PRISM 2.0: A Tool for Probabilistic Model Checking
QEST '04 Proceedings of the The Quantitative Evaluation of Systems, First International Conference
Bio-PEPA: A framework for the modelling and analysis of biological systems
Theoretical Computer Science
INFAMY: An Infinite-State Markov Model Checker
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Approximation of Event Probabilities in Noisy Cellular Processes
CMSB '09 Proceedings of the 7th International Conference on Computational Methods in Systems Biology
Parallel solution of the chemical master equation
SpringSim '09 Proceedings of the 2009 Spring Simulation Multiconference
SABRE: A Tool for Stochastic Analysis of Biochemical Reaction Networks
QEST '10 Proceedings of the 2010 Seventh International Conference on the Quantitative Evaluation of Systems
Parallel probabilistic model checking on general purpose graphics processors
International Journal on Software Tools for Technology Transfer (STTT) - SPIN 2009
| Hi-index | 0.00 |
Continuous-time Markov chains (CTMC) with their rich theory and efficient simulation algorithms have been successfully used in modeling stochastic processes in diverse areas such as computer science, physics, and biology. However, systems that comprise non-instantaneous events cannot be accurately and efficiently modeled with CTMCs. In this paper we define delayed CTMCs, an extension of CTMCs that allows for the specification of a lower bound on the time interval between an event's initiation and its completion, and we propose an algorithm for the computation of their behavior. Our algorithm effectively decomposes the computation into two stages: a pure CTMC governs event initiations while a deterministic process guarantees lower bounds on event completion times. Furthermore, from the nature of delayed CTMCs, we obtain a parallelized version of our algorithm. We use our formalism to model genetic regulatory circuits (biological systems where delayed events are common) and report on the results of our numerical algorithm as run on a cluster. We compare performance and accuracy of our results with results obtained by using pure CTMCs.