Time of Day
Introduction
This page details the steps taken to determine the most appropriate time period definitions for the Triangle Regional Model (TRMG2). Once determined, this page also determines the directionality, occupancy, and capacity factors for each time period. Caliper used the processed household survey to perform the analysis.
Peak period determination
(To skip to the final period definitions, click here.)
Peak period determination is based on an analysis of the trips in motion throughout the day. First, the day is broken up into 15-minute increments. A trip from the household survey is said to be “in motion” if any portion of the trip occurs within the 15-minute bin. As a result, a single trip can be counted in multiple bins. Determining the peak period considers the distribution of all trips as well as the distribution of trips on work tours individually. The chart below shows these two distributions, which look as expected with the AM peak being shorter and more condensed than the PM.
The next step is to determine the peak hour for all trips and those on work tours. In the tables below, the AM and PM peak hours by type are presented. At a minimum, the AM and PM peak periods should contain the respective peak hour for work trips and all trips. The chart below shows that the peak hour for work and all trips are exactly the same in the Triangle region based on the surveys as is often, but not always, the case.
| Trip Purpose | Peak Start | Peak End |
|---|---|---|
| Work | 07:00:00 | 08:00:00 |
| All | 07:00:00 | 08:00:00 |
| Trip Purpose | Peak Start | Peak End |
|---|---|---|
| Work | 16:45:00 | 17:45:00 |
| All | 16:45:00 | 17:45:00 |
Final Period Definitions
Based on the trips in motion profile, there are four distinct periods of the day. AM and PM peaks have the highest intensity of trip making, followed by mid-day, with the overnight period containing the fewest trips in motion. Boundaries for these periods are defined such that the variance of trips in motion within periods is smallest while variance between periods is largest.
The final period definitions are shown in the table below including the mid-day (MD) period. The remaining hours of the day are captured in the night (NT) period. In the chart, the final period is represented by the gray rectangle.| Period | From | To | Hours |
|---|---|---|---|
| AM | 07:00:00 | 09:00:00 | 2.00 |
| MD | 09:00:00 | 15:30:00 | 6.50 |
| PM | 15:30:00 | 18:15:00 | 2.75 |
| NT | 18:15:00 | 07:00:00 | 12.75 |
The table below shows the average 15-minute trips in motion during each period. These period definitions accurately capture the disparate characteristics of each.
| Time of Day | Mean Trips in Motion |
|---|---|
| AM | 321743 |
| MD | 262349 |
| PM | 397634 |
| NT | 71885 |
Time of day factors
With the periods defined, the percent of trips produced by purpose and time of day must be determined. These factors are calculated based on the departure time of each trip rather than using the trips in motion table. This ensures that each trip is only counted once, regardless of duration, and that it is included in the right period. These factors are used to divide the daily person trips created during trip generation into time of day (by purpose).
Directionality factors are calculated separately in the next section. As a reference, the time period definition is shown again first followed by the TOD factors.
| Period | From | To | Hours |
|---|---|---|---|
| AM | 07:00:00 | 09:00:00 | 2.00 |
| MD | 09:00:00 | 15:30:00 | 6.50 |
| PM | 15:30:00 | 18:15:00 | 2.75 |
| NT | 18:15:00 | 07:00:00 | 12.75 |
Homebased
| Trip Type | AM | MD | PM | NT |
|---|---|---|---|---|
| N_HB_K12_All | 39.6% | 25.1% | 21.5% | 13.8% |
| N_HB_OD_Long | 10.3% | 30.5% | 24.8% | 34.4% |
| N_HB_OD_Short | 16.6% | 31.0% | 27.6% | 24.8% |
| N_HB_OME_All | 3.8% | 47.4% | 22.9% | 25.9% |
| N_HB_OMED_All | 15.5% | 60.7% | 17.3% | 6.5% |
| W_HB_EK12_All | 53.1% | 6.2% | 26.4% | 14.3% |
| W_HB_O_All | 15.2% | 15.0% | 30.1% | 39.7% |
| W_HB_W_All | 28.9% | 19.3% | 28.3% | 23.5% |
NonHomebased
| Trip Type | AM | MD | PM | NT |
|---|---|---|---|---|
| N_NH_K12_All | 27.4% | 34.4% | 29.0% | 9.2% |
| N_NH_O_All | 13.8% | 45.8% | 24.8% | 15.6% |
| N_NH_OME_All | 4.9% | 60.1% | 18.8% | 16.2% |
| W_NH_EK12_All | 50.7% | 14.2% | 30.5% | 4.6% |
| W_NH_O_All | 11.0% | 44.8% | 30.8% | 13.4% |
| W_NH_WR_All | 8.2% | 65.0% | 21.1% | 5.7% |
Directionality factors
For most steps in a trip-based model, the trips are said to be in “Production/Attraction” (PA) format. In this format, all home-based trips are considered to start at home and end somewhere else (even if the person is actually traveling back home). This simplification of reality is done for a number of reasons related to model estimation, but is not actually how travel occurs. As a result, before highway assignment can take place, the PA format must be converted to “Origin/Destination” (OD) format. In this format, a trip from work to home starts at work and ends at home.
