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- W1969409877 abstract "A well-known discrete-time, single-server queueing system with mean arrival rate λ and mean departure rate μ is considered from the perspective of the area, A, swept out by the queue occupation process during a busy period. We determine the exact form of the tail of the distribution, Pr(A > x); in particular, we show that Pr(A > x) ~ Cx−1/4 exp(−Dx1/2) for all ρ ≠ 1, where ρ ≡ λ/μ, and expressions for C and D are given. For the critical case ρ = 1 we show that Pr(A > x) ~ C'x−1/3, with C' also given. A simple mapping, used in the derivation, establishes a connection with compact directed percolation on a square lattice. As a corollary, therefore, we are also able to specify the large-area asymptotic behaviour of this model at all points in the phase diagram. This extends previous scaling results, which are only valid close to the percolation threshold." @default.
- W1969409877 created "2016-06-24" @default.
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- W1969409877 date "2004-08-18" @default.
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- W1969409877 title "On a random area variable arising in discrete-time queues and compact directed percolation" @default.
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- W1969409877 doi "https://doi.org/10.1088/0305-4470/37/35/002" @default.
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