ABSTRACTThis paper discusses a new time-of-day departure time choice model, or "peak spreading" model, as developed for the San Francisco Bay Area. The model is a simple binomial logit choice model with the choices of AM peak (two-hour) period departure and non-AM peak period departure. The choice is applied to daily home-to-work auto person trips. This home-based work departure time model is estimated using data from the 1990 Bay Area household travel survey, using data variables such as free-flow and AM peak period congested travel time, trip distance, household income, and dummy variables for bridge crossers, carpooling and retail employment. Highway assignments were calibrated and validated against 1990 daily and peak period traffic volumes and peak period speeds.
The problems with using this model in future year forecasts are discussed. This simple
peak-spreading model has a tendency to divert trips from the peak period to the shoulders of the peak
period due to increased congestion levels. The result is that the peak period traffic volumes are
sometimes lower than the peak shoulder period traffic volumes, yielding too fast speeds in the peak
period and too slow speeds in the shoulder periods. This is our "snow plow" effect, with traffic piling
up on the shoulders to allow traffic to flow during the peak period. The quick fix to this problem was
to prepare four-hour AM peak period traffic assignment based on peaking factors derived from household
travel surveys. The slower of the two-hour and four-hour AM peak period assignments are used to feed
back to all mode choice models for purposes of forecast equilibration.
Other logit departure time models have been estimated and are discussed. They include multinomial choice models (peak period, shoulder period, off-peak period) and binomial choice model (peak period, shoulder period) based on four-hour AM peak auto person trips.
The purpose of this paper is to document new time-of-day choice models developed by staff of the Metropolitan
Transportation Commission (MTC). MTC is the metropolitan planning organization for the nine-county San Francisco
Bay Area. A review of the literature of time-of-day choice models is included in reference (1).
Background MTC research on time-of-day travel patterns is included in a 1990 MTC
household travel survey report (2). Detailed MTC memorandum discussing the estimation, validation and
application of the home-to-work departure time choice models is included in two technical memoranda (3,
4). In terms of general peaking characteristics, 66 percent of the vehicle trips in the AM peak period
(0630-0830 AM) are home-based work trips. In comparison, just 40 percent of the vehicle trips starting in the PM
peak period (0400-0600 PM) are home-based work trips. In the Bay Area, the PM peak period has about 26 percent more
vehicle trip starts than the AM peak period.
Traditional time-of-day factors (post mode choice, pre-assignment) are shown in Table
1. These convert daily, production-attraction format person trip tables by trip purpose and travel mode into AM
peak hour vehicle trips. These factors are typically derived from local household travel surveys. Important to note
are the higher peaking factors for home-based work share ride trips compared to home-based work drive alone trips.
This suggests that drive alone commuters have more flexibility in work time arrival compared to formal carpools. It
is also interesting to note the gradual "spreading of the peak" represented by these declining home-to-work trip
factors between the 1965 and 1990 surveys. The major problem with this traditional approach is that these constant
factors can't be used to simulate any "spreading of the peak" and will tend to over-estimate congested travel times
in future year scenarios.
The new "hybrid" approach to peak trip factoring is shown in Table 2. In the new MTC
travel model system, traditional peaking factors are used to convert daily non-work trips into peak period vehicle
trips; and a new, binomial logit choice model is used to split daily home-to-work trips into trips that start
during the AM peak period; and trips that don't start during the AM peak period. Also shown in Table 2 are the four-hour peaking factors that are used to complement the two-hour traffic
The final binomial choice home-to-work departure time choice model is provided in Table
3. The shared ride dummy variable is positive and reflects the higher probability of carpoolers to start their
travel during the peak periods. The second degree polynomial of auto distance reflects the tendency of very short
distance and very long distance commuters to begin their commute outside the two-hour AM peak period. The negative
coefficients for the "bridge crossing dummy" and the "San Francisco Oakland Bay Bridge crossing dummy" reflect the
high propensity of bridge users to begin their commute outside the two-hour AM peak period. And lastly, the "retail
industry" variable indicates the higher probability of retail workers to begin their commute after the 0630-0830 AM
One of the major concerns with using this departure time choice model was the potential to reduce the peak
period demand, thereby increasing traffic during the "shoulder" hours of the commute period (0530-0630 and
0830-0930 AM). In extreme cases, shoulder hour travel demand would be higher than the peak period travel demand,
yielding an "inverted" greater peak period, or a "snow plow" effect (traffic volumes and travel times that are
higher in the peak shoulders than during the center of the peak period!)
This "snow plow" effect is summarized in Figure 1. This scatterplot shows the MTC
regional highway links with their two-hour congested speeds on the x-axis, and the four-hour congested speeds on
the y-axis. In normal circumstances, four-hour speeds are faster than two-hour speeds. This is represented as links
above the diagonal line. The abnormal situation occurs when the four-hour speeds are slower than two-hour speeds,
represented by the data points below this diagonal line. For example, some links show a 50 mile per hour speed
during the two-hour peak period, yet a 15 mile per hour speed during the four-hour peak period. This is not an
acceptable feature. This inverted speed, or "snow plow" phenomena wasn't that extensive with only 4 percent of the
22 thousand links in the MTC high network exhibiting this trait.
The "quick fix" that MTC included in future year forecasts was to feed back the lower of the two travel speeds
into mode choice, the reasoning being that the lower speed is a more accurate and believable reflection of the AM
peak two-hour peak (and that the MTC mode choice models were estimated using AM peak two-hour travel times and
Regional forecasts using this new peak spreading model is shown in Table 4. This table
shows the peak versus non-peak choice for auto person trips for 1990 through 2020, stratified by vehicle occupancy
level. Overall the peak share of daily home-to-work auto person trips are forecasted to decrease from about 56
percent of trips in 1990 to about 53 percent of trips by the year 2020. On a corridor specific level the
expectation is for a much wider variation due to direction and intensity of the commute. Between 1990 and 2020 the
prediction is for a 33 percent increase in the amount of home-to-work vehicle trips starting in the AM peak period;
and a 47 percent increase in home-to-work vehicle trips starting outside the AM peak period. This is a very
significant change from past practice!
Other time-of-day models have been tested in the Bay Area. Multinomial departure time choice models that have
the peak, the shoulder of the peak, and the other hours of the day as a three-alternative model are shown in
Table 5. On the other hand, non-work departure time choice models were attempted but none
The last point to be made is the importance of peak spreading models used in conjunction with steeper speed-flow
models. It is very important to include some sort of peak spreading models when using steeper speed-flow models, or
the analyst may end up exaggerating the shifts to other travel modes, or exaggerating future congestion levels.
Peak spreading models are a great tool to moderate congestion forecasts in over-saturated situations, and are a
practical extension to traditional trip-based "four step" travel model systems.
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