The waiting time distribution for a TDMA model with a finite buffer and state-dependent service

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=λW. We also demonstrate that our methodology provides a concise treatment of various special cases that have been studied over the past half century.