Analysis of queueing networks with batch movements of customers and control of flows among clusters

Mitrofanov, Yu. I.; Rogachko, E. S.; Stankevich, E. P.

doi:10.3103/s0146411615040094

Cited by 5 publications

(2 citation statements)

References 17 publications

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“…In the paper, we analyze the assembly of independent Poisson flows which is interpreted as connection of customers with the same order numbers taken from different flows. The assembly processes may be found in computer networks [1], in conveyor systems for the manufacture of products [2][3][4], in open queueing networks with a single input flow, division and merging of customers and with sufficiently general configuration of network [5,6], in closed queueing networks with discrete time transitions of batches of customers and dynamic control of service rates [7]. However, the study of the flow of customers coming out after the assembly is a very complicated problem.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Analysis of Intensity of Poisson Flows Assembly

Tsitsiashvili¹,

Moiseev

Voytikov

2021

Information Technologies and Mathematical Modelling. Queueing Theory and Applications

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The paper is devoted to obtaining estimations of the rate of convergence of the intensity of an assembly of Poisson flows to the intensity of a stationary Poisson flow. Analysis of the results shows that this problem should combine analytical and numerical studies. An important role is played by the Central limit theorem for both random variables and stochastic processes which is understood in the sense of C-convergence. Exact asymptotic formulas are derived for intensity of the assembly flow of identical Poisson flows, and estimations of the convergence rate are build for the case of non-identical original flows.

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Section: Introductionmentioning

confidence: 99%

Asymptotic Analysis of Intensity of Poisson Flows Assembly

Tsitsiashvili¹,

Moiseev

Voytikov

2021

Information Technologies and Mathematical Modelling. Queueing Theory and Applications

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“…the standard textbooks [2,34]. Several papers, such as [35,36,37,38,39,40], consider queues with batch arrivals and batch services and find product-form results, but these typically neither cover our multiplicative update rule nor allow the transition rates to be affected by an environmental process. We also refer to the related papers [41,42,43].…”

Section: Introductionmentioning

confidence: 99%

Modelling complex stochastic systems: approaches to management and stability

Patch¹

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This thesis is about coping with variability in outcomes for complex stochastic systems. We focus on systems where jobs arrive randomly throughout time to utilise resources for a random amount of time before departure. The systems we investigate are primarily concerned with the communication and storage of data. The thesis is partitioned into two parts. The first part studies systems where Publications included in this thesis Journal articles (peer-reviewed)

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A Versatile Stochastic Dissemination Model

Chan

Mandjes

2023

Methodol Comput Appl Probab

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This paper considers a highly general dissemination model that keeps track of the stochastic evolution of the distribution of wealth over a set of agents. There are two types of events: (i) units of wealth externally arrive, and (ii) units of wealth are redistributed among the agents, while throughout Markov modulation is allowed. We derive a system of coupled differential equations describing the joint transient distribution of the agents’ wealth values, which translate into linear differential equations when considering the corresponding means and (co-)variances. While our model uses the (economic) terminology of wealth being distributed over agents, we illustrate through a series of examples that it can be used considerably more broadly. Indeed, it also facilitates the analysis of the spread of opinions over a population (thus generalizing existing opinion dynamics models), and the analysis of the dynamics of a file storage system (thus allowing the assessment of the efficacy of storage policies).

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Analysis of queueing networks with batch movements of customers and control of flows among clusters

Cited by 5 publications

References 17 publications

Asymptotic Analysis of Intensity of Poisson Flows Assembly

Asymptotic Analysis of Intensity of Poisson Flows Assembly

Modelling complex stochastic systems: approaches to management and stability

A Versatile Stochastic Dissemination Model

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