Trip Distribution Modeling Part III

1
Trip Distribution Modeling Part III

• CE 573 Transportation Planning
• Lecture 14

2
Objectives

• Growth factoring
• Types of constraints
• Methods

3
Growth Factoring

• Concept
• XFUTURE XNOW(growth factor)
• Applications
• Beyond regional scope
• Gravity model inadequate
• Too difficult to forecast independent variables

4
Definitions and Constraints

• The trip matrix total T
• Tij is the number of trips going from origin i to
  destination j.
• TLDk is the number of trips in cost-bin k
• Typical trip matrix constraints

5
Growth Factor Methods

• t initial OD matrix
• Uniform growth factor?Tij ttij.
• Singly constrained growth-factor methods

OR
6
Growth Factor Methods (cont.)

• Doubly constrained growth factors?have growth
  factors for origins and destinations (), where
• instead of ai and bj being the growth factors for
  origin i and destination j, they are adjustments
  made to each O-D pair volume in order to achieve
  the target values Oi and Dj required by the
  growth factors for the origins and destinations

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Growth Factor Methods (cont.)doubly constrained

• BI-PROPORTIONAL ALGORITHM
• Step 1 Set bj to 1.0, determine initial trip
  matrix, and solve for ai that meet origin
  constraints, given the latest bj values.
• Recalculate Tij with new ai values
• Step 2 Solve for bj that meet the destinations
  constraints given the latest ai values and the
  previous bj values.
• Recalculate Tij with new bj values and the latest
  ai values.
• m-1 indicates previous iteration

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Growth Factor Methods (cont.)doubly constrained

• Step 3 Keeping the bj values fixed solve for ai
  that satisfy origin constraints given the ai from
  the last iteration (iteration m-1).
• m-1 indicates previous iteration
• Repeat steps 2 and 3 until changes in ai and bj
  are sufficiently small.
• Note This algorithm assumes that both sets of
  constraints can be satisfied simultaneously. In
  other words, the following must be true

9
Advantages and limitations of growth-factor
methods

• Advantages
• simple
• Disadvantages
• requires an initial O-D matrix
• no consideration given to changes in transport
  costs