School of Information Technologies Poisson-1 The Poisson Process Poisson process, rate parameter e.g. packets/second Three equivalent viewpoints of the.

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Presentation transcript:

School of Information Technologies Poisson-1 The Poisson Process Poisson process, rate parameter e.g. packets/second Three equivalent viewpoints of the Poisson process are illustrated in the next 3 slides....

School of Information Technologies Poisson-2 First Viewpoint Behaviour in small time interval –Bernoulli distribution –1 event with probability  t –0 events with probability 1-  t time  t

School of Information Technologies Poisson-3 Second Viewpoint Behaviour over a long time interval –Poisson distribution time t

School of Information Technologies Poisson-4 Third Viewpoint Behaviour between events –Negative exponential distribution time t

School of Information Technologies Poisson-5 3 Equivalent Viewpoints 1) and arrivals are memoryless, i.e. independent of what has happened before. 2) i.e. a Poisson distribution, with parameter t. 3)The probability density function of the times between events (the interarrival times) is negative exponential, with parameter, i.e.

School of Information Technologies Poisson-6 Sums of Poisson Processes Consider superposition of several Poisson processes –m independent Poisson Processes, rates i, i=1,2,...,m Sum is also a Poisson process, rate  i

School of Information Technologies Poisson-7 Sums of Poisson Processes