Resilience Insights

While the typical assumptions that hold true for a traditional four-step travel demand forecasting model apply to the Analyst Transportation Module, the MXD component of the module requires some additional assumptions to be set. These assumptions are used to post-process auto trips and adjust the auto mode trip counts generated from the traditional mode choice model. Broadly, the MXD model performs the following steps:

There are other assumptions underlying each step of the model, which are explained in the following sections.

To estimate the number of vehicle trips either produced or attracted to a given parcel, the standard ITE trip generation rates are used to generate initial vehicle trip counts. These rates differ according to the target parcel's household type and employment sector composition. They are discussed in more detail in the Input Parameters section (regarding the default rates used in the system).

For trips associated with residential land uses, trip generation accounts for three residential dwelling unit types:

In the trip generation step, the number of trips produced by households is estimated by multiplying the number of occupied residential dwelling units of a given type by the corresponding stated trip generation rate. For example, the number of trips produced by households living in single-family dwelling units is given by the following equation:

The logic for estimating trips associated with other land uses is similar. In the trip generation step, the number of trips associated with the following eight non-residential land uses are calculated:

For typical employment, trips are calculated according to the following equation:

Trips associated with retail, entertainment, and restaurant destinations are handled differently than other trips are handled. Their numbers are calculated via the following equation (explained in detail after the equation):

For these particular trips (retail, entertainment, and restaurant), an alternate estimate of the number of jobs is used. This estimate is determined according to set area-job conversion rates that describe the average number of jobs per building area for various programming types. The default rate is two jobs for every 1,000 square feet of building area.

Total K-12 school trips are estimated as a percentage of total residential trips. The module uses a default rate of 0.097 (K–12 school trip per residential trip)³². Currently the number of college/university trips defaults to zero in the released version of the module in Analyst.

Trips are re-grouped into the following five categories:

These trips are further grouped by subcategory and direction (attraction or production). Currently the module considers three trip subcategories:

The National Cooperative Highway Research Program (NCHRP) person trip rates³³ have been adapted for identification of the proportion of total trips that are allocated to each trip category. These proportions are used to weight the previously computed trip counts (which are based on ITE trip generation rates) into the trip categories. For a better understanding of the application of the NCHRP person trip rates, an example focusing on residential trips is set out below.

First, assume there are Nr occupied residential dwelling units (DU) for a given parcel. Current default rates for the module are as follows:

These factors are represented in N, is the number of residential dwelling units per parcel.. In this table, each category represents a percentage of the total trips. The calculation in each cell illustrates the previously generated ITE residential trips.

In the Analyst Transportation module, all residential NHB production trips³⁶ are, by default, external trips with both trip ends outside the project area. Specifically, it is assumed that:

To accommodate this assumption, all residential production trips that are NHB are removed. Next, HBW and HBO other trips are scaled up proportionally to replace the removed NHB trip counts. In other words, residential NHB production trips and associated VMT are attributed to residents in the project area no matter if they are external or internal to the project area.

The same process is used for other non-residential trips. In each instance, proportions are calculated according to the paired NCHRP data for each trip type.

The last step of trip generation is categorizing the trips in each category as internal or external. By definition, both ends of internal trips lie within the project area. On the other hand, external trips either originate or end in areas outside of the project area.

Currently, the module only estimates external HBW trips, primarily because of the limited availability of datasets for building estimation models (to predict external percentages for HBO and NHB trips).

A percentage of HBW trips will be designated external trips, allowing for the balance of internal-internal production and attraction trips in the project area. For each project, the percentage of trips types where either the origin or the destination is external to the project site is estimated via a Decision Tree (DT). A DT is a non-parametric supervised learning method that we employ to develop a regression within the model.

The decision tree algorithm first finds similar projects, in a pool of representative project samples, as the target project. It does so by categorizing all projects based on a list of attributes, such as employment household ration, sum of dwelling units by type, and summary stats of intersection density³⁷. The algorithm then predicts the external trip percentage for the target project by taking a weighted average of external trip percentages of those similar projects.

The final output of trip generation is vehicle trip counts categorized according to whether they are internal or external, whether their purpose is HBW, HBO, or NHB, and whether they are production or attraction trips.

