Travel Demand Models
|Network Software||Mainframe UTPS||Microcomputer MINUTP|
|Zonal System||550 zones (expanded to 700 zones)||1099 zones|
|Model Estimation Software||SAS, CS-LOGIT (mainframe)||SAS, ALOGIT (microcomputer)|
|Model Application Software||FORTRAN (mainframe); Assembly; UTPS||FORTRAN (MS-DOS); MINUTP|
|Workers in Household||Binomial Logit (non-working vs working household)||Nested Logit (non-working, single, multi-worker household)|
|Auto Ownership||Multinomial Logit, LOGSUM linkages with HBWD model||Nested Logit, linked with workers in household model.|
|Trip Purposes||4 - HBW, HBSH, HBSR, NHB
Off-model: HBSch, I/X, Commercial
|6 - HBW, HBSH, HBSR, HBSch, NHB,
Off-model: I/X (interregional)
|Trip Generation||Hybrid (Cross-classification, regression). Motorized person trips, only.||Hybrid (Cross-classification, regression). Total person trips, including bicycle and walk.|
|Trip Distribution||HBW - Logit Destination Choice with LogSum from HBW Mode Choice; Others - Gravity||All purposes - gravity models based on peak highway time or blend of peak/off-peak highway time.|
|Mode Choice||HBW - Multinomial Logit
NW - Binomial Logit
|Nested Logit for all except for HB Grade School (multinomial logit)|
|Time-of-Day||-- Peaking factors derived from household travel surveys||HBW - Departure Time Binomial Logit
All other purposes - peaking factors derived from household travel surveys
|Transit Network||UNET "unintegrated"||MINUTP "integrated"|
|Highway Assignment||LOVs/HOVs in "layered" assignment.||LOVs/HOVs in "simultaneous" assignment.|
|Capacity Restraint Algorithm||Standard BPR from UTPS||Customized: CS = FFS/[1+0.2(v/c)**10]|
|Market Segmentation||Income tertiles through HBW distribution; auto ownership tertiles input to HBW mode choice. Primary/secondary worker segmentation for HBW trips. Non-working versus working household segmentation.||Income quartiles and auto ownership tertiles through HBW mode choice. Auto ownership tertiles in home-based non-work generation and mode choice. Non-working, single worker and multi-worker household segmentation.|
The most significant improvements in the new BAYCAST-90 model system in comparison to the old MTCFCAST-80/81 model system are:
In terms of simplifications in the new BAYCAST system relative to the old MTCFCAST system, these issues relate to:
Of these three issues, the most problematic is the exclusion of the relative transit/auto accessibility variable from the auto ownership level model. This problem can probably be amended in future work by incorporating extra variables in the existing WHHAO (workers in household / auto ownership) choice model. Accessibility variables (how many jobs are within "x" minutes by transit and auto) will be tested in future model improvements as a tractable extension to the existing WHHAO model.
The work trip distribution model is improved in terms of market segmentation (calibration by household income quartile level) but is worse in terms of sensitivity to transit travel times. The new work trip gravity distribution model is based on AM peak period drive alone travel times, only; the old work trip logit destination choice model was based on the "logsum" of the work trip mode choice model (i.e., including drive alone, carpool and transit times and costs), factored by a scaling parameter and adjusted by work trip length distribution. Logit destination choice models are difficult to estimate and calibrate, and future development of these models may not succeed. Other options for improved distribution models may include probability-weighted gravity models based on multimodal travel times (drive alone, carpool, transit, walk and bicycle).
The MTC workers and vehicles in household model (WHHAO) is a nested logit choice model applied at the zone-of-residence level. The input to the WHHAO model application are number of households stratified by household income quartile level. Variables in this choice model include mean household income, mean household size, the share of households residing in multi-family dwelling units, the share of persons age 62-or-older, and gross population density. Coefficients for the final nested choice model, model #9W, are shown in Table 1. Detailed definition of variables in this and other models are included in Appendix Table A.1.
