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Trip End Models
Trip end models are developed only for the intra-city trips made by the residents of the study area. All other trips viz., I-E, E-I, E-E, are modelled by growth factors. The trip ends of internal trips for the base year can be obtained from the validated O-D matrices. Also, the trip end models can be developed using stepwise multiple linear regression technique. In general the multiple linear regression equation has the following form:

Y = a + b₁X₁ + b₂X₂+…+bnXn (2)
where Y is the trip production or attraction, X₁, X₂,…X_n are planning variables, a is the constant error term, and b₁, b₂,…b_n are the regression coefficients. Calibrating a multiple linear regression model involves finding out the values of the constant error term and the regression coefficients.

The values of planning variables for each zone can be obtained through various primary and secondary sources. An inter correlation matrix is prepared to know the extent of correlation of the independent variables to be used in trip end models. The potential variables that can enter the models are decided based on their correlation with the dependent variables. Two variables having high correlation coefficient can not be used together in the same model. Different regression models for trip production and attraction can be tried. Based on the goodness of fit of the models indicated by coefficient of determination R2, standard error SE and t-values, the best models are adopted.

Trip Distribution Model for Intra-city Trips
A doubly constrained gravity trip distribution model of the following form can be calibrated to represent the base year travel pattern for intra-city trips, within the study area:

T_ij = a_i P_i b_j A_jf(c_ij) --------- (3)
Subject to:


where T_ij is the forecast flow produced by zone i and attracted to zone j, P_i is the forecast number of trips produced by zone i, A_j is the forecast number of trips attracted to zone j, c_ij is the impedance or cost of travel between zone i and zone j, f(c_ij) is the friction factor between zone i and j, ai is the balancing factor for row i given as


b_j is the balancing factor for column j given as


The interzonal travel impedance is taken in terms of travel time. It is to be noted that the generalised cost cannot be used here, as the study deals with only the passenger trips irrespective of the mode used. A suitable friction factor function such as, exponential, inverse power, or gamma, is to be defined, for calibration and application of the gravity model. The exponential function of the form


is generally found to give better results than the others, here, r is the calibration parameter (Caliper 1996).

Calibrating the gravity model consists of evaluating the parameters of the friction factor function so that the gravity model reproduces, as closely as possible, the base year productions and attractions and trip length distribution. The calibration can be done by using the base year P-A matrix, the impedance matrix, and a geographic zone layer in GIS to generate the observed trip length frequency distribution (OTLD). The aim of the calibration is to match OTLD and estimated trip length frequency distribution (ETLD) as closely as possible.

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