Lecture 4 Flashcards
(9 cards)
What type of process are modeled by COUNTINOUS time discrete-state Markov Models?
are used to model systems that evolve continuously over time but have a countable (often finite) number of states. No Memory. Eg. Reliability and Maintenance !!
What are the assumptions of the continuous Markov model model?
Once again, Memoriless.
Continuous: transition can happen at any point in time, not only at discrete intervals
How can you compute the transition rate matrix from the continuous-time transition probability matrix?
Transition probability –> Discrete
Transition Rate –> Continuous
The idea is that the time interval of the transition is so small that only one event can happen within it
How can you compute the steady-state probabilities in continuous- time discrete-state Markov processes. What do they represent?
They represent how much time the system steps at each state in the long term.
= average fraction of time the system is functioning
= average fraction of time the system is down (i.e., under repair)
Define the system failure intensity for a general system modelled by continuous-time discrete-state Markov processes. How can you compute it?
YSTEM FAILURE INTENSITY, W_f = Rate at which system failures occur =
= expected number of system failures per unit of time =
= rate of exiting a success state to go into one of fault
which is basically: Rate x Probability
Define the system repair intensity for a general system modelled by continuous-time discrete-state Markov processes. How can you compute it?
SYSTEM REPAIR INTENSITY, W_r
Rate at which system repairs occur =
= expected number of system repairs per unit of time =
= rate of exiting a failed state to go into one of success
again, it is a: Rate x Probability
How can you compute the average time of occupancy of a state in continuous-time discrete-state Markov processes. What is the probability distribution that describe this time? Why?
time the system remains in state i before it departs towards another state with constant rate
How can you generally compute the availability of any system using continuous-time discrete-state Markov processes?
