?
On mean-field GI/GI/1 queueing model:existence and uniqueness
P. 182–186.
Existence and uniqueness has been established for a mean-field version of the GI/GI/1 queueing model
Publication based on the results of:
Afanaseva L., Bashtova E., Grishunina S., , in: Methodology and Computing in Applied ProbabilityVol. 22: Methodology and Computing in Applied Probability. Issue 4: Methodology and Computing in Applied Probability.: Netherlands: Springer, 2020. Ch. 3 P. 1439–1455.
We study the stability conditions of the multiserver system in which each customer requires a random number of servers simultaneously. The input flow is supposed to be a regenerative one and a random service time is identical at all occupied servers. The service time has an exponential or a phase-type distribution. We de fine an auxiliary ...
Added: February 2, 2021
Netherlands: Springer, 2020.
ASMDA 2017 ...
Added: February 2, 2021
Netherlands: Springer, 2020.
The Volume includes a Special Section on "Analytical and Computational Methods in Probability" ...
Added: February 2, 2021
Grishunina S., Theory of Probability and Its Applications 2019 Vol. 64 No. 3 P. 456–460
This paper is focused on stability conditions of a multiserver queueing system with regenerative input flow where a random number of servers is simultaneously required for each customer, and each server completion time is constant. It turns out that the stability condition depends on the rate of the input flow rather than on its structure. ...
Added: March 18, 2020
Veretennikov A., Queueing Systems 2020 Vol. 94 No. 3 P. 243–255
A mean-field extension of the queueing system \(GI/GI/1\) is considered. The process is constructed as a Markov solution of a martingale problem. Uniqueness in distribution is also established under a slightly different set of assumptions on intensities in comparison to those required for existence. ...
Added: October 29, 2019
Grishunina S., Теория вероятностей и ее применения 2019 Т. 64 № 3 С. 566–572
This paper is focused on stability conditions of a multi-server queueing system with regenerative input flow where a random number of servers is simultaneously required for each customer and each server's completion time is constant. It turns out that the stability condition depends on the rate of the input flow and not on its structure. ...
Added: August 29, 2019
Grishunina S., , in: Abstracts of the 9-th International Workshop on Applied Probability.: Budapest: [б.и.], 2018. P. 71–71.
We study stability conditions of the multiserver queueing system in which each customer requires a random number of servers simultaneously. The input flow is supposed to be a regenerative one and service time is the same on all occupied servers and equals a constant τ . Discipline is FIFO. We define an auxiliary service process ...
Added: December 9, 2018
Budapest: [б.и.], 2018.
Abstracts of the 9-th International Workshop on Applied Probability ...
Added: December 9, 2018
Afanaseva L., Gridnev M., Grishunina S., , in: IX Moscow International Conference on Operations Research (ORM2018) Moscow, October 22–27, 2018.: [б.и.], 2018. P. 264–269.
The purpose of the proposed study is an estimation of the carrying capacity of the automobile road, crossed by a crosswalk. Under the capacity we mean the upper limit of the intensity of the flow of cars, when the queue of cars does not tend to infinity. This means that the stability condition for the ...
Added: December 9, 2018
Grishunina S., , in: IX Moscow International Conference on Operations Research (ORM2018) Moscow, October 22–27, 2018.: [б.и.], 2018. P. 333–337.
We study stability conditions of the multiserver queueing system in which each customer requires a random number of servers simultaneously. The input flow is supposed to be a regenerative one. We consider two models: the system where service time is the same on all occupied servers and equals a constant b and the system where service times ...
Added: December 9, 2018
Afanaseva L., Bashtova E., Grishunina S., Methodology and Computing in Applied Probability 2019 P. 1–17
We study the stability conditions of the multiserver system in which each customer requires a random number of servers simultaneously. The input flow is supposed to be a regenerative one and a random service time is identical at all occupied servers. The service time has an exponential or a phase-type distribution. We de fine an auxiliary ...
Added: September 5, 2017
Afanaseva L., Grishunina S., Lobachevskii Journal of Mathematics 2017 Vol. 38 No. 5 P. 864–869
In this paper we investigate multi-server queueing systems with regenerative input flow and independent service times with finite mean. Various service disciplines are considered: systems with a common queue and systems with parallel queues when an arrived customer chooses server in accordance with a certain rule and stays in a chosen queue until the moment ...
Added: June 23, 2017
Manita A.D., Theory of Probability and Its Applications 2009 Vol. 53 No. 4 P. 155–165
We study the Markov exclusion process for a particle system with a local interaction in the integer strip. This process models the exchange of velocities and particle-hole exchange of the liquid molecules. It is shown that the mean velocity profile corresponds to the behavior which is characteristic for incompressible viscous liquid. We prove the existence ...
Added: June 20, 2017
Kashtanov V., Зайцева О. Б., В кн.: Бесконечномерный анализ, стохастика, математическое моделирование: новые задачи и методы.: М.: Издательство РУДН, 2015. С. 247–252.
We construct the optimal strategy for management system with variable structure, which is described by a controlled semi-Markov process with a finite set of states. An algorithm for solving the problem and the results of numerical experiments ...
Added: February 23, 2016
Manita A., Theory Probability and its Applications 2015 Vol. 59 No. 4 P. 707–710
On the talks that were given at the meeting of the General Seminar of the Department of Probability. ...
Added: December 5, 2015
Tkachenko A., Afanasyeva L. G., Journal of Mathematical Sciences 2016 Vol. 218 No. 2 P. 119–136
Convergence rates in total variation are established for some models of queueing theory and reliability theory. Analysis is based on renewal technique and asymptotic results for the renewal function. It is shown that convergence rate has an exponential asymptotics when distribution function of regeneration period satisfies Cramer's condition. Results concerning polynomial convergence are also obtained. ...
Added: October 14, 2015
A.D. Manita, Theory of Probability and Its Applications 2009 Vol. 53 No. 1 P. 155–161
We consider a basic stochastic particle system consisting of N identical particles with isotropic k-particle synchronization, ${k\ge 2}$. In the limit when both the number of particles N and the time $t=t(N)$ grow to infinity we study an asymptotic behavior of a coordinate spread of the particle system. We describe three time stages of $t(N)$ ...
Added: March 20, 2015
Manita A., / Series "Working papers by Cornell University". 2014. No. arXiv:1409.2919.
http://xxx.tau.ac.il/abs/1409.2919 We propose stochastic N -component synchronization models, whose dynamics is described by Levy processes and synchronizing jumps. We prove that symmetric models reach synchronization in a stochastic sense: differences between components have limits in distribution as t→∞. We give conditions of existence of natural (intrinsic) space scales for large synchronized systemsю. It appears that ...
Added: March 18, 2015