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Takács' asymptotic theorem and its applications: a survey (Q966495)

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Language	Label	Description	Also known as
English	Takács' asymptotic theorem and its applications: a survey	scientific article

Statements

scholarly article

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Takács' asymptotic theorem and its applications: a survey (English)

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Vyacheslav M. Abramov

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Acta Applicandae Mathematicae

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publication date

23 April 2010

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full work available at URL

https://arxiv.org/abs/0712.2480

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zbMATH Keywords

asymptotic analysis

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Tauberian theory

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Ballot problems

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queueing theory

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applications of queueing theory

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MaRDI profile type

MaRDI publication profile

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Optimal control of a dam using <i>P</i><sub>λ,τ</sub><sup>M</sup> policies and penalty cost when the input process is a compound Poisson process with positive drift

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Optimal control of a finite dam using <i>P</i><sup><i>M</i></sup><sub>λΤ</sub> policies and penalty cost: total discounted and long run average cases

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On a property of a refusals stream

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On losses in<i>M</i><sup><i>X</i></sup>/<i>GI</i>/1/<i>n</i>queues

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Asymptotic analysis of the \(GI/M/1/n\) loss system as \(n\) increases to infinity

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Asymptotic Behavior of the Number of Lost Messages

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Optimal Control of a Large Dam

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The Effective Bandwidth Problem Revisited

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On loss probabilities in presence of redundant packets and several traffic sources

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Average cost under the <i>P</i><sup><i>M</i></sup><sub>λ, τ</sub> policy in a finite dam with compound Poisson inputs

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Asymptotic buffer overflow probabilities in multiclass multiplexers: an optimal control approach

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Sharp results on convergence rates for the distribution of <i>GI</i>/<i>M</i>/1/<i>K</i> queues as <i>K</i> tends to infinity

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Asymptotic behavior of loss probability in GI/M/1/\(K\) queue as \(K\) tends to infinity

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Exact convergence rate for the distributions of \(GI\)/\(M\)/\(c\)/\(K\) queue as \(K\) tends to infinity

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On the remaining service time upon reaching a given level in \(M/G/1\) queues

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Buffer overflow period in a MAP queue

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Analysis of packet loss processes in high-speed networks

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On the busy periods for the <i>M</i>/<i>G</i>/1 queue with finite and with infinite waiting room

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On the relationship between the distribution of maximal queue length in the <i>M/G/</i>1 queue and the mean busy period in the <i>M/G</i>/1/<i>n</i> queue

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The remaining service time upon reaching a high level in \(M/G/1\) queues

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Queueing and fluid analysis of partial message discarding policy

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Optimal control of finite dams: discrete (2-stage) output procedure

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The ballot theorem strikes again: packet loss process distribution

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\(q\)-generalization of a ballot problem

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Optimal control of a finite dam: Wiener process input

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<i>P</i><sub>λ</sub><sup><i>M</i></sup>-policy for a dam with input formed by a compound Poisson process

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First-crossing and ballot-type results for some nonstationary sequences

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On finite-time ruin probabilities for classical risk models

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A link between wave governed random motions and ruin processes

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A batch-ballot problem and applications

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Complementary generating functions for the<i>M<sup>X</sup>/GI/</i>1<i>/k</i>and<i>GI/M<sup>y</sup>/</i>1<i>/K</i>queues and their application to the comparison of loss probabilities

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Consecutive customer losses in regular and oscillating \(M^{X}/ G /1/ n\) systems

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Consecutive customer losses in oscillating \(GI^X/M//n\) systems with state dependent services rates

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ON THE NUMBER OF REFUSALS IN A BUSY PERIOD

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Characterizing losses during busy periods in finite buffer systems

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A note on losses in <i>M</i>/<i>GI</i>/1/<i>n</i> queues

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On the length and number of served customers of the busy period of a generalised <i>M</i>/<i>G</i>/1 queue with finite waiting room

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Bertrand's work on probability

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A comparison of the stationary distributions of <i>GI</i>/<i>M</i>/<i>c</i>/<i>n</i> and <i>GI</i>/<i>M</i>/<i>c</i>

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Some comments on a theorem of Hardy and Littlewood

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On dams of finite capacity

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On the Classical Ruin Problems

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On the distribution of the maximum of sums of mutually independent and identically distributed random variables

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A single-server queue with limited virtual waiting time

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Combinatorial and analytic methods in the theory of queues

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On the Busy Periods of Single-Server Queues with Poisson Input and General Service Times

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Ballots, queues and random graphs

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Optimal stopping on trajectories and the ballot problem

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Heavy-traffic limits for loss proportions in single-server queues

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A note on the equilibrium <i>M/G</i>/1 queue length

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The output of a switch, or, effective bandwidths for networks

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Sample path large deviations for queues with many inputs

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Losses per cycle in a single-server queue

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Two-stage output procedure of a finite dam

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Identifiers

zbMATH Open document ID

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10.1007/s10440-008-9337-9

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:966495

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