A certain type component has two states: 0 = off and 1 = operating. In state 0, the process remains in the state an exponential amount of time with rate a, and then moves to state 1. The component spends an exponential amount of time with rate ß in state 1 after which the process returns to state 0. A system consists of two such components A and B. Assume the amounts of time the components spend in the states are independent of one another and have rates given by the following. Component Off Rate (a) Operating Rate (B) A 4 B 3 6 Consider the continuous-time Markov chain with states {0,4,B,2} representing the component currently operating. Enumerate the transition rates V; and the transition probabilities pij of the Markov chain.
A certain type component has two states: 0 = off and 1 = operating. In state 0, the process remains in the state an exponential amount of time with rate a, and then moves to state 1. The component spends an exponential amount of time with rate ß in state 1 after which the process returns to state 0. A system consists of two such components A and B. Assume the amounts of time the components spend in the states are independent of one another and have rates given by the following. Component Off Rate (a) Operating Rate (B) A 4 B 3 6 Consider the continuous-time Markov chain with states {0,4,B,2} representing the component currently operating. Enumerate the transition rates V; and the transition probabilities pij of the Markov chain.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:A certain type component has two states: 0 = off and 1 = operating. In state 0, the process
remains in the state an exponential amount of time with rate a, and then moves to state 1. The
component spends an exponential amount of time with rate ß in state 1 after which the process
returns to state 0. A system consists of two such components A and B. Assume the amounts of
time the components spend in the states are independent of one another and have rates given by
the following.
Component
Off Rate (a)
Operating Rate (B)
A
4
B
3
6
Consider the continuous-time Markov chain with states {0,4,B,2} representing the component
currently operating. Enumerate the transition rates V; and the transition probabilities pij of the
Markov chain.
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