Data on mean household income, mean household size and gross population density is available from Association of Bay Area Governments (ABAG) forecasts. Future year data on share of multi-family units and share of persons age 62-or-more will be derived by MTC staff from 1990 decennial Census data and ABAG county-level age forecasts.
The nested structure for the WHHAO model is shown in Figure 2. The upper level nest of this model splits households into households by workers in household level (0, 1, 2+ workers per household). The lower nest further splits these households by auto ownership level (0, 1, 2+ vehicles per household).
The output from this WHHAO model is the number of households by household income quartile (4) by workers in household level (3) by auto ownership level (3) or 36 different market segments per travel analysis zone.
A detailed example of the calculation of the "logsum" variables used in this WHHAO model is included in a C. Purvis 10/3/95 memo included in Technical Memorandum Compilation, Volume III. The "logsum" is defined as the natural logarithm of the sum of the exponentiated utilities within the particular nest of interest.
Description of adjustments (calibration) to the utility constants, and adjustments to the coefficients by market segment, are included in the separate technical summary on calibration and aggregate validation of the BAYCAST model system.
Trip generation models include both trip production and trip attraction models. Production models are based on trips made by households, workers or students at the home end of home-based trips. Attraction models are based on trips made at the non-home end of home-based trips. Trips as defined in these trip generation models include non-motorized trips (bicycle, walk) as well as motorized modes (auto, transit).
For non-home-based trips, the same production/attraction terminology can be applied, though non-home-based generation models are essentially trip origin (production) and trip destination (attraction) models.
With the exception of the home-based school trip generation models, all of the new trip generation models are multiple regression in form. The home-based shop trip generation model, in particular, is a hybrid of a cross-classification model (stratified by workers in household level) and a multiple regression model.
Coefficients and definition of variables for all trip generation and attraction models are included in Table 2.
The independent variable in these multiple regression trip generation models are either trip rates (e.g., work trips per employed person, home-based shop attractions per retail+service+other job) or trips (e.g., total home-based social/recreation attractions, total non-home-based productions).
The home-based work and home-based school trip generation (production) models are applied to persons who are eligible to take either work or school trips, namely, workers or students. Given difficulty in estimating home-based school trip generation models, the final models are simple trip rate models: 1.314 trips per K-12 student, and 1.157 trips per college student.
Adjustment (calibration) of these trip generation models is included in the separate technical summary on calibration and aggregate validation. This document includes the calibration constants, as well as a discussion on the trip rate "caps" and "floors" that are needed in model application. In terms of aggregate validation, trip generation results are compared, at the MTC superdistrict and county level, to census-based "observed home-based work trips;" or 1990 survey-based observed non-work trips.
Gravity models are the most common form of trip distribution models. Other forms include logit destination choice models (earlier Bay Area models) and intervening opportunities models (Chicago models). Fratar, or growth factor models, are also used for short-term extrapolation of base year trip tables. All of the new Bay Area trip distribution models are gravity in form.
The final set of friction factors used in the BAYCAST gravity trip distribution models are included in Table 3. Essentially these are "lookup" tables to substitute friction values for travel time.
Travel time as used in the BAYCAST gravity trip distribution model is either AM peak period door-to-door drive alone travel time; or a blend of AM peak period and off-peak period door-to-door drive alone travel time.
