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CONTINUOUS-TIME MARKOV CHAINS by

by Ward Whitt , 2006
"... We now turn to continuous-time Markov chains (CTMC’s), which are a natural sequel to the study of discrete-time Markov chains (DTMC’s), the Poisson process and the exponential distribution, because CTMC’s combine DTMC’s with the Poisson process and the exponential distribution. Most properties of CT ..."
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We now turn to continuous-time Markov chains (CTMC’s), which are a natural sequel to the study of discrete-time Markov chains (DTMC’s), the Poisson process and the exponential distribution, because CTMC’s combine DTMC’s with the Poisson process and the exponential distribution. Most properties

Continuous-time Markov Chains

by David F. Anderson , 1991
"... Computational methods for stochastically modeled biochemical reaction networks ..."
Abstract - Cited by 57 (0 self) - Add to MetaCart
Computational methods for stochastically modeled biochemical reaction networks

Simulation for Continuous-Time Markov Chains

by Christel Baiera, Joost-pieter Katoenb, Holger Hermannsb, Boudewijn Haverkortc
"... Abstract. This paper presents a simulation preorder for continuous-time Markov chains (CTMCs). The simulation preorder is a conserva-tive extension of a weak variant of probabilistic simulation on fully prob-abilistic systems, i.e., discrete-time Markov chains. The main result of the paper is that t ..."
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Abstract. This paper presents a simulation preorder for continuous-time Markov chains (CTMCs). The simulation preorder is a conserva-tive extension of a weak variant of probabilistic simulation on fully prob-abilistic systems, i.e., discrete-time Markov chains. The main result of the paper

Verifying Continuous Time Markov Chains

by Adnan Aziz, Kumud Sanwal, Vigyan Singhal, Robert Brayton , 1996
"... . We present a logical formalism for expressing properties of continuous time Markov chains. The semantics for such properties arise as a natural extension of previous work on discrete time Markov chains to continuous time. The major result is that the verification problem is decidable; this is show ..."
Abstract - Cited by 125 (1 self) - Add to MetaCart
. We present a logical formalism for expressing properties of continuous time Markov chains. The semantics for such properties arise as a natural extension of previous work on discrete time Markov chains to continuous time. The major result is that the verification problem is decidable

Model-checking algorithms for continuous-time Markov chains

by Christel Baier, Boudewijn Haverkort, Holger Hermanns, Joost-Pieter Katoen - IEEE TRANSACTIONS ON SOFTWARE ENGINEERING , 2003
"... Continuous-time Markov chains (CTMCs) have been widely used to determine system performance and dependability characteristics. Their analysis most often concerns the computation of steady-state and transient-state probabilities. This paper introduces a branching temporal logic for expressing real-t ..."
Abstract - Cited by 235 (48 self) - Add to MetaCart
Continuous-time Markov chains (CTMCs) have been widely used to determine system performance and dependability characteristics. Their analysis most often concerns the computation of steady-state and transient-state probabilities. This paper introduces a branching temporal logic for expressing real-time

Simulation for Continuous-Time Markov Chains

by Christel Baier, Joost-Pieter Katoen, Holger Hermanns, Boudewijn Haverkort , 2002
"... This paper presents a simulation preorder for continuoustime Markov chains (CTMCs). The simulation preorder is a conservative extension of a weak variant of probabilistic simulation on fully probabilistic systems, i.e., discrete-time Markov chains. The main result of the paper is that the simula ..."
Abstract - Cited by 8 (3 self) - Add to MetaCart
This paper presents a simulation preorder for continuoustime Markov chains (CTMCs). The simulation preorder is a conservative extension of a weak variant of probabilistic simulation on fully probabilistic systems, i.e., discrete-time Markov chains. The main result of the paper

Trace Machines for Observing Continuous-Time Markov Chains

by Verena Wolf, Mila Majster-cederbaum, Christel Baier - in Proc. of the 3rd Int. Workshop on Quantitative Aspects of Programming Languages (QAPL 2005), ENTCS , 2005
"... In this paper, we study several linear-time equivalences (Markovian trace equivalence, failure and ready trace equivalence) for continuous-time Markov chains that refer to the probabilities for timed execution paths. Our focus is on testing scenarios by means of push-button experiments with appropri ..."
Abstract - Cited by 12 (1 self) - Add to MetaCart
In this paper, we study several linear-time equivalences (Markovian trace equivalence, failure and ready trace equivalence) for continuous-time Markov chains that refer to the probabilities for timed execution paths. Our focus is on testing scenarios by means of push-button experiments

The deviation matrix of a continuous-time Markov chain

by Pauline Coolen-Schrijner, Erik A. Van Doorn , 2001
"... The deviation matrix of an ergodic, continuous-time Markov chain with transition probability matrix P (.) and ergodic matrix Π is the matrix D ≡ ∫ ∞ 0 (P (t) − Π)dt. We give conditions for D to exist and discuss properties and a representation of D. The deviation matrix of a birth-death process i ..."
Abstract - Cited by 19 (2 self) - Add to MetaCart
The deviation matrix of an ergodic, continuous-time Markov chain with transition probability matrix P (.) and ergodic matrix Π is the matrix D ≡ ∫ ∞ 0 (P (t) − Π)dt. We give conditions for D to exist and discuss properties and a representation of D. The deviation matrix of a birth-death process

Three-valued abstraction for continuous-time markov chains

by Joost-pieter Katoen, Daniel Klink, Martin Leucker, Verena Wolf - In Proceedings of the International Conference on Computer Aided Verification , 2007
"... Abstract. This paper proposes a novel abstraction technique for continuous-time Markov chains (CTMCs). Our technique fits within the realm of three-valued abstraction methods that have been used successfully for traditional model checking. The key idea is to apply abstraction on uniform CTMCs that a ..."
Abstract - Cited by 36 (8 self) - Add to MetaCart
Abstract. This paper proposes a novel abstraction technique for continuous-time Markov chains (CTMCs). Our technique fits within the realm of three-valued abstraction methods that have been used successfully for traditional model checking. The key idea is to apply abstraction on uniform CTMCs

Quasistationarity Of Continuous-Time Markov Chains With Positive Drift

by Coolen-Schrijner University, P. Coolen-schrijner
"... We shall study continuous-time Markov chains on the nonnegative integers which are both irreducible and transient, and which exhibit discernible stationarity before drift to infinity "sets in". We will show how this `quasi' stationary behaviour can be modelled using a limiting conditi ..."
Abstract - Cited by 1 (0 self) - Add to MetaCart
We shall study continuous-time Markov chains on the nonnegative integers which are both irreducible and transient, and which exhibit discernible stationarity before drift to infinity "sets in". We will show how this `quasi' stationary behaviour can be modelled using a limiting
Results 1 - 10 of 15,693