Average trip generation rates by category presents default trip generation rates used to estimate the number of residential and non- residential trips in each category. ³⁸³⁹⁴⁰

Internal and external trips are distributed slightly differently. For internal trip distribution, all calculations are performed at the traffic analysis zones scale, which is a commonly used geography for travel demand forecasting. All evaluated blocks or parcels will be paired with their parent TAZ, and they will have descriptive attributes inherited from their parent TAZ.

During the trip generation step, trip origins and destinations are determined for each Canvas Geometry based on Land Use Types, Employment Densities, and other resources. These results are aggregated from the Canvas Geometries to the Census TAZs that they lie within and inform the full distance matrix of that scenario.

Next, a full distance matrix is computed. That is, the cost of travel between any two pairs of TAZs is calculated. Travel cost can be measured in various ways. It can be as simple as travel distance or as complex as a composite measure that includes various kinds of travel times (e.g., traffic data) and costs.⁴⁴

By default, the module calculates a modified city grid distance between TAZ centroids and uses it as travel cost. City grid distance is based on the assumption that the relationship between an isosceles triangle’s hypotenuse and two other sides (adjacent and opposite) is roughly modeled by the average circuity of an “as the crow flies” direct line distance and the real path necessitated by the urban road network. Thus, to calculate the “real” distance between two centroids, one would multiply the straight point-to-point distance by the square root of 2 (approximately 1.4142). This value has been increased slightly because of a nationwide study of driving distance versus straight line distance to the nearest hospitals. That is, what was the distance more than the direct, straight line distance that a vehicle had to travel to reach its destination by traveling on available road networks. The study found an average percent difference (that is, a circuity factor) of 1.417.⁴⁵ This circuity factor will be available to users and adjustable for site optimization.

The output of this step is a matrix with the following composition:

Costs are calculated via the (aforementioned) modified city-grid distance between an origin TAZ and a destination TAZ. Trips internal to TAZs are assigned an “average trip length.” This value is calculated by measuring the radius of the smallest circle encompassing the largest single geometry of a given TAZ’s composite geometries (polygons).

The travel distance matrix is then transformed into a travel impedance matrix via a deterrence function, a common method for representing the nonlinear impacts of travel cost changes on travel choices. The module uses an exponential deterrence function and a default initial β of 5. See Input Parameters for more details.

The next step is generating an initial trip matrix, assuming the K factors are equal to 1.⁴⁶ During this step, TAZ i, for example, is taken, which has a number of home-based work trip origins equal to Pi. Pi is allocated to all the TAZs (including itself) according to the equation:

Note that the summation of the above for TAZ j should be equal to 1. In other words, more trips are allocated to TAZ j if it has more trip ends, indicating that it has a larger population and/or more employment (and therefore more “attraction”) if it costs less to travel to, which in this case means being closer to TAZ i.

Depending on the scale of travel impedance values and initial deterrence function parameters, the resulting matrix may contain invalid values as a result of extremely small denominators. To account for this, the module automatically adjusts deterrence function parameters according to a simple decay function. Users can set minimum deterrence function parameters. Currently, the module’s minimum β value for the exponential deterrence function is 0.01.

The next step is balancing the matrix via an iterative proportional fitting (IPF) technique⁴⁷. The initial trip matrix generated during the previous step is an unbalanced matrix because the sum of the allocated trips for each destination TAZ (that is, the sum of the values in each column) does not necessarily match the number of attraction trips estimated during the trip generation step.

Thus, the primary purpose of this step is to adjust trips proportionally until the resulting trip matrix matches the trip generation estimates. Therefore, at this stage the module calculates:

The consequence of this operation is that the number of trips allocated for each origin TAZ is not necessarily equal to the number of production trips estimated for each TAZ. That is, during the first pass, trip allocation does not necessarily match the pre-assessed production trip count for a given TAZ. As a result, each successive iteration scales up the production trips for each TAZ by each TAZ’s corresponding ratio (that is, its ratio of allocated trips to the previously computed production trip count “source of truth”). It is this balancing operation that is “iterated” until convergence. For more information on the application of IPF to trip distribution, please refer to chapter 5 of “Modeling Transport” (Ortuzar, Juan de Dios and Willumsen, Luis G.).

