Mathematical Modelling

Lord Kelvin and Andrey Andreyevich Markov in a queue with single server

A. Bobrowski

Lublin University of Technology, Lublin, Poland

Abstract: We use Lord Kelvin's method of images to show that a certain infinite system of equations with interesting boundary conditions leads to a Markovian dynamics in an $L^1$-type space. This system originates from the queuing theory.

Keywords: queue; method of images; generation theorem; boundary conditions; Markovian dynamics.

UDC: 517.9+519.21+517.958

MSC: 47D03, 47D06, 47D07, 60K25, 60J22

Received: 21.06.2018

Language: English

DOI: 10.14529/mmp180303

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