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CSE 221: Probabilistic Analysis of Computer Systems

CSE 221: Probabilistic Analysis of Computer Systems. Topics covered: Stochastic processes Bernoulli and Poisson processes (Sec. 6.1,6.3.,6.4). Introduction . Example: Count the number of cars in a service station, each time a car departs: In between, two departures, some cars may arrive:

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CSE 221: Probabilistic Analysis of Computer Systems

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  1. CSE 221: Probabilistic Analysis of Computer Systems Topics covered: Stochastic processes Bernoulli and Poisson processes (Sec. 6.1,6.3.,6.4)

  2. Introduction • Example: Count the number of cars in a service station, each time a car departs: • In between, two departures, some cars may arrive: • Family of random variables:

  3. Introduction (contd..) • State space of the process: • Parameter index:

  4. Classification of processes • Discrete vs. continuous state-space: • Discrete vs. continuous parameter space: : • Four types of processes:

  5. Discrete-state, discrete-parameter process • Example: Number of cars in a service station, at the departure of each car.

  6. Discrete-state, continuous-parameter process • Example: Number of cars in a service station at time t.

  7. Continuous-state, discrete-parameter process • Example: Average waiting time for service, at the departure of each car.

  8. Continuous-state, continuous-parameter process • Example: Total service time of all the cars in the system, at time t.

  9. Bernoulli process • Sequence or a family of Bernoulli random variables: • Type: • Parameters:

  10. Bernoulli process (contd..) • Random variable Yn – Number of successes in n trials: • Random variable Ti – Number of trials until the first success:

  11. Poisson process • Count the number of event arrivals in an interval: • Successive occurrence of events:

  12. Poisson process (contd..) • Superposition of Poisson processes:

  13. Poisson process (contd..) • Decomposition of a Poisson process:

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