Introduction to Transportation
Systems
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PART II: FREIGHT
TRANSPORTATION
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Chapter 15: Railroad Terminals: P-MAKE Analysis to Predict Network Performance 3
Terminals ‹ Terminal
performance is a major
determinant of network
performance.
Terminal
Performance
Variability in
Arrival of
Incoming Trains
Figure 15.1 4
Terminal Performance:
Another Look
Performance
lower performance
“robust” plan
higher performance
“sensitive” plan
Variability in
Arrival of
Incoming Trains
Performance includes a measure of cost -- if one is
measuring terminal performance not only on
throughput of the terminal but also on the resources
used -- robustness may involve a more
conservative use of resources. It may involve
having redundancy in the system.
Figure 15.2
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LOS and Routing over the
Rail Network
‹
‹
Level-of-service in rail freight
operations is a function of the number
of intermediate terminals at which a
particular shipment is handled.
Empirical research shows the major
determinant of the LOS is not the
distance between origin and
destination, but rather the numbers of
times the shipment was handled at
intermediate terminals, which is really
an operating decision on the part of the
railroads.
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Direct Service C
B
A
Figure 15.3 D
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Terminal Operations Classification Yard Inbound
Train
Receiving
Yard
Hump
Classification
Departure
Bowl
Yard
Outbound
Train
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A P-MAKE Function
f (AVAIL)
P-MAKE
2 hr
8 hr
12 hr AVAIL
Available time in terminal
in hours (AVAIL)
Figure 15.5
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Average Yard Time Now, average yard time -- E(YT) -- will be a
function of the available time (AVAIL) to make
that connection. In this model, E(YT) -- the
average yard time -- will have two components
-- the time spent in the yard if the connection is
made, in which case, with probability P-MAKE,
the terminal time is AVAIL. With probability
(1 - P-MAKE), the car will spend (AVAIL + the
time until the next possible train).
E(YT) = P-MAKE * (AVAIL) + (1 - P-MAKE) * (AVAIL + time until next
possible train)
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E(YT)
for a given
P-MAKE
function
“sweet spot”
AVAIL
We can calibrate these curves and calculate an “optimal” AVAIL for the particular terminal. Figure 15.6
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Origin-Destination
Performance
A
12 hrs.
Origin
Figure 15.7
B
12 hrs.
C
12 hrs.
D
Destination
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P-MAKE Functions
f (AVAIL)
more
efficient
terminal
less
efficient
terminal
AVAIL
Figure 15.8
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Another P-MAKE Function
ƒ (AVAIL)
1.0
0.9
8
Figure 15.9 AVAIL
32
14
Missed Connection
Probability Yard Time (for
AVAIL = 8 for both yards) 0
[f(AVAIL)]2
16 1
2 f(AVAIL)*[1f(AVAIL)]
40 2
[1-f(AVAIL)]2
64 15
Total Yard Time as a f(Avail)
Probability
AVAIL = 8
0.81
f(AVAIL) = P-MAKE = 0.9
0.18
0.01
16
40
Probability
64
Total Yard
Time
AVAIL = 8
f(AVAIL) = P-MAKE = 0.8
0.64
0.32
0.04
16
40
64
Total Yard
Time
f(AVAIL) = P-MAKE = 0.9
Average O-D Time = 56.8
Variance O-D Time = 103.7
f(AVAIL) = P-MAKE = 0.8
Average O-D Time = 61.6
Variance O-D Time = 184.3
Figure 15.10
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Available Yard Time
A
B
C
D
E
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More Frequent Trains (1)
ƒ (AVAIL)
‹
P-MAKE Function
P-Make = 0.9
8
Probability
‹
Total Yard Time
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AVAIL
ƒ (AVAIL) = P-Make = 0.9
0.81
Twice daily frequency
0.18
0.01
16
28
40
Total Yard
Time
Average O-D Time = Average Yard Time + 36 = 52.96
Variance O-D Time = 25.91
Figures 15.12, 15.13
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More Frequent Trains (2)
‹ So,
by having trains run twice a
day, the average yard time and
variance of yard time goes down.
‹ This system is a more expensive
system, but provides a better levelof-service. This is the classic
cost/LOS trade-off [Key Point 14].
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Bypassing Yards
Total Yard Time with Bypassing One Yard
Probability
0.9
0.1
8
Figure 15.14
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Total Yard
Time
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