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Analysis of a MX/G(a,b)/1 queueing system with vacation interruption

M. Haridass, R. Arumuganathan (2012)

RAIRO - Operations Research

In this paper, a batch arrival general bulk service queueing system with interrupted vacation (secondary job) is considered. At a service completion epoch, if the server finds at least ‘a’ customers waiting for service say ξ, he serves a batch of min (ξ, b) customers, where b ≥ a. On the other hand, if the queue length is at the most ‘a-1’, the server leaves for a secondary job (vacation) of random length. It is assumed that the secondary...

Analysis of a two-unit standby redundant system with three states of units

Antonín Lešanovský (1982)

Aplikace matematiky

A cold-standby redundant system with two identical units and one repair facility is considered. Units can be in three states> good (I), degraded (II), and failed (III). We suppose that only the following state-transitions of a unit are possible: I → I I , I I → I I I , I I → I , I I I → I . The repair of a unit of the type I I → I can be interpreted as a preventive maintenance. Its realization depends on the states of both units. Several characteristics of the system (probabilities, distribution functions or their Laplace-Stieltjes transforms...

Analysis of an M|G|1|R queue with batch arrivals and two hysteretic overload control policies

Yuliya Gaidamaka, Alexander Pechinkin, Rostislav Razumchik, Konstantin Samouylov, Eduard Sopin (2014)

International Journal of Applied Mathematics and Computer Science

Hysteretic control of arrivals is one of the most easy-to-implement and effective solutions of overload problems occurring in SIP-servers. A mathematical model of an SIP server based on the queueing system M [ X ] | G | 1 ⟨ L , H ⟩ | ⟨ H , R ⟩ with batch arrivals and two hysteretic loops is being analyzed. This paper proposes two analytical methods for studying performance characteristics related to the number of customers in the system. Two control policies defined by instants when it is decided to change the system’s mode are considered....

Analysis of an MMAP/PH₁,PH₂/N/∞ queueing system operating in a random environment

Chesoong Kim, Alexander Dudin, Sergey Dudin, Olga Dudina (2014)

International Journal of Applied Mathematics and Computer Science

A multi-server queueing system with two types of customers and an infinite buffer operating in a random environment as a model of a contact center is investigated. The arrival flow of customers is described by a marked Markovian arrival process. Type 1 customers have a non-preemptive priority over type 2 customers and can leave the buffer due to a lack of service. The service times of different type customers have a phase-type distribution with different parameters. To facilitate the investigation...

Analysis of AQM queues with queue size based packet dropping

Andrzej Chydziński, Łukasz Chróst (2011)

International Journal of Applied Mathematics and Computer Science

Queueing systems in which an arriving job is blocked and lost with a probability that depends on the queue size are studied. The study is motivated by the popularity of Active Queue Management (AQM) algorithms proposed for packet queueing in Internet routers. AQM algorithms often exploit the idea of queue-size based packet dropping. The main results include analytical solutions for queue size distribution, loss ratio and throughput. The analytical results are illustrated via numerical examples that...

Analysis of the Rosenblatt process

Ciprian A. Tudor (2008)

ESAIM: Probability and Statistics

We analyze the Rosenblatt process which is a selfsimilar process with stationary increments and which appears as limit in the so-called Non Central Limit Theorem (Dobrushin and Majòr (1979), Taqqu (1979)). This process is non-Gaussian and it lives in the second Wiener chaos. We give its representation as a Wiener-Itô multiple integral with respect to the Brownian motion on a finite interval and we develop a stochastic calculus with respect to it by using both pathwise type calculus and Malliavin...

Analysis on some linear sets

Robert Kaufman (1971)

Annales de l'institut Fourier

The note discusses a probabilistic method for constructing “small” sets, with regard to differentiable transformations and to quantitative measures of independence.

Analytic and Geometric Logarithmic Sobolev Inequalities

Michel Ledoux (2011)

Journées Équations aux dérivées partielles

We survey analytic and geometric proofs of classical logarithmic Sobolev inequalities for Gaussian and more general strictly log-concave probability measures. Developments of the last decade link the two approaches through heat kernel and Hamilton-Jacobi equations, inequalities in convex geometry and mass transportation.

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