In the case of home-based work and home-based school trips, only AM peak period travel times are used. For home-based shop, home-based social/recreation and non-home-based trips, a "blended" travel time based on 32.4% peak and 67.6% off-peak travel time is used. These blending shares are based on time-of-day information by trip purpose from the 1990 MTC household travel survey, as follows:
HBSH, Time HBW HBSH + HBSK NHB HBW + HBSR, TOTAL Period HBSR HBSK NHB AM 1645741 656493 738907 325277 2384648 981770 3366418 Peak 36.9% 10.8% 44.2% 6.9% 38.9% 9.1% 19.9% PM 1345441 1516593 179723 1000769 1525164 2517362 4042526 Peak 30.2% 24.9% 10.8% 21.2% 24.9% 23.3% 23.9% Total 4461255 6096871 1670741 4715609 6131996 10812480 16944476 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% PEAK 2991182 2173086 918630 1326046 3909812 3499132 7408944 (AM+PM) 67.0% 35.6% 55.0% 28.1% 63.8% 32.4% 43.7% OFFPEAK 1470073 3923785 752111 3389563 2222184 7313348 9535532 33.0% 64.4% 45.0% 71.9% 36.2% 67.6% 56.3%
AM Peak Period = 6:00-9:00 AM (3 hours)
PM Peak Period = 3:30-6:30 PM (3 hours)
Off-Peak = 9:00 AM - 3:30 PM; 6:30 PM - 6:00 AM (18 hours)
The home-based work trip distribution model is actually four sets of friction factors applied to HBW trip ends stratified by household income quartile level. Data from the 1990 Census-based "observed" home-based work trip tables were used in calibrating these friction factors.
In addition to friction factors, socio-economic adjustment factors (k-factors) are used in calibrating and validating trip distribution models. These k-factors, along with model validation results, including average trip lengths, regional trip length frequency distributions, and modeled versus observed county-to-county and superdistrict-to-superdistrict trip tables, are included in the separate technical summary on calibration and aggregate validation.
For information purposes, the regional results of the BAYCAST model validation process through trip distribution is represented below:
|Income Quartile 1||534,639||9.47||18.79||5,063,031||10,045,867|
|Income Quartile 2||1,124,801||11.43||21.28||12,856,475||23,935,765|
|Income Quartile 3||1,620,069||12.91||23.15||20,915,091||37,504,597|
|Income Quartile 4||1,284,902||13.31||23.88||17,102,046||30,683,460|
|Total, Home-Based Work||4,564,411||12.25||22.38||55,914,035||102,151,518|
|Home-Based Grade School||842,871||3.20||8.11||2,697,187||6,835,684|
|Home-Based High School||345,542||4.41||10.00||1,523,840||3,455,420|
|Total, Home-Based School||1,626,476||4.97||11.16||8,083,586||18,151,472|
|Total Trips, All Purposes||17,078,173||7.69||15.05||131,345,425||256,981,880|
Home-based work trips comprise 26.7 percent of all trips and yet 42.6 percent of all person miles of travel. Non-home-based trips comprise the largest trip purpose share, at 27.6 percent of all trips in the Bay Area, yet are just 21.9 percent of all person miles of travel.
Home-based shop trips are 24.9 percent of all trips and 18.6 percent of all person miles of travel. Home-based social/recreation trips are 11.2 percent of all trips and 10.7 percent of all person miles of travel.
Home-based school trips are the shortest trips with an average trip length of 4.97 miles. School trips are 9.5 percent of Bay Area trips, and 6.2 percent of Bay Area person miles of travel.
The standard form for mode choice models is the logit choice model. Logit models were introduced by researchers in the late 1960s and entered practice in the Bay Area and elsewhere in the early 1970s. Prior to logit models, the most common form of mode choice model was the "diversion curve" model used to split trips between auto and transit modes.
Various options in logit models are binomial logit (two alternatives); multinomial logit (multiple alternatives, typically 3+); sequential-nested logit (mechanically feeding the logsum from a lower level logit choice model to an upper level choice model); and the simultaneous-nested logit model ("full information" from the lower nest affecting the scaling, or nesting parameter to the upper nest).
Model development in the 1970s was limited to binomial, multinomial and sequential-nested logit choice models. Simultaneous-nested logit procedures were developed in the late 1970s and made available in commercial software (e.g., ALOGIT, LIMDEP) in the late 1980s and early 1990s.
Of the seven mode choice models included in the BAYCAST model set, six are simultaneous-nested logit choice model (hereafter, "nested logit choice") and one, the home-based grade school mode choice model, is multinomial logit. The overall structure of these seven mode choice models is shown in Figure 3. All of the detailed technical memorandum discussing mode choice model development are in the Technical Memorandum Compilation Volume VI.
