scholarly journals Delayed point control of a reaction–diffusion PDE under discrete-time point measurements

Automatica ◽  
2018 ◽  
Vol 96 ◽  
pp. 224-233 ◽  
Author(s):  
Anton Selivanov ◽  
Emilia Fridman
Keyword(s):  
Discrete Time ◽  
Reaction Diffusion ◽  
Point Control ◽  
Time Point

Proportional intensities and strong ergodicity for Markov processes

1983 ◽  
Vol 20 (01) ◽  
pp. 185-190 ◽  
Author(s):  
Mark Scott ◽  
Dean L. Isaacson
Keyword(s):  
Markov Process ◽  
Markov Processes ◽  
Discrete Time ◽  
Continuous Time ◽  
Homogeneous Markov Process ◽  
Strong Ergodicity ◽  
Transition Functions ◽  
The Matrix ◽  
Intensity Functions ◽  
Time Point

By assuming the proportionality of the intensity functions at each time point for a continuous-time non-homogeneous Markov process, strong ergodicity for the process is determined through strong ergodicity of a related discrete-time Markov process. For processes having proportional intensities, strong ergodicity implies having the limiting matrix L satisfy L · P(s, t) = L, where P(s, t) is the matrix of transition functions.

scholarly journals Estimating the Necessary Amount of Driving Data for Assessing Driving Behavior

Sensors ◽  
2020 ◽  
Vol 20 (9) ◽  
pp. 2600 ◽  
Author(s):  
Anna-Maria Stavrakaki ◽  
Dimitrios I. Tselentis ◽  
Emmanouil Barmpounakis ◽  
Eleni I. Vlahogianni ◽  
George Yannis
Keyword(s):  
Discrete Time ◽  
Driving Behavior ◽  
Methodological Framework ◽  
Detailed Data ◽  
Specific Time ◽  
Speed Limits ◽  
Specific Time Point ◽  
Smartphone Sensors ◽  
Over Time ◽  
Time Point

The aim of this paper was to provide a methodological framework for estimating the amount of driving data that should be collected for each driver in order to acquire a clear picture regarding their driving behavior. We examined whether there is a specific discrete time point for each driver, in the form of total driving duration and/or the number of trips, beyond which the characteristics of driving behavior are stabilized over time. Various mathematical and statistical methods were employed to process the data collected and determine the time point at which behavior converges. Detailed data collected from smartphone sensors are used to test the proposed methodology. The driving metrics used in the analysis are the number of harsh acceleration and braking events, the duration of mobile usage while driving and the percentage of time driving over the speed limits. Convergence was tested in terms of both the magnitude and volatility of each metric for different trips and analysis is performed for several trip durations. Results indicated that there is no specific time point or number of trips after which driving behavior stabilizes for all drivers and/or all metrics examined. The driving behavior stabilization is mostly affected by the duration of the trips examined and the aggressiveness of the driver.

Discrete-time point processes in urban traffic queue estimation

1979 ◽  
Vol 24 (1) ◽  
pp. 12-27 ◽  
Author(s):  
J. Baras ◽  
W. Levine ◽  
Tahsin Lin
Keyword(s):  
Discrete Time ◽  
Point Processes ◽  
Urban Traffic ◽  
Time Point
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