This conversion is accomplished using factors stratified by time of day and trip type. As an example, the majority of W_HB_W_All (i.e. HBW) trips in the AM start at home and end at work. As a result, the PA-to-OD factor would be above 0.5. In the PM period, this trend is usually reversed, and the PA factor would be less than 0.5.
These factors can be calculated directly from the survey by comparing the number of home-based trips that start at home to the number home-based trips that start elsewhere. The table below shows the PA factors calculated from the survey by trip type.
| Trip Type | AM | MD | PM | NT |
|---|---|---|---|---|
| N_HB_K12_All | 0.87 | 0.26 | 0.19 | 0.81 |
| N_HB_OD_Long | 0.85 | 0.56 | 0.50 | 0.37 |
| N_HB_OD_Short | 0.68 | 0.56 | 0.44 | 0.45 |
| N_HB_OME_All | 0.69 | 0.47 | 0.45 | 0.32 |
| N_HB_OMED_All | 0.91 | 0.60 | 0.32 | 0.42 |
| W_HB_EK12_All | 0.98 | 0.31 | 0.00 | 0.84 |
| W_HB_O_All | 1.00 | 0.46 | 0.02 | 0.20 |
| W_HB_W_All | 1.00 | 0.62 | 0.07 | 0.64 |
By definition, non-home-based trips are the same in either format; their PA factors are set to .5. The same treatment is applied to commercial vehicles, trucks, and external trips.
Directionality factors are applied after the distribution and modal models. At that point, trip types are collapsed due to sample size limitations in the household survey. As a result, the factors must be estimated using the matching, more-aggregate purposes.
Treatment of skims
In the TRMG2, the directionality factors are used to further improve the period-specific skims. The easiest way to explain the improvement is using the PM period as an example.
In the PM period, 95% of home-based work trips in the survey are traveling back home. Trip productions estimated by the model are in PA format and, with a traditional approach, would see skim times from home to work, which are near free-flow speed. This unrealistic representation of travel time would cause incorrect mode and destination choices to be predicted.
To properly represent aggregate travel times, the PA and AP directions must be combined using a weighted average as shown below:
\[TT_{avg} = f_{pa} * TT_{ij} + (1 - f_{pa}) * TT_{ji}\]
Where:
\(TT_{avg}\) is the average travel time from zone i to j; \(f_{pa}\) is the PA factor; \(TT_{ij}\) is the travel time from zone i to j; and \(TT_{ji}\) is the travel time from zone j to i.
The table below shows the directional factors used to average skims. Note that for non-home-based trips and all off-peak trips, a simple 50/50 split was used. For home-based trips in the off-peak, the survey showed that the directionality was close enough to 50/50 that the extra complexity was not warranted.
| Period | Homebased | Tour Type | PA | AP |
|---|---|---|---|---|
| AM | HB | W | 0.995 | 0.005 |
| AM | HB | N | 0.799 | 0.201 |
| AM | NHB | All | 0.500 | 0.500 |
| PM | HB | W | 0.046 | 0.954 |
| PM | HB | N | 0.421 | 0.579 |
| PM | NHB | All | 0.500 | 0.500 |
| MD | All | All | 0.500 | 0.500 |
| NT | All | All | 0.500 | 0.500 |
Vehicle occupancy factors
In addition to applying directionality factors before assignment, the person trip matrices are converted to vehicles using occupancy factors. These factors are calculated from the household survey, which includes information on the party size of each trip. The rates below meet expectations. The mode categories used are defined as follows:
- SOV: Single occupancy
- HOV2: 2-person occupancy
- HOV3: 3+ person occupancy
Vehicle occupancy for SOV and HOV2 modes are 1.0 and 2.0, respectively. The factors for HOV3 are shown below.
| Trip Type | AM | MD | PM | NT |
|---|---|---|---|---|
| N_HB_K12_All | 3.568 | 3.763 | 3.649 | 3.402 |
| N_HB_OD_Long | 3.474 | 3.836 | 3.397 | 3.664 |
| N_HB_OD_Short | 3.740 | 3.628 | 3.359 | 3.803 |
| N_HB_OME_All | 3.654 | 3.630 | 3.653 | 3.616 |
| N_HB_OMED_All | 3.545 | 3.714 | 3.545 | 3.545 |
| W_HB_EK12_All | 3.381 | 3.415 | 3.557 | 3.415 |
| W_HB_O_All | 3.414 | 3.333 | 3.166 | 3.474 |
| W_HB_W_All | 3.475 | 3.475 | 3.475 | 3.475 |
Roadway assignment in the model is done by vehicle class (sov, hov2, hov3). As a result, “auto pay” and “other modes” must be converted into those classes. The table below shows the homebased trip factors calculated from the survey used to do this.
