HYPE with stochastic events

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

Mean-field analysis of hybrid Markov population models with time-inhomogeneous rates

“…A common feature in each of these hybrid process algebras is the expression of continuous evolution via the embedding of ordinary differential equations in the process model itself. In contrast, Bortolussi et al (2011) have developed stochastic HYPE, a process formalism that generates both discrete and continuously varying dynamics from the semantics of the process model alone.…”

“…We have not endeavoured to express the continuous variables in a process-style language, as in Bortolussi et al (2011). Instead we focus on showing convergence between the ODE solution of the resulting hybrid PCTMC and simulations of the underlying stochastic process.…”

Hybrid semantics for Bio-PEPA

“…The rate of the transition is obtained from the rate function using the relevant species quantities. Molecule counts remain integral in this approach 7 . The second approach is a deterministic approach using the ODEs obtained from the Bio-PEPA model.…”

“…This graph is constructed by considering the instantaneous transitions of the labelled transition systems obtained from the controller of the HYPE model. The reader is referred to [40,7] for further information about well-behavedness and results about controllers that are well-behaved. The following two results (which have appeared previously) straightforward to prove.…”

“…This paper presents a mapping from Bio-PEPA [30] to stochastic HYPE [7,9] with the outcome that the system represented by a Bio-PEPA model can be analysed in a stochastic and hybrid (continuous and instantaneous) fashion, allowing for both continuous and stochastic modelling of reactions, switching dynamically between the different behaviours when appropriate, by the use of instantaneous transitions. This approach is novel, as the mapping provides a well-structured process algebra model that can be further modified, for example, by added additional time-based or threshold-based events in the style of Bio-PEPA with events [26].…”