Asymptotic Condition

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Svetlana Moiseeva - One of the best experts on this subject based on the ideXlab platform.

  • Modeling of Mathematical Processing of Physics Experimental Data in the Form of a Non-Markovian Multi-Resource Queuing System
    Russian Physics Journal, 2019
    Co-Authors: E. Yu. Lisovskaya, Svetlana Moiseeva, Alexander Moiseev, Michele Pagano
    Abstract:

    The paper presents a mathematical model for processing of physics experimental data in the form of a non-Markovian infinite-server multi-resource queuing system with Markov modulated Poisson process arrivals and arbitrary service time. It is proved that the joint steady-state probability distribution of the total volume of the occupied resource of each type converges to a multidimensional Gaussian distribution under the Asymptotic Condition of the growing intensity of the arrival process. The parameters of this Asymptotic distribution are derived.

  • Queueing System GI|GI|\infty with n Types of Customers
    Communications in Computer and Information Science, 2015
    Co-Authors: Ekaterina Pankratova, Svetlana Moiseeva
    Abstract:

    The research of the queuing system with renewal arrival process, infinite number of n different types servers and arbitrary service time distribution is proposed. Expressions for the characteristic function of the number of busy servers for different types of customers in the system under the Asymptotic Condition that service time infinitely grows equivalently to each type of customers are derived.

  • Queueing System MAP/M/ ∞ with n Types of Customers
    Communications in Computer and Information Science, 2014
    Co-Authors: Ekaterina Pankratova, Svetlana Moiseeva
    Abstract:

    The research of the queueing system with incoming MAP, n types of customers, infinite number of servers and exponential service time is proposed. Investigation of n-dimensional stochastic process that characterizes the number of busy servers for different types of customers is held by the method of initial moments. There are expressions for the characteristic function of the number of busy servers for different types of customers in the system MAP/M/ ∞ under the Asymptotic Condition that service time infinitely grows equivalently to each type of customers.

  • Queueing System MAP / M / ∞ with n Types of Customers
    Communications in Computer and Information Science, 2014
    Co-Authors: Ekaterina Pankratova, Svetlana Moiseeva
    Abstract:

    The research of the queueing system with incoming MAP, n types of customers, infinite number of servers and exponential service time is proposed. Investigation of n-dimensional stochastic process that characterizes the number of busy servers for different types of customers is held by the method of initial moments. There are expressions for the characteristic function of the number of busy servers for different types of customers in the system MAP/M/ ∞ under the Asymptotic Condition that service time infinitely grows equivalently to each type of customers.

W N Polyzou - One of the best experts on this subject based on the ideXlab platform.

Alexander Moiseev - One of the best experts on this subject based on the ideXlab platform.

  • Modeling of Mathematical Processing of Physics Experimental Data in the Form of a Non-Markovian Multi-Resource Queuing System
    Russian Physics Journal, 2019
    Co-Authors: E. Yu. Lisovskaya, Svetlana Moiseeva, Alexander Moiseev, Michele Pagano
    Abstract:

    The paper presents a mathematical model for processing of physics experimental data in the form of a non-Markovian infinite-server multi-resource queuing system with Markov modulated Poisson process arrivals and arbitrary service time. It is proved that the joint steady-state probability distribution of the total volume of the occupied resource of each type converges to a multidimensional Gaussian distribution under the Asymptotic Condition of the growing intensity of the arrival process. The parameters of this Asymptotic distribution are derived.

  • Tandem of Infinite-Server Queues with Markovian Arrival Process
    Communications in Computer and Information Science, 2016
    Co-Authors: Alexander Moiseev, Anatoly Nazarov
    Abstract:

    We consider a tandem queueing system with infinite number of servers and Markovian arrival process. Service times at the system stages are i.i.d. and given by distribution functions individually for each stage. The study is performed under the Asymptotic Condition of the arrivals rate growth. It is shown that multi-dimensional probability distribution of customers number at the system stages can be approximated by multi-dimensional Gaussian distribution which parameters are obtained in the paper.

  • Asymptotic Analysis of the Queueing Network $$SM-(GI/\infty )^K$$
    Communications in Computer and Information Science, 2015
    Co-Authors: Alexander Moiseev
    Abstract:

    We consider the infinite-server queueing network with semi-Markov arrivals. The system of differential equations for characteristic function of customers number at the network nodes is derived. The system is solved under Asymptotic Condition of high-rate arrivals. It is shown that probability distribution of customers at the network nodes can be approximated by multi-dimensional Gaussian distribution which parameters are obtained in the paper. Presented results of numerical experiments allow to determine the approximation applicability.

  • Investigation of the Queueing Network GI-(GI|\infty )^K by Means of the First Jump Equation and Asymptotic Analysis
    Communications in Computer and Information Science, 2014
    Co-Authors: Anatoly Nazarov, Alexander Moiseev
    Abstract:

    Analysis of the open non-Markovian queueing network with renewal arrival process, Markovian routing, infinite servers count and general service time distribution is presented in the paper. Equation for characteristic function of the joint distribution of the number of customers in the nodes of the network is derived. Approximations for this characteristic function are presented under Asymptotic Condition of an infinite growth of the arrival rate. Both stationary and non-stationary cases are considered. It is shown that the multi-dimensional distributions under study can be approximated by the multi-dimensional Gaussian distributions. Expressions for parameters of these distributions are obtained.

  • ICUMT - Asymptotic analysis of the infinite-server queueing system with high-rate semi-Markov arrivals
    2014 6th International Congress on Ultra Modern Telecommunications and Control Systems and Workshops (ICUMT), 2014
    Co-Authors: Alexander Moiseev, Anatoly Nazarov
    Abstract:

    Analysis of the infinite-server queueing system with semi-Markov arrivals is presented in the paper. The analysis is performed under an Asymptotic Condition of input rate infinite growth. It is shown that the stationary probability distribution of the number of customers in the system can be approximated by Gaussian distribution when the input rate is great enough. Parameters of the approximation are obtained in the paper. Presented numerical results validate an applicability of the obtained approximation.

Gordon Aiello - One of the best experts on this subject based on the ideXlab platform.

Anatoly Nazarov - One of the best experts on this subject based on the ideXlab platform.