CSE 221: Probabilistic Analysis of Computer SystemsIntroductionIntroduction (contd..)Introduction (contd..)Introduction (contd..)Example of CTMCExample of CTMC (contd..)Birth-death processBirth-death process (contd..)Slide 10Slide 11Slide 12Birth-death process (contd..)CSE 221: Probabilistic Analysis of Computer SystemsTopics covered:Continuous time Markov chains(Sec. 8.1-8.2)IntroductionExample: Counting the number of cars at a service station each time a car departs. Discrete-space, continuous-time:Introduction (contd..) Time spent in each state:Introduction (contd..) Transition rate:Generator matrix: Diagonal entries:Introduction (contd..)State probabilities:Example of CTMCExample: State of a componentGenerator matrix: How to compute the probabilities of being in each one of the states:Example of CTMC (contd..) Balance equations:Steady-state probabilities:Numerical example:Birth-death process Example: Number of cars in a service station, each time a car arrives and departs. Transitions in the state-space:Birth-death process (contd..)Generator matrix: Balance equations:Birth-death process (contd..)Steady-state or limiting probabilitiesBirth-death process (contd..)Finite state space:Transitions in the state space:Birth-death process (contd..)Generator matrix: Balance equations:Birth-death process (contd..) Steady-state or limiting
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