Re: Freight car distribution


Tim O'Connor
 

Good work, Larry! That's what I'm talkin' 'bout!
A 40 car train with 9 SP (not counting T&NO) box
cars.. More than 5 times the 'average' value of
1.6. And the peak CMO value at 20 times its average
of 0.2! And yet, the OVERALL averages are exactly
what we expect, representing the fact that each car
has an equal chance.

Model railroad operations would be much improved if
someone could devise an easy way to do this using
paper car cards and waybills. (Since most people seem
to hate using computer switchlists.)

Tim O'Connor

At 8/17/2008 02:54 PM Sunday, you wrote:
Hi Folks

I ran my "random train" Excel program for 100,000 iterations to test
whether it was working OK. The average number of boxcars per train,
by railroad, seemed to properly mirror the national fleet as
represented by Tim Gilbert's data for 1949:

RR___Number___Nat'l %___Random %
ACL___13,831___1.99%___1.99%
AT&SF___35,234___5.08%___5.09%
B&M___2,755___0.40%___0.40%
B&O___28,683___4.13%___4.12%
C&EI___1,185___0.17%___0.17%
C&NW___23,284___3.36%___3.37%
C&O___21,699___3.13%___3.13%
CB&Q___31,634___4.56%___4.55%
CGA___5,153___0.74%___0.74%
CGW___3,622___0.52%___0.52%
CMO___3,422___0.49%___0.49%
CNJ___1,757___0.25%___0.26%
CNJ-CRP___1,247___0.18%___0.18%
CRI&P___17,160___2.47%___2.46%
D&H___2,469___0.36%___0.36%
DL&W___7,585___1.09%___1.09%
DM&IR___337___0.05%___0.05%
DRG&W___5,094___0.73%___0.74%
EJ&E___1,427___0.21%___0.21%
ERIE___12,070___1.74%___1.74%
GM&O___6,177___0.89%___0.89%
GN___22,399___3.23%___3.24%
GTW___8,556___1.23%___1.22%
IC___21,248___3.06%___3.08%
KCS___2,923___0.42%___0.42%
L&N___13,324___1.92%___1.92%
LV___5,584___0.80%___0.81%
MILW___32,076___4.62%___4.62%
MKT___5,235___0.75%___0.76%
MP___18,112___2.61%___2.61%
MP-IGN___2,572___0.37%___0.37%
N&W___8,986___1.30%___1.31%
NC&SL___3,603___0.52%___0.52%
NH___6,012___0.87%___0.86%
NKP___11,255___1.62%___1.63%
NP___19,317___2.78%___2.77%
NYC___66,867___9.64%___9.64%
P&LE___4,118___0.59%___0.59%
PRR___64,670___9.32%___9.33%
RDG___7,639___1.10%___1.11%
SAL___12,396___1.79%___1.79%
SLSF___13,255___1.91%___1.91%
SOO___8,728___1.26%___1.27%
SOU___26,331___3.80%___3.79%
SP-Pac___27,757___4.00%___4.01%
SP-T&NO___7,438___1.07%___1.07%
SSW___3,700___0.53%___0.54%
T&P___4,288___0.62%___0.61%
UP___23,758___3.42%___3.43%
WAB___11,572___1.67%___1.68%
WM___2,143___0.31%___0.31%
WP___1,995___0.29%___0.28%
Total___693,682___100.00%___100.00%

(The "Number" and "Nat'l %" columns above are from Tim's 1949 list of
boxcars. His data are at "4060totalboxcarsUSownership.xls" in the
files section of this list. The "Random %" column is the average
percentage of cars per train generated by my Excel program after
100,000 iterations. Each train consisted of 40 boxcars.)

While running the program, I tallied the maximum number of cars for
each railroad over all the iterations. In a 40 boxcar train, the
average number of cars would be 40 times the national percentage
shown in the above table. For example, the average number of SP-Pac
cars would 40 * 4% = 1.6 cars ­ 1 or 2 cars per train. Any
particular 40 boxcar train may have more or less SP-Pac cars (0 to
40). After 100,000 trials, there were in fact trains with no SP-Pac
boxcars, but no train had more than 9 of them. Here are the results
for all the railroads:

RR___Nat'l Avg___Max Rnd
ACL___0.80___6
AT&SF___2.03___9
B&M___0.16___3
B&O___1.65___10
C&EI___0.07___3
C&NW___1.34___9
C&O___1.25___8
CB&Q___1.82___9
CGA___0.30___5
CGW___0.21___4
CMO___0.20___4
CNJ___0.10___4
CNJ-CRP___0.07___3
CRI&P___0.99___7
D&H___0.14___4
DL&W___0.44___5
DM&IR___0.02___2
DRG&W___0.29___4
EJ&E___0.08___3
ERIE___0.70___7
GM&O___0.36___5
GN___1.29___8
GTW___0.49___5
IC___1.23___8
KCS___0.17___4
L&N___0.77___6
LV___0.32___4
MILW___1.85___9
MKT___0.30___5
MP___1.04___7
MP-IGN___0.15___4
N&W___0.52___6
NC&SL___0.21___4
NH___0.35___5
NKP___0.65___6
NP___1.11___8
NYC___3.86___14
P&LE___0.24___4
PRR___3.73___13
RDG___0.44___6
SAL___0.71___7
SLSF___0.76___7
SOO___0.50___5
SOU___1.52___9
SP-Pac___1.60___9
SP-T&NO___0.43___5
SSW___0.21___5
T&P___0.25___4
UP___1.37___8
WAB___0.67___6
WM___0.12___4
WP___0.12___3
Total___40.00___NA

("Nat'l Avg" is the average number of boxcars in a 40 car train based
on the national average; "Max Rnd" is the maximum number of boxcars
for any 40 car train after 100,000 iterations of the Excel program.)

Best wishes,
Larry Ostresh
Laramie, Wyoming

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