# Introduction

The Trip Distribution Model specification, calibration targets and calibrated results are presented in below. Logit-based destination choice models are used for resident trip distribution model, while simpler gravity models are used for trucks trips and external-internal/internal-external trips.

# Resident Trips

## Specification

Resident trip distribution is done using discrete choice destination choice models. They are more flexible than traditional gravity models and allow calibration to a better degree. The most common implementation of destination choice is the multinomial logit form. Travelers are hypothesized to choose the destination that maximizes their utility. The utility of a destination is a function of multi-modal accessibilities and preferences, the attractiveness of the destination zone, person and household attributes, and other unknown, un-included attributes of the trip maker or the destination zone. The probability that trip m produced in zone i chooses destination zone j is given by the utility of zone j and the utility of all other possible destinations.

$P_{ijm} = \frac{e^{U_{ijm}}}{\sum_{j} e^{U_{ijm}}}$

$U_{ijm} = \theta * L_{ijm} + \sum_{k} {\beta^k * D_{ij}^k} + \sum_{k} \delta_m^k N_m^k D_{ij}^k + \sum_{k} \gamma_m^k M_i^k IZ_j + \ln(A_{jm})$

In this utility function $$L_{ijm}$$ is the mode choice logsum of trip market $$m$$, $$\beta^k D_{ij}^k$$ are the terms of a distance polynomial; $$N_m^k$$ represent attributes of the trip market such as income or auto availability, usually in the form of indicator variables; $$M_j^k$$ represent attributes of the trip production zone, such as residential density that may be included to represent the utility of the intra-zonal destination; $$A_{ijm}$$ is the size variable; and $$\theta$$, $$\beta^k$$, $$\delta_m^k$$ and $$\gamma_m^k$$ are parameters.

In the formulation above the mode choice logsum is the travel impedance. The size variable is equivalent to the attractions in a gravity model. The distance polynomial terms used in RIVCOM model include, distance and squared distance. The role of the distance polynomial in the utility function is to assist in reproducing the observed trip length frequencies.

It is often difficult to reproduce the observed trip length frequencies using mode choice logsums and size terms alone in the utility function. The specific composition of the distance polynomial is not important, but the entire distance decay function has to be well-behaved, which typically means monotonically decreasing.

Trip distribution models are done at for the following five purpose segmentations:

• HBW: home-based-work
• HBO: home-based-other
• HBSC: home-based-school
• HBU: home-based-university
• NHB: non-home-based

The HBSH and HBO are combined into a single combined HBO purpose at this stage in the model. The parameter file that specifies this purpose aggregation is distribution/d_purp_conversion. It contains the mapping from the purpose segmentation used in trip generation and purpose segmentation used in trip distribution (and downstream models). HBW and HBO uses the same five market segmentations as was used in the trip generation models. The variables and corresponding parameters specified for resident trip distribution can be found in the file distribution/dc_parameters. Shadow pricing based double constraining is applied to all HBW trip segments.

## Resident Trips Calibration Summary

Resident trip distribution targets were prepared from the SCAG 2020 RTP base year (2016) model outputs. Calibration targets for this model were prepared using trips which had either the trip origin or the trip destination within Riverside County. To match with the targets, model summaries were also prepared using only trips that had either trip origin or trip destination within Riverside County.

Tables 1 and 2 below shows the trip length frequency distribution comparison between targets and model for HBW and HBO trip purposes. Table 3 shows the comparison between target mean distance and model mean distance for different resident trip purposes. The model trip length distributions match the targets reasonably well, although there are some deviation due to calibration updates that were made to get better highway assignment validation. Similarly, the model mean distances are reasonably close for HBW and HBU trip purposes categories, while the model mean distances are higher than the targets for HBO and NHB trip categories.

#### HBW Trips

Table 1: HBW Trip Length Frequency Distribution: Target vs. Model
Distance range Target Percentage Model Percentage
0 to 1 miles 2.1 2.5
1 to 3 miles 9.0 9.2
3 to 5 miles 8.4 9.5
5 to 10 miles 16.6 14.3
10 to 25 miles 27.6 30.0
25 to 75 miles 34.3 27.8
75 to 300 miles 2.0 6.8

#### HBO Trips

Table 2: HBO Trip Length Frequency Distribution: Target vs. Model
Distance range Target Percentage Model Percentage
0 to 1 miles 12.6 14.4
1 to 3 miles 26.7 29.9
3 to 5 miles 18.0 15.7
5 to 10 miles 22.1 18.5
10 to 25 miles 17.7 15.7
25 to 75 miles 2.8 5.1
75 to 300 miles 0.0 0.7
Table 3: Mean distance by purpose
Purpose Target Distance Model Distance
HBO 6.6 7.6
HBSC 3.5 4.2
HBU 17.1 18.8
HBW 22.4 25.1
NHB 6.2 6.7
NHBNR 21.3 21.4

