A random sequence of moments of time at which the events of a flow of events take place (e.g. a flow of incoming calls at a telephone station), and for which the differences satisfy the condition of independence and have the same exponential distribution. An elementary flow with distribution
is a particular case of a renewal process (cf. Renewal theory). To an elementary flow is related the Poisson process equal to the number of events of the flow in the time interval . An elementary flow and its related Poisson process satisfy the following conditions.
Stationarity. For any , the distribution of the random variable
does not depend on .
Orderliness. The probability of occurrence of two or more events of the flow in the interval is equal to as .
Lack of memory. For the random variables , , are independent.
It turns out that in these circumstances and under the condition
the flow is elementary with exponential distribution (*).
|||A.Ya. Khinchin, "Mathematical methods in the theory of queueing" , Griffin (1960) (Translated from Russian)|
Elementary flow. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Elementary_flow&oldid=18634