A compositional approach to performance modelling
A compositional approach to performance modelling
Information Processing Letters
Fluid Flow Approximation of PEPA models
QEST '05 Proceedings of the Second International Conference on the Quantitative Evaluation of Systems
CMSB'06 Proceedings of the 2006 international conference on Computational Methods in Systems Biology
Analysis of signalling pathways using continuous time markov chains
Transactions on Computational Systems Biology VI
CMSB'04 Proceedings of the 20 international conference on Computational Methods in Systems Biology
Gene regulation in the pi calculus: simulating cooperativity at the lambda switch
Transactions on Computational Systems Biology VII
On the Approximation of Stochastic Concurrent Constraint Programming by Master Equation
Electronic Notes in Theoretical Computer Science (ENTCS)
Some Investigations Concerning the CTMC and the ODE Model Derived From Bio-PEPA
Electronic Notes in Theoretical Computer Science (ENTCS)
Integrated Simulation and Model-Checking for the Analysis of Biochemical Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
Quantitative Analysis of Web Services Using SRMC
Formal Methods for Web Services
Bio-PEPA: A framework for the modelling and analysis of biological systems
Theoretical Computer Science
Probabilistic Approximations of Signaling Pathway Dynamics
CMSB '09 Proceedings of the 7th International Conference on Computational Methods in Systems Biology
Evaluating fluid semantics for passive stochastic process algebra cooperation
Performance Evaluation
Hybrid dynamics of stochastic programs
Theoretical Computer Science
A fluid analysis framework for a Markovian process algebra
Theoretical Computer Science
Process algebras in systems biology
SFM'08 Proceedings of the Formal methods for the design of computer, communication, and software systems 8th international conference on Formal methods for computational systems biology
Limit behavior of the hybrid approximation of stochastic process algebras
ASMTA'10 Proceedings of the 17th international conference on Analytical and stochastic modeling techniques and applications
Probabilistic approximations of ODEs based bio-pathway dynamics
Theoretical Computer Science
Fluid computation of passage-time distributions in large Markov models
Theoretical Computer Science
Continuous approximation of collective system behaviour: A tutorial
Performance Evaluation
Hi-index | 5.23 |
PEPA and its semantics have recently been extended to model biological systems. In order to cope with massive quantities of processes (as is usually the case when considering biological reactions) the model is interpreted in terms of a small set of coupled ordinary differential equations (ODEs) instead of a large state space continuous time Markov chain (CTMC). So far the relationship between these two semantics of PEPA had not been established. This is the goal of the present paper. After introducing a new extension of PEPA, denoted PEPA+@P, that allows models to capture both mass action law and bounded capacity law cooperations, the relationship between these two semantics is demonstrated. The result relies on Kurtz's Theorem that expresses that a set of ODEs can be, in some sense, considered as the limit of pure jump Markov processes.