Informatics and Applications
2017, Volume 11, Issue 2, pp 112-116
SINGLE SERVER QUEUEING SYSTEM WITH DEPENDENT INTERARRIVAL TIMES
- V. G. Ushakov
- N. G. Ushakov
Abstract
The paper studies a single server queueing system with an infinite number of positions in the queue and random distribution of the service time. The incoming flow of claims is a Poisson flow with a random intensity. The current intensity value is selected from a finite set with given probabilities at the start of the countdown to the next receipt of the claim. Sequential intensities form a Markov chain of a special kind. Particular cases of such flows are hyperexponential flows and flows arising in the study of Bayesian models of queueing systems with a discrete prior distribution. Considered flows describe well the work of queueing systems operating in a random environment with a finite set of different states and Markov relationship between them. Furthermore, such flows can accurately approximate real flows in data networks. The nonstationary behavior of the queue length is studied.
[+] References (6)
- 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. 43:29-41.
- Kamoun, F. 2006. The discrete-time queue with autoregressive inputs revisited. Queueing Syst. 54:185-192.
- Leont'ev, N. D., and V. G. Ushakov. 2014. Analiz sistemy obsluzhivaniya s vkhodyashchim potokom avtoregressionnogo tipa [Analysis of a queueing system with autore
gressive arrivals]. Informatika i ee Primeneniya - Inform. Appl. 8(3):39-44.
- Leont'ev, N. D., and V. G. Ushakov. 2015. Issledovanie sistem obsluzhivaniya s diskretnym vremenem, vkhodyashchim potokom avtoregressionnogo tipa i obratnoy svyaz'yu [A study of queueing systems with discrete time, autoregressive arrivals, and feedback]. Sistemy i Sredstva Informatiki - Systems and Means ofInformatics 25(2):61-71.
- Leont'ev, N. D., and V. G. Ushakov. 2016. Analiz sistemy obsluzhivaniya s vkhodyashchim potokom avtoregressionnogo tipa i otnositel'nym prioritetom [Analysis of a queueing system with autoregressive arrivals and nonpre- emptive priority]. Informatika i ee Primeneniya - Inform. Appl. 10(3):15-22.
[+] About this article
Title
SINGLE SERVER QUEUEING SYSTEM WITH DEPENDENT INTERARRIVAL TIMES
Journal
Informatics and Applications
2017, Volume 11, Issue 2, pp 112-116
Cover Date
2017-06-30
DOI
10.14357/19922264170212
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
Poisson flow; random intensity; hyperexponential flow; Markov chain; single server; queue length
Authors
V. G. Ushakov  ,  and N. 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" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
Institute of Microelectronics Technology and High-Purity Materials of the Russian Academy of Sciences, 6 Academician Osipyan Str., Chernogolovka, Moscow Region 142432, Russian Federation
Norwegian University of Science and Technology, 15A S. P. Andersensvei, Trondheim 7491, Norway
|