In this model, the iterative balancing repeats until one of the following thresholds is met, the first two of which have parameters the user can control:

A simplified version of the method above is applied when assigning trips to areas that lie outside the project area. Because a 150-kilometer buffer area is used to identify development in a broader area in around the project site, the number of Canvas Geometries being evaluated may increase by several orders of magnitude. (Note that this buffer area does not correspond to the optionally defined context area for a project, or the "access area" used by the Walk and Transit Accessibility modules.)

The above approach to distributing external trips would require processing all geometries in the outlying buffer area. To reduce the computational expense, the buffer area is preprocessed to reduce the number of possible origins and destinations external to the project area to a limited series of representative points.

To create the buffer area’s summary point, the module searches for likely origins and destinations according to employment and household densities in the buffer area⁴⁸. Using these attributes, a kernel density estimation (KDE) algorithm smooths data to generate discrete peaks in the project’s surrounding buffer area. Among these peaks, a limited set of external locations are identified, and all external trips starting or ending in the project area will be distributed (to or from) these locations.

External trips are distributed to potential locations according to:

The last step of the trip distribution component of the Transportation Module is calculating an average trip length for each trip category. Below is a walkthrough of this step with examples of home-based work production trips.

In this step, the weights are equal to the quotient of the number of trips from TAZ i to a given destination and the counts of the trip origins of TAZ i. The average production trip lengths from TAZ i are calculated next. These are equal to the product of the distances between each TAZ i and the other TAZs, and the corresponding weights, as shown in the following equation:

Variable definitions:

Forms of Deterrence Functions presents the deterrence functions available to users. Users can also adjust the coefficient parameters used in each deterrence function available.

In the formulas above, c is the raw cost of traveling between origin i and destination j. What it represents can be as simple as travel distance or as complex as a generalized cost that includes various other factors.

A logistic regression model predicts the probability of an event according to the variable attributes assigned to each geometry in the broader area. In this context, the model is used to determine whether a trip is a vehicle trip or a walk, transit, or internal trip. This determination is based on a series of variables and the following equation:

The variable t is a linear function of one or more variables and is referred to as “log-odds”⁴⁹ and is described by the following equation:

The operator Ln indicates the natural logarithm of each built environment “D” variable (VAR in the equation above). The result of this operation is multiplied by a variable-specific coefficient (Coeff in the equation above).

The results of the calculation for each variable VAR are summed and added to the variable Constant, which produces the logarithmic odds of travel being an internalized, pedestrian, or transit trip. The variables of the MXD equations are listed below.

Explanatory and outcome variables in MXD equations contains two sections, “Outcome Variables” and “Explanatory Variables.” The second section, “Explanatory Variables,” is often associated with the “D” variables that affect trip generation. These include development density, diversity, design, destination accessibility, distance from transit, development scale, and demographics. The output of the hierarchical modeling involved in the MXD model’s research and development included the individual and combined effects of the seven types of “D” variables on the travel characteristics of 239 targeted mixed-use development areas. Via this research, the variables above were determined significant.

Analyst dynamically calculates these explanatory variables at the appropriate resolution using the current scenario’s canvas data. In other words, these variables reflect different land use patterns and other built environment characteristics of each scenario that a user creates. To ensure that explanatory variables reflect “average” characteristics of a given parcel and its surrounding, various sizes of buffers are applied to derive representative measures of each location. For example, a quarter-mile buffer is used to derive resident population and employment density that is representative of local activity level of a given parcel.

However, such calculation can be computationally intensive, depending on its implementation, especially for large projects that contain hundreds of thousands of canvas shapes. To ensure that the Transportation Module can finish within a reasonable amount of time even for large parcel projects, data are aggregated to standard grids. With that, efficient algorithms can be applied, which allows quick generation of explanatory variables for all canvas shapes in a project.

For internal capture, the dependent variable is the natural log of the odds of an individual making a trip whose origin and destination lie within the same parcel. Depending on the trip-purpose, this probability is related to the development scale, a variety of mixed-use land variables, the measured urban design quality of the MXD, and several demographic variables. The log-odds probability of walking to external destinations is related to the MXD’s size, density, development mix, urban design, demographics, and the number of jobs within a mile. The probability of a vehicle trip being shifted to a transit trips is a function of demographics and the accessibility of the site’s transit to the rest of the region. This accessibility is expressed in terms of jobs within a 30-minute transit trip. The tables in the “Input Parameters” section present the values of parameters used in the log-odds equation.

