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Stability Analysis of a Multi-server Model with Simultaneous Service and a Regenerative Input Flow
Ch. 3. P. 1439–1455.
Afanaseva L., Bashtova E., Grishunina S.
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 service process that is the number of served customers under assumption that always there are customers at the system. Then we construct the sequence of common regeneration points for the regenerative input flow and the auxiliary service process. Basing on relation between the real and auxiliary service processes we obtain the upper and lower estimates for the mean of the really served customers during the common regeneration period. It allows us to deduce the stability criterion of the model under consideration. It turns out that the stability condition does not depend on the structure of the input flow, only the rate of this process plays a role. Nevertheless the distribution of the service time is a very important factor. We give an example which shows that the stability condition can not be expressed in terms of the mean of the service time.
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Vol. 22: Methodology and Computing in Applied Probability. Issue 4: Methodology and Computing in Applied Probability. , Netherlands: Springer, 2020.
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proBDNF and its main proteolytic product BDNF play crucial roles in maturation of neuromuscular junctions during development or reinnervation. We investigated the mechanisms of acute proBDNF effects on synaptic transmission in mouse motor synapses regenerating after nerve crush. The cleavage-resistant proBDNF mimicked the previously shown effect of cleavable proBDNF– GIRK-mediated decrease in the miniature endplate ...
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Spiny mice (Acomys cahirinus) exhibit the ability to regenerate the damaged myocardium and functionalindices of the heart. demonstrated in various models of cardiac pathologies. Cardioregenerative potentialof Acomys is associated with partial preservation of the neonatal phenotype of cardiac tissue in adult animals.The electrophysiology and mechanisms regulating the heart rhythm in Acomys are extremely poorlyunderstood. The ...
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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
Ermakov A., Popov A., Ermakova O. et al., Materials Science and Engineering C 2019 Vol. 104 P. 109924
We report the first experimental evidence for the mitogenic action of cerium(IV) oxide and cerium(III) fluoride nanoparticles (CONs and CFNs) on the regeneration of a whole organism – freshwater flatworms Schmidtea mediterranea (planarian). Both types of cerium-containing nanoparticles are shown to be a highly potent mitogen for planaria. Both CONs and CFNs, in micro- and nanomolar concentrations, ...
Added: May 27, 2020
Ermakov A. M., Ermakova O. N., Popov A. L. et al., Journal of Photochemistry and Photobiology B: Biology 2020 Vol. 202 Article 111714
Planarian freshwater flatworms have the unique ability to regenerate due to stem cell activity. The process of regeneration is extremely sensitive to various factors, including light radiation. Here, the effect of low-intensity LED light of different wavelengths on regeneration, stem cell proliferation and gene expression associated with these processes was studied. LED matrices with different ...
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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
Tkachenko A., Afanasyeva L. G., Theory of Probability and Its Applications 2019 Vol. 63 No. 4 P. 507–531
This paper is focused on the multichannel queueing system with heterogeneous servers, regenerative input flow, and a regenerative process of interruptions. Two service disciplines are studied: preemptive-repeat-different service discipline and preemptive resume service discipline. We consider discrete as well as continuous-time cases. We introduce an auxiliary service flow, which does not depend on the input ...
Added: March 3, 2020
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
Zlotnik A., Lomonosov T., / Series math "arxiv.org". 2018.
We consider explicit two-level three-point in space finite-difference schemes for solving 1D barotropic gas dynamics equations. The schemes are based on special quasi-gasdynamic and quasi-hydrodynamic regularizations of the system. We linearize the schemes on a constant solution and derive the von Neumann type necessary condition and a CFL type criterion (necessary and sufficient condition) for weak conservativeness in L2 for ...
Added: March 28, 2018
Злотник А.А., Ломоносов Т.А., В кн.: Межвузовская научно-техническая конференция студентов, аспирантов и молодых специалистов им. Е.В. Арменского.: М.: МИЭМ НИУ ВШЭ, 2017. С. 37–38.
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Added: December 16, 2017
Zlotnik A., Lomonosov T., , in: Differential and Difference Equations with ApplicationsVol. 230.: Springer, 2018. P. 635–647.
We consider explicit two-level three-point in space finite-difference schemes for solving 1D barotropic gas dynamics equations. The schemes are based on special quasi-gasdynamic and quasi-hydrodynamic regularizations of the system. We linearize the schemes on a constant solution and derive the von Neumann type necessary condition and a CFL type criterion (necessary and sufficient condition) for ...
Added: December 16, 2017
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