On Transient Queue-Size Distribution in a Single-Machine Production System with Breakdowns

Abstract:

An operation of a single-machine manufacturing system is modeled by an unreliable finite-buffer-type queuing system with Poisson arrivals, in which service times, failure-free times and times of repairs are totally independent and exponentially distributed random variables. Applying the idea of embedded Markov chain and the formula of total probability a system of integral equations for the transient conditional queue-size distributions of jobs present in the system at fixed time t is built. The solution of the corresponding system written for Laplace transforms is obtained in a compact form using the potential technique.

• Periodical: Advanced Materials Research (Volume 1036)
• Pages: 505-510
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.1036.505
• Online since: October 2014
• Authors: Wojciech M. Kempa*, Iwona Paprocka, Krzysztof Kalinowski, Cezary Grabowik
• Keywords: Finite-Buffer Queue, Machine Breakdown, Markov Moment, Queue-Size Distribution, Total Probability Formula

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