Geodesic
Stationary cycles in a deterministic service system
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 14 (2018) no. 1, pp. 40-50 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The article describes a deterministic service system, which receives requests from three queues. Characteristics of the service system such as intensity and rate of service request are stable and do not depend on time. The paper introduces definitions of the stationary mode and the cycle of service for requirements from queues. The main aim this article is to find necessary and sufficient conditions imposed on the duration of the service cycles, under which the existence of a stationary mode of operation of the service system is obtained and guaranteed. When a stationary service mode is implemented, the possibility of infinite accumulation of requests is excluded, while the order of servicing queues is set in advance and does not change in the future. Within the framework of the mathematical model of the deterministic service system, some technological limitations have been introduced. The fulfillment of these limitations is necessary for the construction of an adequate model. In particular, it is assumed that the service of the requirement can't be interrupted. The proof of the main result of the item is based on the solution of inequalities obtained by considering the mathematical model of the functioning of the service system. In the proof was given a geometric interpretation of the set of admissible (providing a stationary mode) durations of continuous service for requests received from the queues. Refs 12. Figs 2.
Keywords: deterministic system service, service cycle, steady state. 
@article{VSPUI_2018_14_1_a4,
     author = {V. M. Bure and A. N. Elfimov and V. V. Karelin},
     title = {Stationary cycles in a deterministic service system},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {40--50},
     year = {2018},
     volume = {14},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2018_14_1_a4/}
}
TY  - JOUR
AU  - V. M. Bure
AU  - A. N. Elfimov
AU  - V. V. Karelin
TI  - Stationary cycles in a deterministic service system
JO  - Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
PY  - 2018
SP  - 40
EP  - 50
VL  - 14
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VSPUI_2018_14_1_a4/
LA  - ru
ID  - VSPUI_2018_14_1_a4
ER  - 
%0 Journal Article
%A V. M. Bure
%A A. N. Elfimov
%A V. V. Karelin
%T Stationary cycles in a deterministic service system
%J Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
%D 2018
%P 40-50
%V 14
%N 1
%U http://geodesic.mathdoc.fr/item/VSPUI_2018_14_1_a4/
%G ru
%F VSPUI_2018_14_1_a4
V. M. Bure; A. N. Elfimov; V. V. Karelin. Stationary cycles in a deterministic service system. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 14 (2018) no. 1, pp. 40-50. http://geodesic.mathdoc.fr/item/VSPUI_2018_14_1_a4/

[1] Ivchenko G. I., Kashtanov V. A., Kovalenko I. N., Queuing theory, Vishaya shkola Publ., M., 1982, 256 pp. (In Russian)

[2] Gazis D., Traffic theory, Kluwer Academic Publ., Kluwer, MA, 2002, 259 pp. | MR | Zbl

[3] Haddad J., De Schutter B., Mahalel V. et al., “Optimal steady-state control for isolated traffic intersections”, IEEE Transactions on Automatic Control, 55:11 (2010), 2612–2617 | DOI | MR | Zbl

[4] Haddad J., Mahalel D., Ioslovich I., Gutman P.-O., “Constrained optimal steady-state control for isolated traffic intersections”, Control Theory Tech., 12:1 (2014), 84–94 | DOI | MR | Zbl

[5] Elfimov A. N., “Control problem of service system with two queuing”, Control Processes and Stability, 2:1 (2015), 605–611 (In Russian)

[6] Bure V. M., Karelin V. V., Elfimov A. N., “On one control problem of a deterministic service system”, Vestnik of Saint Peterburg University. Series 10. Applied Mathematics. Computer Science. Control Processes, 2015, no. 4, 100–112 (In Russian)

[7] Karelin V. V., Bure V. M., Polyakova L. N., Elfimov A. N., “Control problem of a deterministic queuing system”, Applied Mathematical Sciences, 10:21–24 (2016), 1023–1030 | DOI

[8] Karelin V., Bure V., Elfimov A., “Deterministic queuing system”, Proceedings VIII Moscow Intern. Conference on Operations Research, v. 1, 2016, 93–96

[9] Elfimov A. N., Bure V. M., “On the existence of stationary cycles in a deterministic service system with a constraint on the length of a cycle”, Control Processes and Stability, 3:1 (2016), 633–637 (In Russian)

[10] Polyakova L. N., Karelin V. V., Bure V. M., Chitrov G. M., “Exact penalty functions in the control problem of one queuing system”, Vestnik of Saint Peterburg University. Series 10. Applied Mathematics. Computer Science. Control Processes, 2015, no. 1, 73–81 (In Russian)

[11] Yakushev V. P., Karelin V. V., Bure V. M., Parilina E. M., “Soil acidity adaptive control problem”, Stochastic Enviromental Research and Risk Assessment, 29:6 (2015), 1671–1677 | DOI | MR

[12] Chernikov S. N., Linear inequalities, Nauka Publ., M., 1968, 488 pp. (In Russian)