TRANSFORMATIONS OF POISSON STREAMS AND THEIR APPLICATION TO COMMUNICATION SYSTEMS.

Queueing systems modeling communication networks usually comprise a large number of nodes and customer streams in transit. We study the correlation properties of a sequence of transformations of a Poisson stream. The j-th transformation changes the coordinate x//i(j) of the point i according to x//i(j) equals x//i(j minus 1) plus S//i//j, j greater than equivalent to 1, where S//i//j are jointly independent positive random variables exponentially distributed with the parameter mu j, x//i(0) is the initial coordinate of the point i.