### Bio-PEPAd: integrating exponential and deterministic delays for biological modelling

Over the last two decades stochastic process algebras (SPA) have proved to be
a useful and successful modellling paradigm. In many SPA the delays associated
with actions are assumed to be governed by an exponentially distributed random
variable. In these cases there is a straightforward relationship between the labelled
transition system underlying the process algebra and a continuous time Markov
chain (CTMC) which may be used as the basis for analysis. This analysis may be
conducted via numerical solution of the CTMC, stochastic simulation or fluid approximation
in terms of ordinary differential equations (ODEs). In other SPA, more general
distributions have been used to determine the delays associated with actions, and as
a consequence the underlying stochastic process is similarly more complex. In these
cases a Generalised Semi-Markov Process is usually used to give a semantics to the
models constructed and analysis is restricted to be conducted via stochastic simulation.
In a new SPA, Bio-PEPAd, motivated by modelling biological processes, we define a process
algebra in which actions have two phases: an exponential phase followed by a
deterministic phase. This represents a separation of the occurence of an action, at the
end of the exponential phase, and its effects, at the end of its deterministic delay. In
this talk we will give a high level account of Bio-PEPAd, particularly focussing
on its motivations for biological modelling and analysis of delayed systems.