In many of the steps of a Travel Demand Model, there is a consideration of the difficulty of travel, between zones in Trip Distribution, by different modes in Mode Choice, or by different links within the same mode in Trip Assignment. When the difficulty of travel is measured in units of time, then impedance will be expressed in units of time. When measured as distances, impedance will be expressed in units of distance. When measured as costs, impedance will be expressed in units of cost. When that difficulty of travel is a weighted combination of many factors, it is often referred to as a dimensionless ‘utility’ and impedance is expressed in units of that utility.
Mode Choice is traditionally computed after Trip Distribution in a Travel Demand Model. The impedance used in Trip Distribution should thus be the impedance of travel between zones by each available mode combined into a weighted average, i.e. composite, of the impedance by each mode.
In the logit choice model used in many Mode Choice steps, the dominator in that logit equation is the weighted sum of impedances by all modes for each zone pair. The form of the logit equation is such that this is expressed as the weighed sum of the negative exponential, i.e. natural log, of the utility, i.e. impedance, for each mode. This is often shortened to the term logsum (i.e. sum of the logs) of modal utility weighted by the percentage travelling by each mode.
Accessibility is measured by the amount of potential travel attracted by a zone, multiplied by the difficulty of travel relative to the accessibility of all zones. This is precisely the same concept that is used in the Trip Distribution step. That step computes the attractions in a zone multiplied by the friction factor (a function of the difficultly of travel) to that zone divided by the sum for all zones of the attractions times the friction factors. Thus the term in the Trip Distribution equation after the productions in the origin zone, is virtually identical mathematically to the definition of accessibility.
In order understand how to do this, it is useful to focus on the AA, Average Annualized, separately from the D, Daily.
Average annualized means that multiplying by 365.25, the number of days in an average year (including leap years), will produce an annual number. By contrast, Travel Demand Models TDMs, generally forecast weekday demand.
TDMs often produce volumes on its links during congested (e.g. AM Peak and PM peak) and uncongested (e.g. and Night) Time of Day, TOD, periods during those average weekdays. Unless the TDM also reports Daily volumes, it may be necessary to add the TOD link volumes to get those daily volumes. Also AADTs are typically reported as the sum in both directions on a link. TDMs will compute the volumes by direction on a link, e.g. the volume, and performance, from the A node to B node on a link is computed differently than those from the B node to A node.). Again if the TDM does not report the bi directional volume on a link, these directional links volumes may need to be added.
It is possible to convert the daily weekday, bi-directional volumes from a TDM to AADTs by using the same factors that Caltrans’ traffic counting section uses to convert short duration counts, e.g. 48-hour counts, to AADTs. The conversion between a Weekday and Average Annualized volume might be different depending on the type of road (e.g. the weekday/weekend split will be different for a recreational road and a road in a downtown) and on the type of volume being reported, (e.g. the weekday to weekend conversion may be different for trucks and autos. According to USDOT’s Traffic Monitoring Guide, TMG, averaged over all road types, the weekday volume for trucks is 123% of the AADT for trucks and the weekday volume for autos is 104% of the AADT for autos.)
Assignments are almost always done using Origin to Destination, OD, tables. Production to Attraction, PA, tables are computational formats that make it possible, in trip based Travel Demand Models, to ensure that round trips will also return to the starting origin. For example, for commuting round trips that begin at the home, and return home after spending time at work, the first trip, which has an origin at the home, and the return trip which has a destination at the home are both said to be PRODUCED at the home, while the first trip which has a destination at work and the return trip which has an origin at work, are both said to be ATTRACTED to work. Travel Demand Models will typically include a step to convert a PA table to an OD table.
Since the PA table was created to forecast transportation demand, the PA table is often the name given to all tables of demand that are forecast by Travel Demand Models. This is true even when the PA table is identical to the OD table, as is the case for non-home based person trips and all truck trips.
The algorithm that is typically used in assignment, produces a user optimal solution. This can be thought of as an “every man for himself” solution. The sum of the impedances (e.g. some combination of time, cost, or other considerations) on the links of the paths used to connect an origin and a destination, are all the same. Switching to any unused path will only increase the impedance between the origin and destination.
The sum of all of the user optimal solutions is probably NOT the system optimal solution, the lowest possible impedance of all travelers. To achieve a system optimal solution, it may be necessary for some travelers to choose a path whose impedance is greater than the user optimal impedance. The erroneous expectation that the sum of the user optimal solution is the system optimal solution has resulted in Braess’s Paradox. Stated less formally, in order to achieve what is best for the team, i.e. a system optimal solution, some players may have to “take one for the team”, i.e. choose a path that is not user optimal.
All of the economic impacts can not be forecast by Travel Demand Models alone. Travel Demand Models forecast the link demand and performance, e.g. the transportation implications, of economic forecasts, e.g. the number and locations of persons and jobs. They do not forecast the location and number of those persons or jobs. Land Use and Economic models forecast the number and location of jobs and people by assuming a fixed cost, impedance, between each origin and destination. Travel Demand Models forecast the cost of traveling between zones assuming a fixed number and location of persons and jobs. In reality neither transportation costs or the number and location of jobs are fixed. In order to capture the dynamic effect of both changes, TDM and Land Use and Economic Models may have to be operated iteratively. If Land Use and/or Economic models are not used iteratively with Travel Demand Models, an attempt is often made to estimate their impacts by “inducing” transportation trips.