### County to county Flows

For work trips, an additional comparison is made, by comparing County-to-County worker flow between model outputs and 2012-2016 American Community Survey (ACS) based Census Transportation Planning Products (CTPP) worker flow. This is shown in the two tables below. In table 4 and 5, rows are production (home) county and columns are attraction (work) county. The final matrix is row normalized and row percentages are calculated. Note that during these calculation workers living or working outside of Riverside County, San Bernardino County, Orange County and San Diego County are excluded.

Table 4: Work flow targets from CTPP(Row percentages)
Production County 1_San Bernardino 2_Riverside 3_Orange 4_San Diego
1_San Bernardino 84.7 9.7 5.3 0.3
2_Riverside 11.7 74.5 8.7 5.1
3_Orange 1.1 1.1 96.9 0.9
4_San Diego 0.1 0.5 0.9 98.5
Table 5: Model work trip flows (Row percentages)
Production County 1_San Bernardino 2_Riverside 3_Orange 4_San Diego
1_San Bernardino 81.2 13.0 3.8 2.0
2_Riverside 13.5 73.7 7.3 5.5
3_Orange 1.7 3.1 91.6 3.7
4_San Diego 0.8 2.0 3.5 93.6

# Truck Trips

Truck trips are distributed using a gravity model. Truck production are attractions are specified in an identical way. so even though the distribution model is specified as a production constrained gravity model, it could be described as doubly-constrained also. The gamma function friction factor based gravity models are used in the specification.Note that TransCAD formulates the gamma function with negative coefficients for $$b$$ and $$c$$. As a result, positive values indicate an aversion to travel impedance.

$F(t_{ij}) = a * t_{ij}^{-b} * e^{-c(t_{ij})}$

Where:

F = Friction Factor;

t = travel impedance (general cost);

i,j = the from and to zone, respectively;

a, b, c = model parameters; and

e = base of natural logarithms.

The gamma function parameters by truck segment (CV, SUT and MUT) and time period is specified in the file cv/truck_distribution. The calibration targets and the model summary for the mean truck trip distance by truck segment is shown in the table below.

Table 6: Mean distance by truck segment
Truck Segment Target Distance Model Distance
CV 9.3 11.0
SUT 9.2 12.9
MUT 20.7 22.0

# External Trips

This section describes the distribution models for both the external-external (EE) trips and internal-external/external-internal (IE/EI) trips.

## External-External Trips

EE trips distribution essentially determines the external zone to external zone travel matrix, also called as the through trip matrix. EE trip distribution model is an Iteration proportional Fitting (IPF) model, that uses the marginals calculated by the generation model and a seed matrix to determine the final through trip matrix. The seed matrix is created from the SCAG 2020 RTP base year (2016) model outputs. Truck EE trips are also calculated in the same way using the truck EE trip marginals computed by the Truck EE generation model. The final EE trip matrix for the passenger car and truck EE trips are shown in the tables below. As noted in the external trip generation section, only a subset of external stations have EE trips. First, because only some combinations of EE trip origin-destination makes sense, given the configuration of external stations. Second, because the SCAG base year model outputs was used in identifying the stations that has EE trips and in those outputs only few of these interchanges had EE trips

Table 7: EE trip matrix by external gate
Orig 3483 3487 3495 3499 3505
3,483 0 0 120 95 95
3,487 0 0 1,209 645 645
3,495 120 1,209 0 0 0
3,499 95 645 0 0 0
3,505 95 645 0 0 0
Table 8: EE truck trip matrix by external gate
Orig 3483 3487 3495 3499 3505
3,483 0 0 438 175 175
3,487 0 0 507 1,807 1,807
3,495 438 507 0 0 0
3,499 175 1,807 0 0 0
3,505 175 1,807 0 0 0

## Internal-External and External-Internal

IE/EI trips are modeled jointly at the trips distribution stage also. A gamma function friction factor based gravity model is used for IE/IE models, similar to the truck trip distribution model. The gamma function parameters for IE/EI trips by time period is specified in the file external/ieei_distribution. IEEI truck distribution follows a similar structure. The parameters for the truck IE/EI trips are specified in the parameter file external/ieei_truck_distribution.

IE/EI trips trip flow is summarized using the districts system shown in the map below to compare against targets.