| trip_type | sov | hov2 | hov3 |
|---|---|---|---|
| N_HB_K12_All | 0.035 | 0.334 | 0.632 |
| N_HB_OD_Long | 0.142 | 0.456 | 0.402 |
| N_HB_OD_Short | 0.212 | 0.237 | 0.551 |
| N_HB_OME_All | 0.125 | 0.597 | 0.278 |
| N_HB_OMED_All | 0.065 | 0.760 | 0.174 |
| W_HB_EK12_All | 0.000 | 1.000 | 0.000 |
| W_HB_O_All | 0.528 | 0.279 | 0.193 |
| W_HB_W_All | 0.482 | 0.276 | 0.242 |
For non-homebased trips, the factors are calculated by tour type (work or non work). They are shown in the table below.
| tour_type | sov | hov2 | hov3 |
|---|---|---|---|
| NonWork | 0.53 | 0.227 | 0.243 |
| Work | 0.51 | 0.148 | 0.342 |
Period capacity factors
In aggregate period assignment regimes, hourly capacities must be converted to period capacities in a manner that accurately captures the balance of congestion. In the real world, the hourly capacity of a road is generally the same throughout the day; it is the demand that changes. This change in demand causes congestion levels to change over time. Consider the stylized example below of a real world street segment.
Qualitative example
Note that capacity remains fixed while demand changes.
| Time | Capacity | Demand | Percent |
|---|---|---|---|
| 6-7 | 1050 | 500 | 47.62 |
| 7-8 | 1050 | 900 | 85.71 |
| 8-9 | 1050 | 500 | 47.62 |
The easiest way to represent this in a period assignment would be to add up the total capacity and total demand from each hour.
| Time | Capacity | Demand |
|---|---|---|
| 6-9 | 3150 | 1900 |
In this simple representation, no one experiences congestion. This does not match the real world graph, which shows that nearly half the vehicles in the period experience congested conditions. This occurs between 7:00 am and 8:00 am. This discrepancy between the real world and a naive period representation can cause numerous errors in the model, including:
- Longer trip lengths
- Incorrect route choices
- Lower diversion to transit
- Incorrect link assignment
The period capacity factor (PCF) corrects for this, and is the inverse of a similar concept from traffic engineering: the peak hour factor (PHF). In traffic engineering, the PHF adjusts hourly volume based on the highest 15-minute volume within the hour. While the PHF is used to adjust demand given a fixed capacity, the PCF adjusts period capacity based on the highest-volume hour of the period.
Consider our example of a three-hour period from 6:00 am to 9:00 am. If the actual demand was evenly distributed across the period, the PHF would be .33. The PCF, the inverse of the PHF, would be 3. In this scenario, the hourly capacity would be multiplied by 3, which would lead to the capacity shown in the table above. Instead, using the actual demand from our example, the PHF would be:
\[PHF = 900 /(500 + 900 + 500) = 0.474\]
Taking the inverse gives a PCF of:
\[PCF = 1 / .474 = 2.11\]
The period capacity that most-accurately reflects congestion would be:
\[Period Capacity = 1050 * 2.11 = 2215\]
That capacity is shown relative to the period demand in the chart below. This relationship is a better representation of real world conditions.
| PCF | Demand | Capacity | % of Capacity |
|---|---|---|---|
| PCF = 3.00 | 1900 | 3150 | 60.32 |
| PCF = 2.11 | 1900 | 2216 | 85.74 |
Calculation from survey
The PCFs for the model can be calculated from the trips in motion table using the same approach. The results are shown in the table below.
| Period | From | To | Length (hrs) | PHF | Model Capacity (hrs) |
|---|---|---|---|---|---|
| AM | 07:00:00 | 09:00:00 | 2.00 | 0.54 | 1.86 |
| MD | 09:00:00 | 15:30:00 | 6.50 | 0.20 | 4.88 |
| PM | 15:30:00 | 18:15:00 | 2.75 | 0.39 | 2.56 |
| NT | 18:15:00 | 07:00:00 | 12.75 | 0.32 | 3.14 |
The approach above is most appropriate in the short peak periods to accurately capture peak congestion. However, the long duration of the MD and NT periods and overall light congestion lead the approach to overstate congestion. For this reason, additional capacity is added. The final period factors are shown below.
| Period | From | To | Length (hrs) | Model Capacity (hrs) |
|---|---|---|---|---|
| AM | 07:00:00 | 09:00:00 | 2.00 | 1.86 |
| MD | 09:00:00 | 15:30:00 | 6.50 | 5.50 |
| PM | 15:30:00 | 18:15:00 | 2.75 | 2.56 |
| NT | 18:15:00 | 07:00:00 | 12.75 | 4.00 |
TransCAD GIS Software, 2022