منابع مشابه
Gaussian queues in light and heavy traffic
In this paper we investigate Gaussian queues in the light-traffic and in the heavy-traffic regime. Let Q X ≡ {Q X (t) : t ≥ 0} denote a stationary buffer content process for a fluid queue fed by the centered Gaussian process X ≡ {X(t) : t ∈ R} with stationary increments, X(0) = 0, continuous sample paths and variance function σ 2(·). The system is drained at a constant rate c > 0, so that for a...
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In this paper we investigate Gaussian queues in the light-traffic and in the heavy-traffic regime. The setting considered is that of a centered Gaussian process X ≡ {X(t) : t ∈ R} with stationary increments and variance function σ X(·), equipped with a deterministic drift c > 0, reflected at 0: Q (c) X (t) = sup −∞<s≤t (X(t)−X(s)− c(t− s)). We study the resulting stationary workload processQ (c...
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We consider the maximum waiting time among the first n customers in the GI/G/1 queue. We use strong approximations to prove, under regularity conditions, convergence of the normalized maximum wait to the Gumbel extreme-value distribution when the traffic intensity p approaches 1 from below and n approaches infinity at a suitable rate. The normalization depends on the interarrival-time and servi...
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ژورنال
عنوان ژورنال: Queueing Systems
سال: 2012
ISSN: 0257-0130,1572-9443
DOI: 10.1007/s11134-011-9270-x