The Science of Cities and Regions by Alan Wilson

Author:Alan Wilson
Language: eng
Format: epub
Publisher: Springer Netherlands, Dordrecht

(5.16)

If Oi and Dj are the total number of origins in zone i and destinations in zone j, and Tij is the flow between i and j, then the standard doubly constrained spatial interaction model is

(5.17)

with

(5.18)

(5.19)

To model congestion, we need to know the flows on each link. Let quvh be the flow on link (u, v, h) and let Quvh be the set of origin–destination pairs at level h that use the (u, v, h) link. Then

(5.20)

We then want γuvh to be a function of the flow:

(5.21)

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