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Conference 7.286::digital

Title:The Digital way of working
Moderator:QUARK::LIONELON
Created:Fri Feb 14 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:5321
Total number of notes:139771

5146.0. "Calculating Probability..." by WOTVAX::HILLN (It's OK, it'll be dark by nightfall) Wed Feb 19 1997 04:55

    We need some help with the following probability problem.
    
    We want to model the messages coming from pieces of automated equipment
    in a factory.
    
    There are N pieces of equipment which cycle through three states: IDLE
    - PROCESS - UNLOAD and back to IDLE.
    
    The time spent IDLE is evenly distributed between values x and y 
    The time spent in PROCESS is from 1p to 25p, with a mean of 22p
    The time spent in UNLOAD is from 1r to 25r, with a mean of 22r
    
    When the state changes one message is sent.
    
    How do we calculate the probability of n messages arriving in time t?
    
    Nick
T.RTitleUserPersonal
Name
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5146.1half an answerBBPBV1::WALLACEjohn wallace @ bbp. +44 860 675093Wed Feb 19 1997 05:0513
    Find a queing theory expert (is there a MATHS notesfile?) or a serious
    expert in factory floor operations design.
    
    Or a maths/simulation package with a queueing option and a good manual.
    (Simscript? Matlab??).
    
    Or a manufacturing simulation package (e.g. Seewhy from AT+T Istel -
    serious money required unless there's now an el-cheapo PC version).
    
    Turn the way-back dial three years back and ask the MIACT (oh, shucks,
    they've almost all gone...).
    
    
5146.2Essential readingULYSSE::virenq.vbe.dec.com::ULYSSE::HEMMINGSLanterne RougeWed Feb 19 1997 05:158
Hey Nick, do you want a copy of M J Moroney's "Facts from Figures"? - best remembered quote -

Pat: "Rome wasn't built in a day"

Mick: "but oi wasn't on dat job"

Seriously, I wouldn't calculate, I'd simulate.  It's easy to generate random values of the times 
once you have their distributions.  Then you just let it run for a while and look at the results.
5146.3TEKVAX::KOPECConsider a spherical chicken; ..Wed Feb 19 1997 06:429
    I think you're missing some information; what's the distrubution of the
    PROCESS and UNLOAD times? 
    
    This is pretty standard queueing theory stuff, unfortunately I haven't
    done queueing theory since I was in grad school hundreds of years ago.. 
    
    
    
    ...tom
5146.4BSS::JILSONWFH in the Chemung River ValleyWed Feb 19 1997 09:525
The POLYCENTER Capacity Planner group has a number of people with a lot of 
knowledge in queuing theory.  They may be able to provide consultancy in 
this endeavor.  Contact Melur Raghuraman DTN 381-1373 (DISCOS::RAGHU).

Jilly
5146.5ptr to math notes fileCPEEDY::BRADLEYChuck BradleyWed Feb 19 1997 17:1010
the math notes files is at
RUSURE::NOTES1:[NOTES$LIBRARY]MATH.NOTE;7
there is a fair amount of statistical knowledge there.

sometimes an analytic solution is possible.  often it is not.
even when an analytic solution is possible, simulation is often
the best way to go.  simulation makes it easy to evaluate the
sensitivity to small changes in the assumptions.

5146.6DDJ23329::CIMAFRANCAWed Feb 19 1997 21:366
    A recent issue of Dr. Dobb's Journal (no older than November 96)
    covered the Denver Airport baggage-handling fiasco.  The article
    included code used for simulating the baggage flow.  Might be worth a
    look.
    
    --Dominic