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what is the assumption behind modelling inter-arrival waiting time as an exponentially distributed variable?

what is the assumption behind modelling inter-arrival waiting time as an exponentially distributed variable?

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The assumption behind modeling inter-arrival waiting time as an exponentially distributed variable is that the occurrence follows Poisson process.

In case of Poisson process, occurrence of events are independent of all previous states and depends upon current state only. This is equivalent to memory-less property which holds in case of exponential distribution. In Poisson process, number of occurrence follows Poisson distribution whereas inter-arrival time follows Exponential distribution.

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