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Journal Article

Exponential Limiting Distributions in Queueing Systems with Deadlines

M. Drmota and U. Schmid
SIAM Journal on Applied Mathematics
Vol. 53, No. 1 (Feb., 1993), pp. 301-318
Stable URL: http://www.jstor.org/stable/2102287
Page Count: 18
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Exponential Limiting Distributions in Queueing Systems with Deadlines
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Abstract

This paper contains some general theorems on the limiting distribution of a certain random variable ST arising in the context of recurrent events. ST is especially meaningful to the investigation of discrete-time queueing systems subjected to service time deadlines. It may be viewed as a sum of mutually independent conditional random variables BT having the same distribution. It is assumed that BT depends on a parameter T and tends to an unconditional random variable B for T → ∞. Under some weak conditions concerning the conditional probability generating function BT(z), it follows that ST is approximately exponentially distributed with parameter λT = 1/μT, μT = B'T(1)/(1 - BT(1)), which tends to infinity for T → ∞. Provided here are uniform asymptotic expansions for the appropriate probabilities and for all moments, also.

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