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

Marcel F. Neuts, Jun Guo, Moshe Zukerman, Hai Le Vu

Research output: Contribution to journalArticleResearchpeer-review

13 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1522-1533
Number of pages12
JournalIEEE Transactions on Communications
Issue number9
Publication statusPublished - 1 Sep 2005
Externally publishedYes


  • Finite buffer
  • Queueing model
  • State-dependent service
  • Time division multiple access (TDMA)
  • Waiting time distribution

Cite this