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Finite Buffer Closed Lines - Illustration of Buffering Principle and Diminishing Returns Principle

We consider a closed line with four stations wih 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.  The following figure plots the throughput as a function of WIP for various buffer sizes.   Note that WIP level refers to the total number of jobs allowed in the line, which is held constant, while the buffer sizes refer to the maximum number of jobs that can accumulate between stations.
 
 
 
 

• Buffering Principle: The above figure shows that for any WIP level, increasing the size of the buffers increases (or at least does not decrease) throughput.  For instance, at a WIP level of 2, throughput is the same for buffer sizes of 0,1,2,3.  The reason is that when we have only two jobs in the system, jobs virtually never queue up behind stations and therefore almost no blocking/starving occurs even when buffer sizes are zero.  However, at a WIP level of 8, we see that throughput is higher for buffer size of 3 than 2, and higher for 2 than 1, etc.  The reason is that with 8 jobs in the system, the amount of blocking/starving is significant when buffers are very small (0 or 1).  Hence, additional buffer space serves to keep the bottleneck (Station 3) running more consistently and hence increases throughput.
  
• Diminishing Return to Buffer Principle: The above figure also illustrates how throughput shows diminishing returns to additional buffer space.  For instance, at a WIP level of 8, the increase in throughput that results from increasing buffer sizes from 0 to 1 is larger than that from increasing them from 1 to 2.   Each additional buffer space will have a smaller impact on performance, which is ultimately bounded by the stand alone throughput of the bottleneck (i.e., we cannot do better than keep the bottleneck busy 100% of the time).

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