Discrete Feedback

[gbackus@boulder.earthnet.net]

Relatvie to discrete systems, Joel Rahn asked "Do you have a reference or two
for this kind of analysis (mode splitting)? I am not sure I see how it can be
done in a discrete-event model. Is the feedback you mention here based on
policies or is it purely random (a certain percentage of defective items may be
re-worked one or more times)?

Here I ma have fell into a semantics problem. Regime splitting may be a better
language. The system goes from one model of behavior of average through-put to a
lower level what it the "discrete" system get well out side the expected
operating parameters. The model I note is a proprietary but built for an auto
manufacturer to study a flexible manufacturing system where multiple products
are manufactured ont eh sme system but the sequence/location of machining,
queues, and storage are different for each piece. Futher based on the priority
of the part, other parts are stored (taken out of the queue). Thus, the system
become non-linear(we could say bifurcated, but over many runs the "results
become smooth and "look" mlike a simple non-linearity - e.g. on average 7% of
the pieces go temprarily into storage because of priority criteria. In this
system, parts visit the same machine multiple times for new processing and
rework. This causes the feed back. Further, some machines are CNCs (computer
controlled tooling) and can take on other tasks as the other machines fail. The
stready state operation is a nebulous term for this sytem becasue the mix of
parts always changes. The effort is to design a system that handles routine
loads, does not "lock-up" on overload, and degrades gracefully as load increase
beyond processing capability- possibly due to machine outages. Graceful
degradation is not exactly what such a system does. As machines fail under
various part type mixes, rerouting creates new bottlenecks that reset priority
sequencing and the sytem "jumps" to different operating conditions that look far
dififerent than the system would look if all machines were running or the part
mix were even slightly different. Many machines drop to loadings well below what
they had with lower flow. During some types of high system flows, some machines
may suddenly be totally bypassed because any routing to them cause more
probelms that they solve.

After studying many runs, I find I can approximate the system well by smooth
non-linear functions at the (on-off) decision points. I can then simulate, in
the continuous SD model,the drop-out of a machine(s) or change the mix with
single-pass run and not only see the feedback dynamics (even make myself beleive
I understand them) but I also get answers adequately close to the resutls of
running the actual thousand pass discrete-simulation

There was also a question about the "/" in the parameter/distribution
uncertainty. Here I meant what is called "higher order uncertainty" -- see the
may issue of IEEEs "Sytems, Man and Cybernetics." The parameters in the model
are often uncertain. They have a distribution just like the failure rate
distribution or input load distribution. These parameters in essence affect the
uncertainty of the uncertainty -- geez! Some examples, are mean failure rates,
mean repair times, expected product mix and input flows, machine set-up times,
etc.

This is an interesting area for SD as an approximation of the discrete system to
understand design criteria and control (feedback) issues. Nonetheless, The
standard OR tools do work and the SD approach open a big can of worms on the
statistical interpretation side of "single pass-run" SD model results.

Did I get the question right? Any remote chance on the answer side?

George

George Backus Email: gbackus@boulder.earthnet.net
Policy Assessment Corporation phone: (303) 467-3566; fax: (303) 467-3576
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