Finite Buffer Closed Lines

Finite Buffer Closed Lines - Principles

As in the case of infinite buffer closed lines we can characterize a finite buffer closed line with the following parameters

Bottleneck rate: the rate of the workstation in the line having the highest utilization.
Raw processing time: the sum of the long-term average process time of each station in the line.
Congestion co-efficient: a unitless quantity that is zero when congestion is minimum and increases as congestion increases.

In addition, the line is effected by the added constraints imposed by the presence of the finite buffers. We can think of these as increasing the congestion coefficient - the smaller the buffer, the more it increases congestion due to the blocking caused by the buffer. But because the congestion coefficient is a highly aggregated measure of many factors causing congestion, it is useful to analyze the impacts of buffers directly. Since

Throughput = Bottleneck Rate × Fraction of Time Bottleneck is Busy

we can understand most of the logistical impacts of buffers by focusing on how they impact the fraction of time the bottleneck station is busy. In particular, we can derive the following principles:

Principle (Buffering): The throughput of a closed line is non-decreasing in the size of any buffer.

Principle (Diminishing Return to Buffering): The increase in throughput from adding a unit of buffer space at a station in a closed line decreases as the size of the buffer increases.

Principle (Buffer Position): If all non-bottleneck machines are identical and all buffers are of equal size, then the increase in throughput from adding an additional buffer space will be largest either directly before or after the bottleneck station.

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