Title :
Fluid Approximation of CTMC with Deterministic Delays
Author :
Bortolussi, Luca ; Hillston, Jane
Author_Institution :
Dept. of Math. & Geosci., Univ. of Trieste, Trieste, Italy
Abstract :
We compare population models in terms of Continuous Time Markov Chains with embedded deterministic delays (delayed CTMC), in which an exponential timed transition can only update the state of the system after a deterministicdelay, and delay differential equations (DDE). We prove a fluid approximation theorem, showing that, when the size of the population goes to infinity, the delayed CTMC converges to a solution of the DDE.
Keywords :
Markov processes; approximation theory; biology; differential equations; continuous time Markov chain; delay differential equation; embedded deterministic delay; exponential timed transition; fluid approximation; population model; Biological system modeling; Clocks; Delay; Mathematical model; Sociology; Statistics; Stochastic processes; Continuous Time Markov Chains; Delay Differential Equations; Fluid Approximation; Genetic Networks With Delays; Mean Field Approximation; Stochastic Simulation With Delays;
Conference_Titel :
Quantitative Evaluation of Systems (QEST), 2012 Ninth International Conference on
Conference_Location :
London
Print_ISBN :
978-1-4673-2346-8
Electronic_ISBN :
978-0-7695-4781-7
DOI :
10.1109/QEST.2012.13
