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.
Summary
Analyses a discrete-time queuing system, with a Markov-modulated batched arrival process and a deterministic single server, of relevance to telecommunications traffic modelling, deriving a closed-form exact solution for expected queue length and delay along with equations for the probability the queue exceeds a given length.
bibtex
@article{clegg2010markovqueuing,
author = {Richard G. Clegg},
title = {A discrete-time Markov-modulated queuing system with batched arrivals},
journal = {Performance Evaluation},
year = {2010},
volume = {67},
number = {5},
pages = {376--385},
doi = {10.1016/j.peva.2009.11.001}
}
Venue
Performance Evaluation, 67(5), pp. 376-385