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2009 Contest Problems

MCM PROBLEMS

PROBLEM A: Designing a Traffic Circle

Many cities and communities have traffic
circles—from large ones with many lanes in the circle (such as at the
Arc de Triomphe in Paris and the Victory Monument in Bangkok) to small
ones with one or two lanes in the circle. Some of these traffic circles
position a stop sign or a yield sign on every incoming road that gives
priority to traffic already in the circle; some position a yield sign
in the circle at each incoming road to give priority to incoming
traffic; and some position a traffic light on each incoming road (with
no right turn allowed on a red light). Other designs may also be
possible.

The goal of this problem is to use a model to determine how best to
control traffic flow in, around, and out of a circle. State clearly the
objective(s) you use in your model for making the optimal choice as
well as the factors that affect this choice. Include a Technical
Summary of not more than two double-spaced pages that explains to a
Traffic Engineer how to use your model to help choose the appropriate
flow-control method for any specific traffic circle. That is, summarize
the conditions under which each type of traffic-control method should
be used. When traffic lights are recommended, explain a method for
determining how many seconds each light should remain green (which may
vary according to the time of day and other factors). Illustrate how
your model works with specific examples.

PROBLEM B: Energy and the Cell Phone

This question involves the “energy” consequences of the cell phone
revolution. Cell phone usage is mushrooming, and many people are using
cell phones and giving up their landline telephones. What is the
consequence of this in terms of electricity use? Every cell phone comes
with a battery and a recharger.

Requirement 1

Consider the current US, a country of about 300 million people.
Estimate from available data the number H of households, with m members
each, that in the past were serviced by landlines. Now, suppose that
all the landlines are replaced by cell phones; that is, each of the m
members of the household has a cell phone. Model the consequences of
this change for electricity utilization in the current US, both during
the transition and during the steady state. The analysis should take
into account the need for charging the batteries of the cell phones, as
well as the fact that cell phones do not last as long as landline
phones (for example, the cell phones get lost and break).

Requirement 2

Consider a second “Pseudo US”—a country of about 300 million people
with about the same economic status as the current US. However, this
emerging country has neither landlines nor cell phones. What is the
optimal way of providing phone service to this country from an energy
perspective? Of course, cell phones have many social consequences and
uses that landline phones do not allow. A discussion of the broad and
hidden consequences of having only landlines, only cell phones, or a
mixture of the two is welcomed.

Requirement 3

Cell phones periodically need to be recharged. However, many people
always keep their recharger plugged in. Additionally, many people
charge their phones every night, whether they need to be recharged or
not. Model the energy costs of this wasteful practice for a Pseudo US
based upon your answer to Requirement 2. Assume that the Pseudo US
supplies electricity from oil. Interpret your results in terms of
barrels of oil.

Requirement 4

Estimates vary on the amount of energy that is used by various
recharger types (TV, DVR, computer peripherals, and so forth) when left
plugged in but not charging the device. Use accurate data to model the
energy wasted by the current US in terms of barrels of oil per day.

Requirement 5

Now consider population and economic growth over the next 50 years. How
might a typical Pseudo US grow? For each 10 years for the next 50
years, predict the energy needs for providing phone service based upon
your analysis in the first three requirements. Again, assume
electricity is provided from oil. Interpret your predictions in term of
barrels of oil.

ICM PROBLEM

PROBLEM C: Creating Food Systems: Re-Balancing Human-Influenced Ecosystems

Click the title below to download a PDF of the 2009 ICM Problem.

Creating Food Systems: Re-Balancing Human-Influenced Ecosystems

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