Transportation Theory and Applications

Transcription

1 Fall MTAT Transportation Theory and Applications Lecture IV: Trip distribution A. Hadachi

2 outline Our objective Introducing two main methods for trip generation

3 objective Trip generation is about destination choice. Introducing the problematic Knowing: Productions and attractions for each zone meaning the origin and destination Determine: the number of trips from each zone to all other zones. This means that we are interested in generating ODmatrix

4 objective This means that we are interested in estimating future OD-matrix based on basic trip matrix t. Tij are the number of trips from zone i to zone j Qi are production potential of zone i Conditions:

5 Trip distribution 2 methods Growth-factor model Gravity model (based on analogy)

6 Growth-factor model Uniform growth-factor Singly constrained growth-factor Doubly constrained growth-factor

7 Growth-factor model Uniform Growth-factor OD- matrix observed trips traffic count 1. base matrix Estimated trips 2. Growth-factor In case the only information available is the general growth rate for the whole study area Then, for each cell we can apply : And

8 Growth-factor model Example: Let s consider the matrix in the table below 4/4 yeas based. if we know that the growth in traffic is expected to grow by 20%. what will be the expected future matrix? Since the growth is expected to be 20% then

9 Growth-factor model Singly Constrained Growth-factor In case we have information about expected growth in specific trips originating from each zone, such as a shopping trips or working trips. Thus, we have to apply the origin-specific growth factor to the appropriate row. The same thing applies if we know extra information about the destination trips then we apply to the concerned column for origin specific factor for destination specific factor

10 Growth-factor model Example: Let s suppose we have a table with predicted growth for origins we have just to multiply with ratio:

11 Growth-factor model Doubly constrained growth-factors Knowns as Fratar or Furness methods Ai and Bj are balancing factors and growth factors elements of basic matrix t. for simplification we will introduce factors: and Hence, and condition: in some cases to respect the condition you may require correcting trip-end estimates produced by the trip generation models.

12 Growth-factor model Process: 1.Set bj =1 2.with bj solve for ai to satisfy trip generation constraint 3.with ai solve bj to satisfy trip attraction constraint 4.update matrix and check for errors 5.repeat steps 2 and 3 till convergence. Error is calculated as: : actual productions from zone i : calculated productions from zone i : actual attraction from zone j : calculated attraction from zone j

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17 Gravity model Computing gravitational attraction between planets Gij is gravitational force between i and j g is gravitational constant mi, mj is mass of planet i and j dij is the distance between i and j Tij is number of trips from zone i to j is the measure of average trip intensity Oi, Dj is production potential of zone i and attraction potential of zone j f(cij) is accessibility of j from i

18 Gravity model Formula Assumptions Tij is number of trips from zone i to j is the measure of average trip intensity Oi, Dj is production potential of zone i and attraction potential of zone j f(cij) is accessibility of j from i we will assume that the number of trips between an origin and destination is promotional to: Production factor at the origin or Attraction factor at the destination or factor depends on the cost

19 Gravity model By introducing balancing factors the formula become (Ai and Bj): if we apply: and Hence, Balancing factor: Bj depends on Ai thus:

20 Gravity model Process: 1.Set Bj=1, find Ai using 2.Find Bj using 3.Compute the error as : actual productions from zone i : calculated productions from zone i : actual attraction from zone j : calculated attraction from zone j 6.Again set Bj=1 and find Ai, also find Bj. 7.Repeat the steps until convergence.

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