Time-dependent solution for the manufacturing line with unreliable machine and batched arrivals

Modern Technologies in Industrial Engineering 2015

Kempa, W.M.^1 ; Paprocka, I.^2 ; Grabowik, C.^2 ; Kalinowski, K.^1

Silesian University of Technology, Faculty of Applied Mathematics, Institute of Mathematics, 23 Kaszubska Str., Gliwice

44-100, Poland^1

Silesian University of Technology, Faculty of Mechanical Engineering, Institute of Engineering Processes Automation and Integrated Manufacturing Systems, Konarskiego 18A, Gliwice

44-100, Poland^2

关键词: Distributed random variables;    Exponential distributions;    Manufacturing lines;    Queue size distribution;    System of integral equations;    Time-dependent solutions;    Total probabilities;    Unreliable machine;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/95/1/012094/pdf
DOI  :  10.1088/1757-899X/95/1/012094

来源: IOP

【 摘 要 】

Time-dependent queue-size distribution in a finite-buffer manufacturing line with unreliable machine is investigated. Successive jobs arrive in batches (groups) with sizes being generally distributed random variables, and are being processed individually with exponential service times. Applying the approach based on the memory less property of exponential distribution and the total probability law, a system of integral equations for the transient queue- size distribution conditioned by the initial level of buffer saturation is derived. The solution of the corresponding system written for Laplace transforms is found via linear-algebraic approach..