One key indicator in reviewing mode choice models is the "value of time" (Table 4). This value of time concept is useful in understanding tradeoffs between travel time (typically in-vehicle travel time) and trip cost. The rule of thumb for work trips is that the value of time is 25 to 50 percent of the average wage rate for the area. Given an average wage rate of $20.82 per hour for the Bay Area, the expected work trip value of time ranges from $5.20 to $10.41 per hour. The final nested work trip mode choice model yields an average value of time of $9.65 per hour, or 46.4 percent of the average Bay Area wage rate.
The rules of thumb for non-work trip values of time are not as well agreed upon as the value of time for work trips. The general feeling is that non-work value of time should be some fraction of work trip value of time. The values of time for BAYCAST non-work mode choice models range from a high of $6.58 per hour for home-based shop trips (68 percent of the work trip value of time) to a low of $0.23 per hour for home-based high school trips (2.4 percent of the work trip value of time). All of these values of time for non-work trips are fairly reasonable and well within acceptable practice for analyzing value of time.
An important characteristic of most BAYCAST mode choice models (with the exception of the three home-based school mode choice models) is that both AM peak period and off-peak period travel times and trip costs are used in the model application. In previous versions of MTC model systems, home-based work trips were only sensitive to peak period travel times and costs; and non-work trips were only sensitive to off-peak times and costs. This improvement in the model system means that mode choice for these trip purposes is sensitive to changes in both the peak and off-peak period, as opposed to just one or the other.
All mode choice models incorporate non-motorized alternatives: bicycle and walk-only. Travel times for bicycle and walk are based on a "non-motorized network" based on the standard regional highway network, excluding freeway facilities where bicycles and pedestrians are not allowed (and including freeway facilities where bicycles and pedestrians are allowed!) Uniform speeds of 3 miles per hour for pedestrians and 12 miles per hour for bicyclists are used to convert non-motorized distance into travel time.
The home-based work mode choice model is the only two-level nested choice model in the BAYCAST model set. Trips are first split into motorized modes, bicycle and walk-only modes. Motorized trips are then split into drive alone, shared ride 2, shared ride 3+ and transit. Lastly, transit trips are split into transit with walk access versus transit with auto access. Market segmentation into the HBW mode choice model is zone-to-zone trips by AO level (3) by household income quartile level (4). Where the auto ownership is zero, work trips are prohibited from taking the drive alone or transit-auto access modes. Coefficients for the final nested HBW mode choice model (Model #97) are shown in Table 5.1. Definitions for these variables are included in Appendix Table A.1.
As is typical with mode choice models, the BAYCAST home-based work mode choice model include variables about tripmaker demographics (auto ownership, income, household size, workers in the household); trip characteristics (travel time and trip cost); and neighborhood characteristics (employment density; "dummy" variables to represent high bicycle commute shares in Stanford, Palo Alto and Berkeley; and "dummy" variables for regional "core" zones in the San Francisco financial district).
Modal constants are estimated for six of the seven modal utilities in the HBW mode choice model. These modal constants are then calibrated (adjusted) on a district-to-district interchange basis so that model predicted trips reasonable match observed trips by mode. These changes, or "deltas" to the modal constants are included in the separate technical summary on calibration and aggregate validation.
The coefficients for the final home-based shop/other mode choice model (model #73W-2) are shown in Table 5.2. Both the home-based shop and home-based social/recreation mode choice models include six alternatives (drive alone, shared ride 2, shared ride 3+, transit, bicycle, walk) and one nest (either motorized or group modes). The nest for the HBSH model splits motorized trips from bicycle and walk trips in the upper nest; and drive alone, shared ride 2, shared ride 3+ and transit in the lower nest. As with the HBW model, trips where the auto ownership level is zero are prohibited from using drive alone or auto access to transit. The home-based shop mode choice model is the only model where a total travel time variable is used. All other models were successful in terms of separating in-vehicle travel time (IVTT) from out-of-vehicle travel time (transit wait times, walk times).
