NEW VOLUME DELAY FUNCTION Waclaw Jastrzebski

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NEW VOLUME DELAY FUNCTIONWaclaw Jastrzebski
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The Overcapacity Problem
VolumegtgtCapacity
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Problem
Using standard VDF functions, sometimes the
forecasted demand results in volumes greater than
capacity, whereas the actual capacity may in fact
be sufficient .
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Model representation of human behaviors using
the language of mathematic

• To travel or not to travel. ?
• To the city center or closer to home ?
• By car or by transit ?
• Which route?

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Four Step Model
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Reality vs. Model Curves
capacity
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Mathematical Conditions for VDF Function
- F(x) is a strictly increasing function for the
variable between 0 and ? (F(0)gt0) - F(0) T0,
where T0 is the free-flow time - F(x)
existing and is strictly increasing that means
that function is convex this last condition is
not essential but desirableThe calculation
time for the new function should not use more CPU
time than BPR function,
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Behavioral Conditions

• Time spent in traffic congestion weights much
  more for the traveler than the travel time at the
  acceptable speed
• Within the range of 0.2-0.8 of capacity, the
  average speed of traffic shows little sensitivity
  to the volume of traffic. After reaching the
  capacity level the travel time increases
  substantially
• Traveler chooses a path based on previous
  experience
• Traveler can adjust the path as new information
  on traffic situation is acquired.

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The Modeling Conditions

• The function should force the algorithm to
  seek additional paths in order to minimize the
  number of links with volume greater then
  capacity
• The free-flow-speed is the actual average speed
  as determined through the surveys (regardless of
  legal limitations such as speed limits).
• The function takes into account that traffic
  lights decrease the average speed

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Various Mathematical Formulas for VDF
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Various Mathematical Formulas for VDF
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Various Mathematical Formulas for VDF
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Surveys Results
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Surveys Results
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Surveys Results
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New Function
b odd integer gt1
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Mathematical Condition
b odd integer gt1 so b 1 is even
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Continuity
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New Function
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What Does it Mean
free flow speed?
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Function and Surveys
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EMME Implementation

• a fd27 el1 (1 1.35 ((volau / el2) 9)
  .65 volau / el2)
• .2 (volau .gt. el2) (volau - el2)
• a fd30 el1 (1 100 ((volau / el2 - .44) 7
  .44 7)
• .45 volau / el2) .4 (volau .gt. el2)
  (volau - el2)
• a fd31 el1 (1 90 ((volau / el2 - .43) 7
  .43 7)
• .44 volau / el2) .4 (volau .gt. el2)
  (volau - el2)
• a fd32 el1 (1 70 ((volau / el2 - .4) 7
  .4 7)
• .3 volau / el2) .4 (volau .gt. el2)
  (volau - el2)
• a fd33 el1 (1 28 ((volau / el2 - .42) 5
  .42 5)
• .28 volau / el2) .4 (volau .gt. el2)
  (volau - el2)

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Equilibrium Assignment
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Equilibrium Assignment


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How Does It Work?

- capacity 700 pcu/h - free flow speed 70 km/h
- speed on the capacity limit 20 km/h -
practical capacity 0,65 capacity - speed on the
practical capacity limit 45 km/h
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Various Functions



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Results for Various Functions
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Matrix Reduction to Eliminate Overcapacity
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• NO FUNCTION IS PERFECT!

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Disadvantages
ASSIGNMENT 2035
132000 min
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Reason? No alternative paths
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Solution

• Check network carefully and add new possible
  links even local to add extra capacity
• Add extra capacity or additional centroid
  connector