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The waiting time distribution for a TDMA model with a finite buffer and state-dependent service
Neuts, M.F.; Jun Guo; Zukerman, M.; Hai Le Vu;
Communications, IEEE Transactions on
Volume 53,
Issue 9,
Sept. 2005
Page(s):1522
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1533
Abstract:
We obtain detailed analytic formulas for the density and probability distribution of the waiting time in a time-division multiple-access (TDMA) model with a finite buffer and state-dependent service. On successive intervals of length equal to the duration of a slot, the density is expressed as a linear combination of beta densities with positive coefficients. A recursive scheme, obtained by a matrix-analytic derivation, allows for the highly efficient computations of the coefficient sequences. An expression for the mean waiting time is derived using the classical queueing formula L=/spl lambda/W. We also demonstrate that our methodology provides a concise treatment of various special cases that have been studied over the past half century.
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