The output shows relatively small deviations
repetition and the final summary statistics. Long
in all cases for all months. The standard devia-
output is available to show each trip segment's
tions, in general, are only 12% of the means for
variables and values, the statistics for each repeti-
tion, and the final summary statistics. The long
all categories of interest, except for hours of ice-
output is useful for debugging and for very de-
breaker escort required in August, for which it
tailed analysis of a voyage. It is generally used for
was 3.4%. This analysis establishes an objective
just a few repetitions. Otherwise, the amount of
measure of the model's inherent scatter due to
output can be unmanageable.
nothing more than the chance variation from us-
ing probabilistic data.
RESULTS OF SIMULATIONS
Number of voyages
The model is capable of simulating any num-
Sensitivity analyses
ber of voyages between zero and 500. We con-
ducted a series of runs to determine what effect, if
Model repeatability
any, the number of voyages had on the categories
We tested the model's repeatability by running
of interest. To be economical with our time, we
the same set of user inputs several times. For this
wanted to simulate as few voyages with each set
test, we assumed a Noril'sk-class ship having a
of input parameters as possible as long as there
daily cost of ,000 and a daily escort rate of
was no appreciable degradation of results. As pre-
,500. A flat miscellaneous fee was not applied.
viously mentioned, a simulation of 500 voyages
The summaries of two separate runs, each simu-
required approximately 2 min to complete when
lating 500 voyages in April, are presented in Table
generating the short output format. A 100-voyage
14. We then switched to simulations of 100 voy-
simulation took only 21 s.
ages in each of the four months, with the same
user inputs. For each month, we repeated the
We used the same set of parameters as for
the repeatability study (see Model repeatability),
runs five times, and the results of the April and
and progressively lowered the number of voy-
August transits are also presented in Table 14.
Table 14. Sensitivity study of model repeatability.
IB
Total
No. of
Time
Speed
escort
cost
Cost/hr
Cost/mi
voyages
(hr)
(kn)
(hr)
(US$)
(US$)
(US$)
500
566
5.6
520
720,456
1272
230
500 (repeat)
562
5.6
517
715,153
1272
229
April transits
100
563
5.5
514
715,400
1271
230
100
564
5.6
516
716,695
1271
229
100
567
5.6
522
720,410
1270
229
100
566
5.5
522
720,170
1273
231
100
563
5.6
517
717,220
1273
230
Mean (100 voyages)
565
5.6
518
717,979
1272
230
Std. dev.
2
0.05
4
2213
1.3
0.8
Std. dev. relative to
the mean (%)
0.4
0.9
0.8
0.3
0.1
0.4
August transits
100
325
9.7
71
349,635
1076
112
100
324
9.7
76
349,760
1079
112
100
324
9.7
77
351,350
1084
112
100
326
9.6
77
352,960
1083
113
100
317
10.0
74
342,105
1077
109
Mean (100 transits)
323
9.7
75
349,162
1080
112
Std. dev.
4
0.15
3
4171
3.6
1.5
Std. dev. relative to
the mean (%)
0.4
1.6
3.4
1.2
0.3
1.4
35
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