Title :
Discrete time queues with phase dependent arrivals
Author :
Daigle, J.N. ; Lee, Y. ; Magalhães, M.N.
Author_Institution :
Mitre Corp., McLean, VA, USA
Abstract :
The queueing behavior of many communication systems is well modeled by a queueing system in which time is slotted, and the number of entities that arrive during a slot is dependent upon the state of a discrete time, discrete state Markov chain. Techniques for analyzing such systems have appeared in the literature from time to time, but distributions have been presented in only rare instances In the paper, the authors present the probability generating function (PGF) for joint and marginal buffer occupancy distributions of statistical time division multiplexing systems in this class. They discuss inversion of the PGF using discrete Fourier transforms, and also discuss a simple technique for obtaining moments of the queue length distribution. Numerical results, including queue length distributions for some special cases, are presented
Keywords :
Markov processes; buffer storage; discrete time systems; numerical analysis; packet switching; queueing theory; PGF; communication systems; discrete Fourier transforms; discrete time discrete state Markov chain; joint buffer occupancy distributions; marginal buffer occupancy distributions; moments; phase dependent arrivals; probability generating function; queueing behavior; statistical time division multiplexing systems; Character generation; Communications Society; Discrete Fourier transforms; Equations; Probability; State-space methods; Statistics; Stochastic processes; Stochastic systems; Time division multiplexing;
Journal_Title :
Communications, IEEE Transactions on
DOI :
10.1109/TCOMM.1994.577088
