CSE 221: Probabilistic Analysis of Computer SystemsIntroductionIntroduction (contd..)Classification of processesDiscrete-state, discrete-parameter processDiscrete-state, continuous-parameter processContinuous-state, discrete-parameter processContinuous-state, continuous-parameter processBernoulli processBernoulli process (contd..)Poisson processPoisson process (contd..)Slide 13CSE 221: Probabilistic Analysis of Computer SystemsTopics covered:Stochastic processesBernoulli 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: Family of random variables:Introduction (contd..)State space of the process:Parameter index:Classification of processes Discrete vs. continuous state-space: Discrete vs. continuous parameter space: :Four types of processes:Discrete-state, discrete-parameter process Example: Number of cars in a service station, at the departure of each car.Discrete-state, continuous-parameter process Example: Number of cars in a service station at time t.Continuous-state, discrete-parameter processExample: Average waiting time for service, at the departure of each car.Continuous-state, continuous-parameter process Example: Total service time of all the cars in the system, at time t.Bernoulli processSequence or a family of Bernoulli random variables:Type:Parameters:Bernoulli process (contd..)Random variable Yn – Number of successes in n trials:Random variable Ti – Number of trials until the first success:Poisson processCount the number of event arrivals in an interval:Successive occurrence of events:Poisson process (contd..)Superposition of Poisson processes:Poisson process (contd..)Decomposition of a Poisson
View Full Document
Unlocking...