Characterizing the Output Process of Two-Stage Flow Lines with Unreliable Parallel Machines and Finite Intermediate Buffer

Abstract

This paper analyzes two-stage flow lines where raw material is processed sequentially in two stages to produce finished units. There are multiple machines at each stage that randomly break down and require repair. There is a limited amount of storage space (buffer)
between the two stages. When the buffer is full, some or all machines at the first stage may be blocked (i.e., forced to idle due to the inability to unload a finished unit), and when the buffer is empty, some or all machines at the second stage may starve (i.e., forced to idle due to a lack of jobs for processing). The state changes in the system can be described by a continuous-time Markov chain when processing times, times between machine failures, and repair times are exponentially distributed. The study focuses on the variability and autocorrelation structure of the output stream of finished products from stage two. Efficient algorithms are developed to compute steady-state system characteristics using matrix analytical methods. The paper presents detailed numerical results highlighting the qualitative features of system behavior for a wide range of parameter values. Our key finding is that the output process of the system approximates a Poisson process for buffer size as small as one, and the numbers of machines at the two stages as small as two.