Fluid Approximation of CTMC with Deterministic Delays

Author

Bortolussi, Luca ; Hillston, Jane

Author_Institution

Dept. of Math. & Geosci., Univ. of Trieste, Trieste, Italy

fYear

2012

fDate

17-20 Sept. 2012

Firstpage

53

Lastpage

62

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;

fLanguage

English

Publisher

ieee

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

Type

conf

DOI

10.1109/QEST.2012.13

Filename

6354633