All non-work trip mode choice models use a natural logarithm transformation of trip cost. This was done since the straight, or linear versions of trip cost yielded either unacceptable coefficients for cost or for the calculated value of time. Value of time is calculated using the average trip cost by trip purpose (see Table 4).
Coefficients for the final home-based social/recreation mode choice model (nested model #35) are summarized in Table 5.3. The nest for the HBSR model is a "group nest." The upper nest splits drive alone, group modes, bicycle and walk trips. The lower nest splits shared ride 2, shared ride 3+ and transit trips. The ratio of the out-of-vehicle to in-vehicle travel time coefficients is 2.48 (-0.06806 / -0.02745) which is consistent with a priori expectations. The value of time for home-based social/recreation trips, at $0.78 per hour, is on the low side but is fairly reasonable relative to other trip purposes.
The coefficients for the final nested non-home-based mode choice model, model #14W-2 are shown in Table 5.4. This model includes five alternatives (driver, passenger, transit, bicycle walk) and one nest (motorized trips). The upper nest for the NHB mode choice model splits trips into motorized, bicycle and walk modes. The lower nest splits motorized trips into vehicle driver, vehicle passenger and transit modes. The ratio of the wait time to in-vehicle time coefficients is a very respectable 2.42 (-0.07836 / -0.03232). The ratio of the walk time to in-vehicle time coefficients is 2.35 (-0.07583 / -0.03232). Value of time for non-home-based trips is a reasonable $1.08 per hour. Given that traditional non-home-based trips are not linked with the home characteristics of the trip maker, typical demographic variables such as household income and household size are excluded from this model.
Coefficients for the final multinomial logit choice model for home-based grade school trips (model #21W) are included in Table 5.5. This multinomial logit model has four alternatives: vehicle passenger, transit, bicycle and walk. Grade school students are too young to drive to school, so the vehicle driver alternative is excluded in this model. The ratio of out-of-vehicle to in-vehicle travel time coefficients is on the low side, at 1.09 (-0.06384 / -0.05855). The value of time for home-based grade school trips is also (reasonably) low at $0.36 per hour.
The coefficients for the final nested home-based high school mode choice model (model #18W-3) are included in Table 5.6. There are five alternatives in this model and the home-based college model: vehicle driver, vehicle passenger, transit, bicycle and walk. The upper nest in the home-based high school model splits trips into vehicle driver, "group modes," bicycle and walk. The lower nest splits group modes into vehicle passenger and transit passenger modes. The ratio of out-of-vehicle to in-vehicle time coefficients is also on the low side, at 1.07 (-0.03463 / -0.03228). The value of time is the lowest of all mode choice models, at $0.23 per hour.
The final mode choice model, the home-based college mode choice model (model #28W-2) is documented in Table 5.7. The upper level nest in this model splits motorized modes, bicycle and walk trips. The lower level splits motorized trips into vehicle driver, vehicle passenger and transit passenger modes. To represent the high bike-to-college share to Stanford and Berkeley, "dummy" variables are used to represent residential areas in Stanford, Berkeley and Palo Alto. A separate bicycle time coefficient is estimated in the home-based college model; in comparison, all other models include bicycle travel time as "in-vehicle" travel time. The out-of-vehicle to in-vehicle coefficient ratio is on the low side, at 1.44 (-0.03923 / -0.02731). Value of time is higher for college trips than for grade school or high school trips, at $0.67 per hour.
The mode choice model applications are designed for preparing transit and auto person trip tables for trip assignment. Up to three transit trip tables are output per trip purpose (AM peak auto access, AM peak walk access, midday walk access) for directly assigning transit trips to the appropriate transit path. Auto person trips need to be peak-hour factored using the home-to-work departure time model or peaking factors derived from household travel surveys. Auto person trips also have to be divided by appropriate vehicle occupancy levels to convert auto person trips into vehicle driver trips.
