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The Poisson Process. Poisson process, rate parameter l e.g. packets/second Three equivalent viewpoints of the Poisson process are illustrated in the next 3 slides. D. time. t. First Viewpoint. Behaviour in small time interval Bernoulli distribution 1 event with probability lD t
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The Poisson Process Poisson process, rate parameter le.g. packets/second • Three equivalent viewpoints of the Poisson process are illustrated in the next 3 slides....
D time t First Viewpoint • Behaviour in small time interval • Bernoulli distribution • 1 event with probability lDt • 0 events with probability 1-lDt
time t Second Viewpoint • Behaviour over a long time interval • Poisson distribution
Third Viewpoint • Behaviour between events • Negative exponential distribution time t
2) i.e. a Poisson distribution, with parameter lt. 3) The probability density function of the times between events (the interarrival times) is negative exponential, with parameter l, i.e. 3 Equivalent Viewpoints • and arrivals are memoryless, i.e. independent of what has happened before.
Sums of Poisson Processes • Consider superposition of several Poisson processes • m independent Poisson Processes, ratesli, i=1,2,...,m • Sum is also a Poisson process, rate l=Sli