Mode Choice Input Parameters

The following tables present the relationships used in the following equation:

The constant term, variables (VAR), and coefficients (Coeff) are presented in Log-odds of internal capture (log-log form), Long-odds of walking trips (log-log form), Log-odds of transit trips (log-log form).

The logistic regression model, shown below, transforms log-odds (t) into probabilities. This transformation is represented by the following equation:

For each trip category of all internal trips (i.e. trips with both trip ends inside the project area), the probability of each trip being internal captured, or a walking or transit trip is calculated. The probability is then used to calculate the number of non-vehicle trips (internal capture, transit, and walk) in each of the three trip categories (HBW, HBO, and NHB).

For example, let’s say that the probabilities of internal capture, walking, and transit trips for internal HBW trips in a parcel are 5%, 10%, and 15% respectively. Given that the total number of internal HBW trips is 10000, the probabilities would result in the following trip distribution:

If the examined trips are external trips, we only consider the probability of it being transit trip, not walk or internal capture trip.

VMT is then calculated according to adjusted vehicle trip counts and the corresponding estimated trip lengths. Vehicle trips are first categorized as production or attraction trips according to the production and attraction trip ratio derived in the trip generation step. Take internal HBW production trip as an example. It is calculated via the following equation:

After the number of trips and the corresponding trip length have been computed, the module can calculate VMT.

The module produces a set of MXD vehicle trip variables and a set of VMT variables as the main spatial outputs. The remainder of this section of the documentation will cover how different VMT variables are derived. It will also cover how the results of these operations are summarized for project-wide outputs. These summary operations are applied both to the processed VMT outputs and MXD vehicle trip outputs in a similar fashion.

The module produces both total VMT and VMT per capita (or per household). For the estimation of VMT per capita or per household, only HBW and HBO production trips are considered because they are trips produced by individuals or households in that given parcel. The VMT associated with trips that are attributed to a retail shop in this geometry or a visitor to the area, for example, is not part of this measure.

Let’s take HBW vehicle trips as an example. HBW VMT per household at the parcel level is calculated in two steps. First, the HBW VMT is calculated via the following equation:

Note that HBW attraction vehicle trips are not included in the equation above because they are not taken by households or individuals living in the given parcel.

Second, VMT per household (or capita) is determined via the following equation:

The same logic applies to calculating the per capita and per household VMT associated with HBO vehicle trips. Since residential NHB trips are assumed to be zero in the trip generation step, there is no NHB VMT associated with households⁵⁰. As a result, VMT per household is the sum of HBW VMT per household and HBO VMT per household only:

When it comes to total VMT, the calculation is slightly different. Total VMT for a given parcel includes the VMT associated with not only trips generated from the geometry but also trips attracted to the area.

Again, let us take HBW vehicle trips as an example. To get the total daily VMT associated with internal HBW vehicle trips for a given parcel, the following equation is used:

VMT associated with HBO and NHB, internal or external, are derived using the same functions. Last, total daily VMT, for each parcel, includes VMT of all trip types:

Total annual VMT is derived by applying an annual factor and users can modify this factor:

The module also estimates total daily and annual VMT for the entire project area. Note that it is not the sum of previously derived total daily/annual VMT for each parcel because some trips will be double counted in the process of simply summing all parcels’ total daily/annual VMT.

The reason for this double counting is that half of internal HBW or HBO production trips are trips from home to work/other destinations. As a result, these trips are considered internal HBW or HBO attraction trips in another geometry and will be counted as part of total VMT for that geometry as well. Similarly, one parcel's internal NHB production trip can be another parcel’s internal NHB attraction trip. Essentially, variables at each parcel capture attributes of trip ends whereas project-level variables capture attributes of trips.

The following equation is used to handle the aforementioned double counting issue:

The sum of AdjustedTotalDailyVMT of all parcels is used as the project-level total daily VMT.

Note that double counting is not an issue in the external VMT calculation because the origins/destinations of external trips are outside the project area. In addition, external HBW attraction trips and associated VMT are not typically included in total VMT because they are produced by residents living outside the project area.

The module also estimates the VMT of heavy trucks by applying a truck adjustment factor. Users can modify this factor.