Multi-Point and Multi-Class User Equilibrium Assignment

Yanping Zhang

DCHC MPO/City of Durham

1NC Model User Group Meeting - April 2011

Multi-Point Assignment (MPA)

• Standard User Equilibrium (UE) Assignment

– Using shortest time path between zone centroids– Weak control on trip local loading directions

• MPA 

– Strong control on trip local loading directions– Not a method to assign trips from origins to 

destinations – Used together with UE or other assignment 

methods

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Standard User Equilibrium (UE) Assignment - Example

3NC Model User Group Meeting - April 2011

6th

St

7th

St

Zone Centroid

‐

Origin

Zone Centroid

‐

Destination

CentroidConnector

Access Point

Multi-Point Assignment (MPA) - Example

4NC Model User Group Meeting - April 2011

6th

St

7th

St

Zone Centroid

‐

Origin

Zone Centroid

‐

Destination

CentroidConnector

Access Point

Multi-Point Assignment (MPA) and Loading Strategy

• Fixed Rate Strategy, Robert Shull 1999  (implemented in TModel2) 

• Mixed Strategy 1– Some centroid

connectors got fixed loading rates 

– Other centroid

connectors got the variable rates  determined by UE assignment    

• Mixed Strategy 2– Part of Origin‐Destination (O‐D) trips follows the 

fixed rate strategy– Other O‐D trips follows the UE assignment rules 

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Fixed Rate Strategy for Loading/Receiving

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6th

St

7th

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10%

25%

40%

50%

Mixed Strategy 1 - Example• 40% O‐D Trips Loaded onto West Ave

• 60% O‐D Trips follow UE assignment to other 3 directions, 

i.e. r1+r2+r3=60%

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6th

St

7th

St

r1

r3

40%

50%

Mixed Strategy 2 - Example• 60% O‐Ds follows the fixed rates

• 40% O‐Ds follows the UE assignment rule, r1+r1+3+r4=40% 

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6th

St

7th

St

6% + r1

15% + r4 

24% + r3

50%

What MPA can be used for

• Large Special Zone, e.g. Airport, University Campus,  Shopping mall, …

– with large amount employment– with multiple loading directions– with socio‐economic data that cannot  be split into 

smaller zones

• Zone with Off–Site Loading, e.g. Office with off‐site  parking garage 

• Zones with multiple vehicle class loading and  different loading directions for each vehicle class 

• Special Event Model, Stadium, Theater, …

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Example – Special Zone-RDU Airport

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Example – Zone with Off-Site Loading

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MPA Tool• Coded in GISDK for use in TransCAD

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MPA Application

• Kansas City Metro Area, including the Kansas  City Model, 2005‐2006

• Special Event Traffic Study for the New  Stadium, Scottsdale, AZ, 2009  

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MPA Application• 2005 PM Peak Hour, Kansas City North Shopping  Mall

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MPA Test in TRM

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Suggestions

• System‐wide use of MPA in the regional travel  demand – NOT Suggest at this time

• Use of MPA for a limited number of key zones  in the regional model – Strongly Suggest

• Use of MPA for corridor or small area studies  – Strongly Recommend

• Use of MPA for obtaining better assignment  results – No comment

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