Informatics and Applications
2014, Volume 8, Issue 3, pp 39-44ANALYSIS OF A QUEUEING SYSTEM WITH AUTOREGRESSIVE ARRIVALS
- N. D. Leontyev
- V. G. Ushakov
Abstract
The paper studies a single server queueing system with infinite capacity and with the Poisson batch arrival process. A feature of the system under study is autoregressive dependence of the arriving batch sizes: the size of the nth batch is equal to the size of the (n - 1)st batch with a fixed probability and is an independent random variable with complementary probability. Service times are supposed to be independent random variables with a specified distribution. The main object of the study is the queue length at an arbitrary moment. The relations derived make it possible to find Laplace transorm in time of the probability generating function of the transient queue length, and also a number of additional characteristics such as the residual service time and the distribution of the size of the last batch that arrived before time t.[+] References (4)
- Hwang, G. U., B. D. Choi, and J.-K. Kim. 2002. The waiting time analysis of a discrete-time queue with arrivals as an autoregressive process of order 1. J. Appl. Probab. 39(3):619-629.
- 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.
- Matveev, V. F., and V. G. Ushakov. 1984. Sistemy massovogo obsluzhivaniya [Queueing systems]. Moscow: MSU. 242 p.
- Schechter, S. 1959. On the inversion of certain matrices. Math. Tab. Aids Comput. 13(66):73-77.
[+] About this article
Title
ANALYSIS OF A QUEUEING SYSTEM WITH AUTOREGRESSIVE ARRIVALSJournal
Informatics and Applications2014, Volume 8, Issue 3, pp 39-44
Cover Date
2014-03-31DOI
10.14357/19922264140305Print ISSN
1992-2264Publisher
Institute of Informatics Problems, Russian Academy of SciencesAdditional Links
Key words
queueing theory; transient behavior; batch arrivalsAuthors
N. D. Leontyev
and V. G. Ushakov,
Author Affiliations
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, Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian
Federation