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- W2104045250 abstract "We consider the standard single-server queue with unlimited waiting space and the first-in first-out service discipline, but without any explicit independence conditions on the interarrival and service times. We find conditions for the steady-state waiting-time distribution to have asymptotics of the form x –1 log P ( W > x ) → – θ ∗as x → ∞for θ ∗ > 0. We require only stationarity of the basic sequence of service times minus interarrival times and a Gärtner–Ellis condition for the cumulant generating function of the associated partial sums, i.e. n –1 log E exp ( θS n ) → ψ ( θ ) as n → ∞, plus regularity conditions on the decay rate function ψ . The asymptotic decay rate θ is the root of the equation ψ ( θ ) = 0. This result in turn implies a corresponding asymptotic result for the steady-state workload in a queue with general non-decreasing input. This asymptotic result covers the case of multiple independent sources, so that it provides additional theoretical support for a concept of effective bandwidths for admission control in multiclass queues based on asymptotic decay rates." @default.
- W2104045250 created "2016-06-24" @default.
- W2104045250 creator A5019114258 @default.
- W2104045250 creator A5083215472 @default.
- W2104045250 date "1994-01-01" @default.
- W2104045250 modified "2023-10-03" @default.
- W2104045250 title "Logarithmic asymptotics for steady-state tail probabilities in a single-server queue" @default.
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- W2104045250 doi "https://doi.org/10.2307/3214953" @default.
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