Certain travel modes, namely, vehicle passenger trips, bicycle and walk trips, will not normally be assigned to networks. They will be used in conjunction with other evaluation programs to account for person miles of travel by these modes, but there will not be an ongoing need for assigning these particular trips.
Departure time choice, or time-of-day choice models, are very new to metropolitan transportation practice. Some work on time-of-day choice models was completed in Phoenix, Arizona, though this effort assumed a fixed share of home-to-work trips occurring in a three-hour AM peak period. There is also a fairly rich research literature on time-of-day choice models, though this research literature is aimed at understanding travel behavior as opposed to creating a practical model for a practical travel forecasting system.
The departure time choice model included in the BAYCAST model system is a simple, binomial logit choice model with two alternatives:
The coefficients for the final departure time choice model, model #19W, are in Table 6.
The utility for the off-peak alternative is defined as 0.0. Therefore, the exponentiated utility of the off-peak alternative (exp(0)) is 1.0. In application, the probability of a home-to-work auto person trip starting in the peak period is calculated as:
Probability(Peak Start) = exp(Utility(Peak)) / [ 1 + exp(Utility(Peak)) ]
The departure time choice model includes data from the peak and off-peak highway travel time, distance and toll matrices, and data from the zonal demographic file related to the jobs in the retail industry at place of work.
Detailed writeup on this departure time choice model is included in a 12/5/96 memo by C. Purvis in the Technical Memorandum Compilation Volume V.
1. Planning Section. San Francisco Bay Area 1990 Travel Model Development Project: Compilation of Technical Memorandum Volume I. Metropolitan Transportation Commission, Oakland, California, March 1995.
2. Planning Section. San Francisco Bay Area 1990 Travel Model Development Project: Compilation of Technical Memorandum Volume II. Metropolitan Transportation Commission, Oakland, California, June 1995.
3. Planning Section. San Francisco Bay Area 1990 Travel Model Development Project: Compilation of Technical Memorandum Volume III. Metropolitan Transportation Commission, Oakland, California, March 1996.
4. Planning Section. San Francisco Bay Area 1990 Travel Model Development Project: Compilation of Technical Memorandum Volume IV. Metropolitan Transportation Commission, Oakland, California, June 1996.
5. Planning Section. San Francisco Bay Area 1990 Travel Model Development Project: Compilation of Technical Memorandum Volume V. Metropolitan Transportation Commission, Oakland, California, December 1996.
6. Planning Section. San Francisco Bay Area 1990 Travel Model Development Project: Compilation of Technical Memorandum Volume VI. Metropolitan Transportation Commission, Oakland, California, April 1997.
7. Purvis, Charles L. San Francisco Bay Area 1990 Regional Travel Characteristics: Working Paper #4: 1990 MTC Travel Survey Metropolitan Transportation Commission, Oakland, California, December 1994.
These travel demand models are the product of many years of effort by staff of the Metropolitan Transportation Commission Planning Section. MTC planners were assisted by computer programming staff from MTC's Technical Services Section, and by the consulting firm of Cambridge Systematics, Inc.
MTC management in support of this model development project include:
The transportation analysis unit of the MTC Planning Section were responsible for this model development effort. Staff include:
Lisa Klein, junior transportation planner, assisted in the development of the regional transit network.
Computer programming support was provided by Pat Hackett, senior analyst in the Technical Services Section.
MTC staff are also indebted to the training and assistance provided by Mr. Earl Ruiter and Dr. Yoram Shiftan of Cambridge Systematics, Inc. Their training of MTC staff in the art and science of discrete choice model development was critical to the overall success of this major project.
The Model Coordination Working Group of the Bay Area Partnership provides peer review support, advice and critique for travel model development activities in the Bay Area. MTC staff would like to thank the transportation professionals who work on this Working Group for their contributions to this effort.
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