scholarly journals HITTING PROBABILITIES AND HITTING TIMES FOR STOCHASTIC FLUID FLOWS: THE BOUNDED MODEL

2008 ◽  
Vol 23 (1) ◽  
pp. 121-147 ◽  
Author(s):  
Nigel G. Bean ◽  
Małgorzata M. O'Reilly ◽  
Peter G. Taylor
Keyword(s):  
Fluid Flow ◽  
Performance Measures ◽  
Flow Model ◽  
Fluid Flows ◽  
Hitting Times ◽  
Fluid Level ◽  
Probability Models ◽  
Hitting Probabilities ◽  
Stochastic Fluid Flow ◽  
Stochastic Fluid

We consider a Markovian stochastic fluid flow model in which the fluid level has a lower bound zero and a positive upper bound. The behavior of the process at the boundaries is modeled by parameters that are different than those in the interior and allow for modeling a range of desired behaviors at the boundaries. We illustrate this with examples. We establish formulas for several time-dependent performance measures of significance to a number of applied probability models. These results are achieved with techniques applied within the fluid flow model directly. This leads to useful physical interpretations, which are presented.

scholarly journals Efficient algorithms for transient analysis of stochastic fluid flow models

2005 ◽  
Vol 42 (02) ◽  
pp. 531-549 ◽  
Author(s):  
Soohan Ahn ◽  
V. Ramaswami
Keyword(s):  
Fluid Flow ◽  
Transient Analysis ◽  
Busy Period ◽  
Flow Model ◽  
Flow Models ◽  
Period Distribution ◽  
The Matrix ◽  
Stochastic Fluid Flow ◽  
Stochastic Fluid ◽  
Transient And Steady State

We derive several algorithms for the busy period distribution of the canonical Markovian fluid flow model. One of them is similar to the Latouche-Ramaswami algorithm for quasi-birth-death models and is shown to be quadratically convergent. These algorithms significantly increase the efficiency of the matrix-geometric procedures developed earlier by the authors for the transient and steady-state analyses of fluid flow models.

scholarly journals Hitting probabilities and hitting times for stochastic fluid flows

2005 ◽  
Vol 115 (9) ◽  
pp. 1530-1556 ◽  
Author(s):  
Nigel G. Bean ◽  
Małgorzata M. O’Reilly ◽  
Peter G. Taylor
Keyword(s):  
Fluid Flows ◽  
Hitting Times ◽  
Hitting Probabilities ◽  
Stochastic Fluid

scholarly journals Efficient algorithms for transient analysis of stochastic fluid flow models

2005 ◽  
Vol 42 (2) ◽  
pp. 531-549 ◽  
Author(s):  
Soohan Ahn ◽  
V. Ramaswami
Keyword(s):  
Fluid Flow ◽  
Transient Analysis ◽  
Busy Period ◽  
Flow Model ◽  
Flow Models ◽  
Period Distribution ◽  
The Matrix ◽  
Stochastic Fluid Flow ◽  
Stochastic Fluid ◽  
Transient And Steady State

We derive several algorithms for the busy period distribution of the canonical Markovian fluid flow model. One of them is similar to the Latouche-Ramaswami algorithm for quasi-birth-death models and is shown to be quadratically convergent. These algorithms significantly increase the efficiency of the matrix-geometric procedures developed earlier by the authors for the transient and steady-state analyses of fluid flow models.

Stochastic fluid flow models for determining optimal switching thresholds

2005 ◽  
Vol 59 (1) ◽  
pp. 19-46 ◽  
Author(s):  
V. Aggarwal ◽  
N. Gautam ◽  
S.R.T. Kumara ◽  
M. Greaves
Keyword(s):  
Fluid Flow ◽  
Optimal Switching ◽  
Flow Models ◽  
Stochastic Fluid Flow ◽  
Stochastic Fluid
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