Capacitate​d traffic assignment problem subject to variable demand, a nonlinear formulation cum solution code in gams



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(7)

where is the travel time from origin to destination ; is a parameter to be calibrated using modal split survey data; is a constant value representing maximum possible travel demand () and denotes travel time on alternative transport mode. The inverse travel demand can be easily derived from (7):

(8)

The inverse demand function is integrable, hence the second term of the objective function can be derived as:



(9)

For illustration purpose, we consider travel time obtained from fixed travel demand as the time for the alternative transport mode () and the maximum demand is assumed as twice the fixed demand (). Hence, it ensures setting at equilibrium.


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