MATEC Web Conf.
Volume 112, 201721st Innovative Manufacturing Engineering & Energy International Conference – IManE&E 2017
|Number of page(s)||6|
|Section||Flexible Manufacturing, Automation and Robotics in Technological Processes|
|Published online||03 July 2017|
Distribution of time to buffer overflow in a finite-buffer manufacturing model with unreliable machine
1 Silesian University of Technology, Faculty of Applied Mathematics, Institute of Mathematics, 23 Kaszubska Str., 44-100 Gliwice, Poland
2 Silesian University of Technology, Faculty of Mechanical Engineering, Institute of Engineering Processes Automation and Integrated Manufacturing Systems, 18A Konarskiego Str., 44-100 Gliwice, Poland
* Corresponding author: firstname.lastname@example.org
One of the most important characteristic of each queueing model is time to buffer overflow. In the paper the distribution of that time in a single-channel manufacturing system, modelled by a Markovian finite-buffer queue with machine breakdowns, is studied. By using the analytical approach based on the idea of embedded Markov chain, total probability law and linear algebra, the formula for Laplace transform of the time to buffer overflow conditional distribution is found. Numerical illustration is presented.
© The Authors, published by EDP Sciences, 2017
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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