Abstract
Recently it has been reported that various traffic exhibit long‐range dependence and/or self‐similarity. However, there exist some reports which suggest that traffic may be non‐stationary. In this paper we discuss the average overflow probability JN L(Ly)≡E[N−1Σn=1 NI{Qn L>Ly}] in a finite period [1,N] for a discrete‐time queue Qn L with a non‐stationary multiplexed input from L sources. By using the large deviation principle, we analyze the asymptotic behavior of JN L(Ly) as L increases and obtain an approximation formula of the form Jn L(Ly)≈C(L,y) e−γ(y). We apply the approximation formula to two examples. One is a non‐stationary process with deterministic level shifts and the other is a Gaussian process with spectrum of the form f−ν. The latter is non‐stationary if ν≥1.
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Kobayashi, K., Takahashi, Y. Overflow probability for a discrete‐time queue with non‐stationary multiplexed input. Telecommunication Systems 15, 157–166 (2000). https://doi.org/10.1023/A:1019134726750
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DOI: https://doi.org/10.1023/A:1019134726750