A reliability model based on the gamma process and its analytic theory

1989 ◽  
Vol 21 (4) ◽  
pp. 899-918 ◽  
Author(s):  
Michael L. Wenocur
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Random Process ◽  
Analytic Theory ◽  
Analytical Theory ◽  
Gamma Process ◽  
Reliability Model ◽  
System State ◽  
Model Based ◽  
State Dependent

This paper presents a variation of a state-dependent reliability model first proposed in Lemoine and Wenocur [4], [5], and develops some of its corresponding analytical theory. In particular, we develop a reliability model in which system state is a random process satisfying a stochastic differential equation where the driving process is gamma distributed.

A reliability model based on the gamma process and its analytic theory

1989 ◽  
Vol 21 (04) ◽  
pp. 899-918 ◽  
Author(s):  
Michael L. Wenocur
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Random Process ◽  
Analytic Theory ◽  
Analytical Theory ◽  
Gamma Process ◽  
Reliability Model ◽  
System State ◽  
Model Based ◽  
State Dependent

This paper presents a variation of a state-dependent reliability model first proposed in Lemoine and Wenocur [4], [5], and develops some of its corresponding analytical theory. In particular, we develop a reliability model in which system state is a random process satisfying a stochastic differential equation where the driving process is gamma distributed.

Diffusion Approximation of State-Dependent G-Networks Under Heavy Traffic

2008 ◽  
Vol 45 (2) ◽  
pp. 347-362 ◽  
Author(s):  
Saul C. Leite ◽  
Marcelo D. Fragoso
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Diffusion Approximation ◽  
Numerical Experiments ◽  
Heavy Traffic ◽  
Weak Sense ◽  
Feedforward Network ◽  
State Dependent ◽  
Number Of Customers

This paper is concerned with the characterization of weak-sense limits of state-dependent G-networks under heavy traffic. It is shown that, for a certain class of networks (which includes a two-layer feedforward network and two queues in tandem), it is possible to approximate the number of customers in the queue by a reflected stochastic differential equation. The benefits of such an approach are that it describes the transient evolution of these queues and allows the introduction of controls, inter alia. We illustrate the application of the results with numerical experiments.

Diffusion Approximation of State-Dependent G-Networks Under Heavy Traffic

2008 ◽  
Vol 45 (02) ◽  
pp. 347-362 ◽  
Author(s):  
Saul C. Leite ◽  
Marcelo D. Fragoso
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Diffusion Approximation ◽  
Numerical Experiments ◽  
Heavy Traffic ◽  
Weak Sense ◽  
Feedforward Network ◽  
State Dependent ◽  
Number Of Customers

This paper is concerned with the characterization of weak-sense limits of state-dependent G-networks under heavy traffic. It is shown that, for a certain class of networks (which includes a two-layer feedforward network and two queues in tandem), it is possible to approximate the number of customers in the queue by a reflected stochastic differential equation. The benefits of such an approach are that it describes the transient evolution of these queues and allows the introduction of controls, inter alia. We illustrate the application of the results with numerical experiments.

Model-Based Robust Filtering and Experimental Design for Stochastic Differential Equation Systems

2020 ◽  
Vol 68 ◽  
pp. 3849-3859
Author(s):  
Guang Zhao ◽  
Xiaoning Qian ◽  
Byung-Jun Yoon ◽  
Francis J. Alexander ◽  
Edward R. Dougherty
Keyword(s):  
Differential Equation ◽  
Experimental Design ◽  
Stochastic Differential Equation ◽  
Robust Filtering ◽  
Model Based
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