THE SUPERPOSITION OF ALTERNATING ON-OFF FLOWS AND A FLUID MODEL

An on-off process is a 0-1 process xi(t) in which consecutive 0-period s (T-0,T-n) alternate with 1-periods (T-1,T-n) (n = 1, 2,...). The on and off time sequences are independent, each consisting of i.i.d. r.v. s. By the superposed flow, we mean the process Z(t) = Sigma(l=1)(N) r( e)xi(t)(l), where r(l) > 0 and (xi(t)(1)),...,(xi(t)(N)) are independe nt on-off flows. The process xi(t)(l) is not Markovian; however, with the age component eta(t)(l), the process w(t)(l) = (xi(t)(l), eta(t)(l )) is a piecewise deterministic Markov process. In this paper we study the buffer content process for which the tail of its steady-state dis tribution Psi(b) fulfills inequality C_e(-gamma b) less than or equal to Psi(b) less than or equal to C(+)e(-gamma b), where gamma > 0 is th e solution of some basic nonlinear system of equations.