Relationship between Flow Time and WIP for Worst Case
Principle (Worst Case Performance):
For a
line with a given bottleneck rate and raw process time, the minimum throughput and maximum flow time as a function
of WIP level are given by the following figures.
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Relationship between Flow Time and WIP for Worst Case |
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Relationship between Throughput and WIP for Worst Case |
Note that unlike the best case throughput remains constant at the level which is the lowest for the best case. That is, addition of WIP do not result in any throughput improvement. Similarly, flow time increases sharply with WIP, even for WIP below the critical WIP and is numerically much higher than the best case. To see the mathematical equations for this case click here.
As can be seen from above, the gap between the best case performance and the worst case performance is extremely large. Since few real-world systems are likely to be close to either the best or the worst case, it is useful to have an intermediate case that divides the performance range into "good" and "bad" segments. To do this, we introduce the practical worst case.
The worst case occurs (click here for derivation) when congestion in
the line is at its absolute maximum. This happens when a selected job in the line encounters the maximum
amount of queueing (waiting) at every station. That is, each time the selected job arrives at a station it
finds every other job in the line in front of it waiting at that station. A way for this to happen is if
all jobs are moved between stations in a batch (i.e., the batch size equals the number of jobs in the line).
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