State Space Heterogeneity and Space Determination for Markov Models of Mobility

1989 ◽  
pp. 279-297
Author(s):  
Hubert Jayet
Keyword(s):  
State Space ◽  
Markov Models

Dependability Modeling

2012 ◽  
pp. 53-97 ◽  
Author(s):  
Paulo R. M. Maciel ◽  
Kishor S. Trivedi ◽  
Rivalino Matias ◽  
Dong Seong Kim
Keyword(s):  
State Space ◽  
Case Studies ◽  
Hierarchical Models ◽  
Markov Models ◽  
Modeling Method ◽  
State Space Models ◽  
Evaluation Techniques

This chapter presents modeling method and evaluation techniques for computing dependability metrics of systems. The chapter begins providing a summary of seminal works. After presenting the background, the most prominent model types are presented, and the respective methods for computing exact values and bounds. This chapter focuses particularly on non-state space models although state space models such as Markov models and hierarchical models are also presented. Case studies are then presented in the end of the chapter.

Clustering of Bursts of Openings in Markov and Semi-Markov Models of Single Channel Gating

1997 ◽  
Vol 29 (01) ◽  
pp. 92-113 ◽  
Author(s):  
Frank Ball ◽  
Sue Davies
Keyword(s):  
Markov Chain ◽  
Ion Channel ◽  
State Space ◽  
Continuous Time ◽  
Markov Models ◽  
Numerical Study ◽  
Channel Gating ◽  
Markov Renewal Process ◽  
Time Interval ◽  
Continuous Time Markov Chain

The gating mechanism of a single ion channel is usually modelled by a continuous-time Markov chain with a finite state space. The state space is partitioned into two classes, termed ‘open’ and ‘closed’, and it is possible to observe only which class the process is in. In many experiments channel openings occur in bursts. This can be modelled by partitioning the closed states further into ‘short-lived’ and ‘long-lived’ closed states, and defining a burst of openings to be a succession of open sojourns separated by closed sojourns that are entirely within the short-lived closed states. There is also evidence that bursts of openings are themselves grouped together into clusters. This clustering of bursts can be described by the ratio of the variance Var (N(t)) to the mean[N(t)] of the number of bursts of openings commencing in (0, t]. In this paper two methods of determining Var (N(t))/[N(t)] and limt→∝Var (N(t))/[N(t)] are developed, the first via an embedded Markov renewal process and the second via an augmented continuous-time Markov chain. The theory is illustrated by a numerical study of a molecular stochastic model of the nicotinic acetylcholine receptor. Extensions to semi-Markov models of ion channel gating and the incorporation of time interval omission are briefly discussed.

scholarly journals Nested particle filters for online parameter estimation in discrete-time state-space Markov models

Bernoulli ◽  
2018 ◽  
Vol 24 (4A) ◽  
pp. 3039-3086 ◽  
Author(s):  
Dan Crisan ◽  
Joaquín Míguez
Keyword(s):  
Parameter Estimation ◽  
State Space ◽  
Discrete Time ◽  
Particle Filters ◽  
Markov Models

scholarly journals Strong Truncation Approximation in Tandem Queues with Blocking

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Karima Adel-Aissanou ◽  
Karim Abbas ◽  
Djamil Aïssani
Keyword(s):  
State Space ◽  
Error Bounds ◽  
Numerical Solutions ◽  
Markov Models ◽  
Practical Interest ◽  
Strong Stability ◽  
Tandem Queue ◽  
Closed Form Solutions ◽  
Infinite State

Markov models are frequently used for performance modeling. However most models do not have closed form solutions, and numerical solutions are often not feasible due to the large or even infinite state space of models of practical interest. For that, the state-space truncation is often demanded for computation of this kind of models. In this paper, we use the strong stability approach to establish analytic error bounds for the truncation of a tandem queue with blocking. Numerical examples are carried out to illustrate the quality of the obtained error bounds.

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