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Open Line with Finite Buffers - Example for Illustration of Principles for Finite Buffer Open Lines

We consider a open line with four stations with parameters as given in the following table. All times are in minutes. Moreover, process times  are assumed deterministic (constant) and the time to failure and repair follow the exponential distribution.  Note that, since Station 3 has the longest process time and all failure parameters are identical, it is the bottleneck of the line.
 
 
 

We assume that there is an unlimited buffer in front of Station 1, but that all other buffers (i.e., between Stations 1&2, 2&3, and 3&4) are finite and equal. Note that, this line has exactly the same station configuration as the closed system with finite buffer example, except that this time the line is run as an open system.

The figure below plots the average long term WIP of the line as we increase the number of buffers between each of the stations for various release rates.
 
 

• Minimum Buffering Principle: We see for the case where release rate is 1/1.5 per minute, the system becomes unstable when there are no interstation buffers. With the addition of a buffer space the system stabilizes, even though the average WIP is still very high. Therefore the minimum number of buffers needed to run the system is one for this throughput.
• Buffering Principle: The buffering principle is also illustrated clearly in the above plot. WIP decreases as we increase the buffer space (apart from minor discrepancies due to simulation noise). 
• Diminishing Return Principle: This principle is most clearly visible for the case where the throughput is the highest (equal to 1/1.5 per minute). We see that WIP blows up when the line has no buffers, but comes down to around 45 with the addition of just one buffer space and then to around 18 with two buffer spaces.  For buffer levels above this the decrease in WIP is marginal, with the WIP level converging to around 15. This is precisely what the diminishing returns principle predicts.. That is, we get the largest decrease in WIP with the addition of the first buffer and progressively less from there on. This effect is less pronounced for the other two throughput levels even though it is still present. This is because, the first system has the highest utilization of the line, and thus the greatest need for buffer space. The other lines are relatively less utilized and even with one or two buffers they are fairly close to their infinite buffer performance.

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