A discrete-time Markov modulated queuing system with batched arrivals
arXiv:math/0612476 · doi:10.1016/j.peva.2009.11.001
Abstract
This paper examines a discrete-time queuing system with applications to telecommunications traffic. The arrival process is a particular Markov modulated process which belongs to the class of discrete batched Markovian arrival processes. The server process is a single server deterministic queue. A closed form exact solution is given for the expected queue length and delay. A simple system of equations is given for the probability of the queue exceeding a given length.
to appear Performance Evaluation