The superposition of alternating on-off flows and a fluid model

An on-off process is a 0-1 process .t in which consecutive 0-periods T0,n alternate with 1-periods T1,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 Zt=.N.=1r...t, where r.>0 and .1t,.,.Nt are independent on-off flows. The process ..t is not Markovian; however, with the age component ..t, the process w.t=(..t,..t) is a piecewise deterministic Markov process. In this paper we study the buffer content process for which the tail of its steady-state distribution .(b) fulfills inequality C.e\gammab..(b).C+e.\gammab,where\gamma > 0$ is the solution of some basic nonlinear system of equations.