Systems and Means of Informatics
2015, Volume 25, Issue 2, pp 60-70
A STUDY OF QUEUEING SYSTEMS WITH DISCRETE TIME, AUTOREGRESSIVE ARRIVALS, AND FEEDBACK
- N. D. Leontyev
- V. G. Ushakov
Abstract
The paper studies two discrete-time single server queueing systems
with infinite capacity and feedback. The arrivals in both systems are driven by
discrete autoregressive models, i. e., the size of each arriving batch may be equal
to the size of one of the previously arrived batches with some fixed probability, or
is a random variable independent of the history with complementary probability.
The main object of the study is the stationary queue length. For the system
with discrete autoregressive arrivals of order 1, expressions for queue length
distribution are derived, and for the system with discrete autoregressive arrivals
of order 2, the expected queue length is found.
[+] References (4)
- Leontyev, N.D., and V.G. Ushakov. 2014. Analiz sistemy obsluzhivaniya s vkhodyashchim potokom avtoregressionnogo tipa [Analysis of queueing system with autoregressive
arrivals]. Informatika i ee Primenenija - Inform. Appl. 8(3):39 - 44.
- Hwang, G.U., and K. Sohraby. 2003. On the exact analysis of a discrete-time queueing
system with autoregressive inputs. Queueing Syst. 43(1-2):29 - 41.
- Miao, D.W.C., and H.C. Lee. 2013. Second-order performance analysis of discrete-
time queues fed by DAR (2) sources with a focus on the marginal effect of the additional
traffic parameter. Appl. Stoch. Models Business Industry 29(1):45 - 60.
- Jacobs, P.A., and P.A.W. Lewis. 1978. Discrete time series generated by mixtures.
III: Autoregressive processes (DAR(p)). Monterey, CA: Naval Postgraduate School. 29 p.
[+] About this article
Title
A STUDY OF QUEUEING SYSTEMS WITH DISCRETE TIME, AUTOREGRESSIVE ARRIVALS, AND FEEDBACK
Journal
Systems and Means of Informatics
Volume 25, Issue 2, pp 60-70
Cover Date
2015-01-30
DOI
10.14357/08696527150203
Print ISSN
0869-6527
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
queueing theory; discrete-time queueing systems; discrete autoregressive model; batch arrivals; feedback
Authors
N. D. Leontyev  and V. G. Ushakov , 
Author Affiliations
Department of Mathematical Statistics, Faculty of Computational Mathematics
and Cybernetics, M.V. Lomonosov Moscow State University, 1-52 Leninskiye Gory, Moscow 119991, GSP-1, Russian Federation
Institute of Informatics Problems, Federal Research Center "Computer Science
and Control", Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
|