Markov Equation Notations
The following table defines the notations used in Markov calculation equations. For more information, see Markov Calculation Equations.
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Notation
|
Definition
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|---|---|
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Z(t)
|
State of continuous time Markov chain at time t; it is a random variable.
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|
λ i,j
|
Transition rate from state i to state j.
|
|
TR
|
Transition rate matrix:  |
|
Ω
|
{1, ..., n} state space of the continuous time Markov chain, Z(t).
|
|
Ωu, Ωd, Ωa
|
Set of [up, down, absorbing] states.
|
|
∈
|
Error tolerance.
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|
Pi(t)
|
Probability of state i.
|
|
P(t)
|
State probability vector of Z(t).
|
|
P(0)
|
Initial state probability vector.
|
|
Ci
|
Capacity of state i.
|
|
si
|
Cost for state i per unit time; gain is positive and loss is negative.
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|
ti,j
|
Cost for each transition from state i to state j; gain is positive and loss is negative.
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