Modeling the Suez Canal (NCCTM)

Modeling Traffic
Flow in the
Suez Canal
Dan Teague
NC School of Science and Mathematics
[email protected]
After the Six-Days War in 1967
• The Suez Canal was heavily mined and was
closed to all traffic for 10 years.
• The British eventually cleared the canal of all
mines and the Egyptian government and the
Suez Canal Authority hired mathematician Jeff
Griffiths and his group from Cardiff University
to explore the optimal organization for traffic
in the canal.
Crucial to the Egyptian Economy
• At the time of its closure, the canal
contributed more than 50% of the funds to
the treasury of Egypt.
• Each ship paid an average of $100,000 for
transit through the canal (now $250,000) .
• At the time, on average, 67 ships transited the
canal each day taking 10-14 hours for passage.
The Canal
The Suez Canal was:
• 193 kilometers long
• 169 meters wide (for ship travel)
• 21 meters deep
• The distance between Jeddah
(Saudi Arabia) and the port of
Constanza (Black Sea) is 11771
miles via the Cape of Good Hope,
but only 1698 mile via the Suez
canal, a saving of 86% in distance.
• Almost 7% of sea transported
world trade passes through the
Suez canal each year.
Convoy System
• The width of 169 meters in width is not
enough to allow passage in both directions.
• As a result, the ships must travel, in
convoys either North-South or
South-North and pass each other at
• Generally, the demand for passage is the
same in both directions.
Two Convoys
going NorthSouth
One Convoy
going SouthNorth
No Passing in the Canal
The N-S Convoy and the
S-N Convoy can pass each
other only in the Bitter
Lakes and the Ballah
The N-S Convoy must be
anchored to buoys in the
canal while the S-N
Convoy passes.
The Ballah Bypass has 17 buoys.
The Bitter Lakes has 36 buoys.
Conditions for the Model
1. At most 36 in 1st N-S Convoy (Convoy A).
2. At most 17 in 2nd N-S Convoy (Convoy B).
3. Same number of ships N-S and S-N
each day.
4. Schedule must repeat every 24 hours.
Develop a Mathematical Model
Build a model to capture the current
convoy process. Determine the maximum
number of ships that can transit the canal
each day.
Compare the cost and effectiveness of
modifications to this optimal value.
Standard Ship Model
Speed of all ships is constant at 14 km/hr.
Separation for all ships is 10 minutes.
Ignore (initially) acceleration and
deceleration for docking.
Zero-time docking and undocking for
Modeling a Ship’s Transit
The Ballah Bypass is
10 kilometers in
length, stretching
from the 50 to 60
kilometer mark
south of Port Said.
The Bitter Lakes
extend for 20
kilometers, from 100
to 120 kilometers
south of Port Said.
A 10-ship Convoy A
1. At most 36 in 1st
N-S Convoy (Convoy A).
2. At most 17 in 2nd
N-S Convoy (Convoy B).
3. Same number of ships
N-S and S-N each day.
4. Schedule must repeat
every 24 hours.
5. 14 km/hr & 10 minute
What is the First Natural
1. At most 36 in 1st N-S Convoy
(Convoy A).
2. At most 17 in 2nd N-S Convoy (Convoy B).
3. Same number of ships N-S and S-N each day.
4. Schedule must repeat every 24 hours.
5. 14 km/hr & 10 minute separation
Why Not 106 Ships?
First, create a solution:
then optimize.
What are the Invariants?
100/14 = 7.14
24 – 2(7.14) = 9.72
9.72(60)/10 = 58.3
59 Ships in Convoys
A and C.
A Little Algebra Helps
If we let A, B, and C represent the number of ships
in Convoy A, Convoy B, and Convoy C, respectively,
we require that
A + C = 59
B = 17.
Analytic solution to the
$1,000,000 system of equations.
A + B = C, B = 17, A + C = 59
A = 21, B = 17, and C = 38
Total of 76 Standard ships per day.
A = 21 B = 17 C = 38
Change Speed
• (1) Traveling at 16 km/hr, the first ship in Convoy A
must arrive at the 100 km mark at 6.25 hours.
• (2) The symmetry of the problem requires the last ship
in Convoy C to be at the 100 km mark at 24 – 6.25 =
17.75 hours.
So, we have 11.5 hours of transit time to share
between Convoys A and C. If the ships are 12 minutes
apart, we have room for 58 ships. Then 58 + 17 = 75
ships can make the transit in 24 hours.
The Rest of the Story
• This is a real problem solved by real
• Mathematics isn’t the final arbiter of
what is “best”. People have to accept
the results.
The Rest of the Story
Jeff Griffiths presented his results to
the head of the Suez Canal Authority,
Meseur Meseur, comparing a variety of
alternative to the standard model.
Completing his work, he returned to
Wales. But Jeff kept thinking that he
had missed something simple.
While taking a bath back home, it hit him.
He knew what he had missed.
He immediately returned to Egypt and
made an appointment with Meseur
A 48 Hour Schedule
The Rest of the Story
• Jeff presents his results to Meseur Meseur.
• Meseur Meseur listened carefully and at the
end of Jeff’s presentation, said politely…
The Rest of the Story
Absolutely Not! The Suez Canal has run
on a 24 hour schedule every day since
1869. It is impossible to even think of it.
Professor Griffiths returned to Wales in
Misfortune Strikes the Canal
How to Clear the Backlog?
Meseur Meseur (Head of Suez Canal Authority)
“We have this terrible problem. Ships are
stacked up at both ends of the canal and it will
take weeks to move them all through. What can
we do? What can we do?”
“…and then I had an idea.”
“If we ran the canal on a 48 hour schedule, we
could significantly increase the number of ships
passing through the canal.”
“So, I ordered that we use the 48 hour schedule
until the backlog was clear, then return to the 24
hour schedule.”
Dan Teague at [email protected]

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