Overflow probability for a discrete-time queue with non-stationary multiplexed input

Recently it has been reported that various traffic exhibit long-range depen dence and/or self-similarity. However, there exist some reports which sugge st that traffic may be non-stationary. In this paper we discuss the average overflow probability J(N)(L)(Ly)=E[N(-1)Sigma I-N(n=1){Q(n)(L)> Ly}] in a finite period [1,N] for a discrete-time queue Q(n)(L) with a non-stationary multiplexed input from L sources. By using the large deviation principle, we analyze the asymptotic behavior of J(N)(L)(Ly) as L increases and obtain an approximation formula of the form J(n)(L)(Ly)approximate toC(L,y) e(-ga mma (y)). We apply the approximation formula to two examples. One is a non- stationary process with deterministic level shifts and the other is a Gauss ian process with spectrum of the form f(-nu). The latter is non-stationary if nu greater than or equal to1.