Paper Info
Title
Bio-PEPAd: A non-Markovian extension of Bio-PEPA
Abstract
Delays in biological systems may be used to model events for which the underlying dynamics cannot be precisely observed, or to provide abstraction of some behavior of the system resulting in more compact models. In this paper, we enrich the stochastic process algebra Bio-PEPA, with the possibility of assigning delays to actions, yielding a new non-Markovian stochastic process algebra: Bio-PEPAd. This is a conservative extension meaning that the original syntax of Bio-PEPA is retained and the delay specification which can now be associated with actions may be added to existing Bio-PEPA models. The semantics of the firing of the actions with delays is the delay-as-duration approach, earlier presented in papers on the stochastic simulation of biological systems with delays. This semantics of the algebra is given in the Starting-Terminating style, meaning that the state and the completion of an action are observed as two separate events, as required by delays. We formally define the encoding of Bio-PEPAd systems in Generalized Semi-Markov Processes (GSMPs), as input for a Delay Stochastic Simulation Algorithm (DSSA) and as sets of Delay Differential Equations (DDEs), the deterministic framework for modeling of biological systems with delays. Finally, we prove theorems stating the relation between Bio-PEPA and Bio-PEPAd models. We end the paper with an example model of biological systems with delays to illustrate the approach.
Year
DOI
Venue
2012
10.1016/j.tcs.2011.11.028
Theor. Comput. Sci.
Keywords
DocType
Volume
Bio-PEPAd model,stochastic process algebra,Delay Differential Equations,new non-Markovian stochastic process,Bio-PEPA model,compact model,biological system,Bio-PEPAd system,stochastic simulation,Delay Stochastic Simulation Algorithm,non-Markovian extension
Journal
419,
ISSN
Citations 
PageRank 
0304-3975
9
0.62
References 
Authors
25
2
Name
Order
Citations
PageRank
Giulio Caravagna115616.46
Jane Hillston21657125.09