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Stochastic foundations of the universal dielectric response

Agnieszka Jurlewicz (2003)

Applicationes Mathematicae

We present a probabilistic model of the microscopic scenario of dielectric relaxation. We prove a limit theorem for random sums of a special type that appear in the model. By means of the theorem, we show that the presented approach to relaxation phenomena leads to the well known Havriliak-Negami empirical dielectric response provided the physical quantities in the relaxation scheme have heavy-tailed distributions. The mathematical model, presented here in the context of dielectric relaxation, can...

Stochastic queue core problem with an efficient length on a tree network

Jafar Fathali, Mehdi Zaferanieh (2025)

Kybernetika

In this paper, we consider a stochastic queue core ( S Q C ) problem on a tree network, aiming to identify a path P , called the core, in an M / G / 1 environment system. Let T be a tree network, the S Q C problem on T involves finding a core P , with an optimal length, that minimizes the total weighted travel time from all vertices to the core as well as the average response time to the customer demands. We assume that a mobile server traverses the core to provide services to customers, while customers move to their...

Study of Queuing Systems with a Generalized Departure Process

Mirtchev, Seferin, Statev, Stanimir (2008)

Serdica Journal of Computing

This work was supported by the Bulgarian National Science Fund under grant BY-TH-105/2005.This paper deals with a full accessibility loss system and a single server delay system with a Poisson arrival process and state dependent exponentially distributed service time. We use the generalized service flow with nonlinear state dependence mean service time. The idea is based on the analytical continuation of the Binomial distribution and the classic M/M/n/0 and M/M/1/k system. We apply techniques based...

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