Fluid approximation of CTMC with deterministic delays

Luca Bortolussi; Jane Hillston

doi:10.1109/QEST.2012.13

Fluid approximation of CTMC with deterministic delays

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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 deterministic delay, 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.

Original language	English
Title of host publication	Proceedings of the Quantitative Evaluations of Systems (QEST) Conference
Publisher	Institute of Electrical and Electronics Engineers (IEEE)
Pages	53-62
Number of pages	10
ISBN (Electronic)	978-0-7695-4781-7
ISBN (Print)	978-1-4673-2346-8
DOIs	https://doi.org/10.1109/QEST.2012.13
Publication status	Published - 18 Sep 2012

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10.1109/QEST.2012.13

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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 deterministic delay, 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.",

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AB - 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 deterministic delay, 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.

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PB - Institute of Electrical and Electronics Engineers (IEEE)

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Fluid approximation of CTMC with deterministic delays

Abstract

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