On time-to-buffer overflow distribution in a single-machine discrete-time system with finite capacity

A model of a single-machine production system with finite magazine capacity is investigated. The input flow of jobs is organized according to geometric distribution of interarrival times, while processing times are assumed to be generally distributed. The closed-form formula for the generating funct...

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Bibliographic Details
Published in:Mathematical modelling and analysis Vol. 25; no. 2; pp. 289 - 302
Main Author: Kempa, Wojciech M.
Format: Journal Article
Language:English
Published: Vilnius Vilnius Gediminas Technical University 01.03.2020
Subjects:
Algebra
buffer overflow
Buffers
Discrete time systems
Finite capacity
geometric distribution
Linear algebra
Markov analysis
Markov chains
Markov processes
production line
Production management
queueing model
Queuing theory
Time
transient analysis
transient analysis
queueing model
buffer overflow
production line
geometric distribution
ISSN:1392-6292, 1648-3510
Online Access:Get full text
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Summary:A model of a single-machine production system with finite magazine capacity is investigated. The input flow of jobs is organized according to geometric distribution of interarrival times, while processing times are assumed to be generally distributed. The closed-form formula for the generating function of the time to the first buffer overflow distribution conditioned by the initial buffer state is found. The analytical approach based on the idea of embedded Markov chain, the formula of total probability and linear algebra is applied. The corresponding result for next buffer overflows is also given. Numerical examples are attached as well.
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ISSN:1392-6292
1648-3510
DOI:10.3846/mma.2020.10433