Some Investigations Concerning the CTMC and the ODE Model Derived From Bio-PEPA
Electronic Notes in Theoretical Computer Science (ENTCS)
Parametric analysis of queuing networks
IBM Journal of Research and Development
A modified uniformization method for the solution of the chemical master equation
Computers & Mathematics with Applications
On the Numerical Analysis of Inhomogeneous Continuous-Time Markov Chains
INFORMS Journal on Computing
Simplification of a complex signal transduction model using invariants and flow equivalent servers
Theoretical Computer Science
Quasi product form approximation for markov models of reaction networks
Transactions on Computational Systems Biology XIV
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Most Markov chains that describe networks of stochastic reactions have a huge state space. This makes exact analysis infeasible and hence the only viable approach, apart from simulation, is approximation. In this paper we derive a product form approximation for the transient probabilities of such Markov chains. The approximation can be interpreted as a set of interacting time inhomogeneous Markov chains with one chain for every reactant of the system. Consequently, the computational complexity grows only linearly in the number of reactants and the approximation can be carried out for Markov chains with huge state spaces. Several numerical examples are presented to illustrate the approach.