The world's northern-tier nations and territo-
given that future conditions do not depart signifi-
ries have become increasingly attracted to the idea
cantly from those observed in the past. Monte Carlo
of a trade route that will open new markets to
simulation techniques, which we applied, are well
their exports as well as generate income for their
matched to this type of data because they select
own economies acting as ports of call along the
random samples of different combinations of con-
route.
ditions based on their probability of occurrence
within the data set.
Other data, such as market-related variables that
Further development needed
The challenge of the physical environment of
describe historic fluctuations in exchange rates, fuel
the Northern Sea Route requires the development
and insurance costs, tariffs, and transit fees, are
and exploitation of technologies pertaining to ship
less well known or more poorly behaved and thus
design as well as to ship operations. Public policy
less likely to be indicative of future trends. Accu-
alternatives will need to be investigated, some of
rate simulation of such variables using Monte Carlo
which pose difficult trade-offs between economic
methods is unlikely to be reliable because a single
development and other considerations, such as
probability density function (derived from past
social well-being and environmental protection.
observations) cannot be used to describe both past
Establishing a viable year-round cargo trans-
and future patterns of variability. In other words,
portation system will require advances in several
past events do not necessarily predict future events.
areas, including:
Data such as these can be handled in several ways.
Further development of markets for cargoes,
Either a single fixed estimate can be established
Development of more powerful and eco-
for all simulations, random samples can be selected
nomical icebreaking ships,
from a range of discrete values with equal prob-
Improvement in the navigation infrastructure,
ability of occurrence, or a series of simulations can
Consideration of the rights and well-being
be run to produce estimates of transit cost at each
of the region's indigenous peoples,
of several discrete values.
Reduced risk to vessels, cargoes, and the en-
vironment, leading to more affordable insur-
Monte Carlo simulation
ance rates.
We selected values for most parameters in the
All these improvements should serve to make the
model using a Monte Carlo (MC) approach. MC
NSR alternative more competitive with other
methods make random drawings from pools of
routes and hence more attractive to international
possible values. We weighted each drawing by a
shipping.
priori knowledge of the frequency with which each
value occurs in the real world. For instance, if we
wish to make a simplistic simulation of New York
City's April weather, we need to know how many
THE TRANSIT MODEL
April days in past years were rainy and how many
Simulation software successfully mimics real-
were sunny. After searching weather observations
world phenomena only to the extent that two con-
recorded at nearby LaGuardia Airport for the past
ditions are met. First, data sets that describe vari-
40 years, we find that, over the long term, four
ables on which predictions ar e based must
April days in ten were rainy and the remaining six
accurately reflect real-world conditions. Second,
were sunny. Our simulation must reflect this fre-
the method chosen to model possible outcomes
quency distribution so we bias the random draw-
must be appropriate to the data. The algorithms
ings such that, on average, 40% of the time it's
that underlie our model have been constructed to
raining and 60% it's sunny. We do this by con-
ensure that both conditions are satisfied to the
straining the range of random numbers that are
greatest extent possible within constraints gov-
generated such that they fall between one and ten
erned by the data that are available.
inclusive. If one, two, three, or four is drawn, it's
Northern Sea Route data such as ice conditions,
raining; five through ten mean it's sunny. Since,
sea state, conditions that degrade visibility, and
by definition, a random drawing means that all
meteorology come primarily from Soviet and Rus-
values are equally likely to occur on any given
sian observations acquired over long time peri-
selection, over the long run it will rain 40 times in
ods. The nature of these data allow probability
100 and the sun will shine the remaining 60 times.
density functions to be constructed that reflect the
Our model thus simulates the ratio of rainy to
probability of encountering specific environments,
sunny days observed at LaGuardia Airport.
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