delay before happening. In this paper we refine the notion of non-urgent actions, to make such actions governed by a probability distribution. As a consequence of this we now give HYPE a semantics in terms of Transition-Driven Stochastic Hybrid Automata, which are a subset of a general class of stochastic processes termed Piecewise Deterministic Markov Processes.