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Huntington, West Virginia 25712
TRIP DISTRIBUTION
INTRODUCTION
The objective of the trip distribution phase is to ascertain where a trip produced in a TAZ will be attracted. This is depends on the travel time between the trip-producing zone and the trip attracting zone. Trip distribution models are formulated based on the Newton's law of gravity, i.e the trip interchanges between 2-TAZ's is directly proportional to the produced in the origin zone and the trips attracted by destination zone and inversely proportional to the impedance between the zones. The outputs from this phase is the internal trip table, which gives the destination zones for all trips produced from a signal TAZ.
MODEL SPECIFICATION
A central assumption of the trip distribution model is that each traveler making a trip chooses a destination from all of the of the available destinations on the basis of the characteristics of each destination. For each trip purpose, the destination choices will be determined by the relevant variables chosen in the model. The two most significant factors for destination choice are relative attractiveness of a zone, measured by the number of attraction trip ends, and relative impedance between the production zone and attraction zone, measured as a function of time and cost.
TRIP DISTRIBUTION MODELS
Two basic types of trip distribution models are used: the gravity model and growth factor model (Fratar). One distinction between these models is the data requirement. The gravity model require data on the attractiveness of a zone (from the trip generation model), and the growth factor models require both a base estimate of origin and destination trips and a growth factor. The gravity model, the most common trip
distribution in practice today, is used at KYOVA to distribute the trips produced by the trip generation models.
The growth factor (Fratar) model is frequently used for distributing external (through) trips for producing incremental updates of trip tables when full application of the trip distribution model is not warranted.
The gravity model is based on Newton's law of gravity, which describes the gravitational force between two bodies. The gravitational force, in transportation models, is a function of the attractiveness of a zone (measured in the number of trip
attractions) and the impedance (measured as a travel time or friction factor) to the Zone: Its mathematical form is:
Where
Ti,j = number of trips produced in zone I and attracted to zone j
Pi = number of trips produced in zone I
Aj = number of trips attracted in zone j
(t i,j ) = travel time in minutes between zone I and zone j
F(t i,j ) = empirically derived travel time factor, friction factor, that expresses the average area wide effect of spatial separation on trip interchanges between zones that are (t i,j ) apart.
The gravity model, in its traditional form, assumes that trip productions are fixed and iterates to estimate the trip attractions in each zone. This procedure that people choose where to work or shop, based upon where they live.
The friction factors, F(t i,j ), are developed from the travel impedance distribution. Friction factors are calculated from a comparison of the estimated and observed trip length frequency distributions, and research has shown that these distributions (or average trip length ) remain relatively stable over time. Thus, the previously developed friction factor values, shown in Table 4.1, are used in this 1990 model validation.
IMPEDANCE
The gravity model requires a measure of impedance from each origin zone to each destination zone. Impedance generally represents the travel time, based on speed and distance, and cost, expressed in minutes ( as a value of time). The 1990 base year highway modeling network is determined the trip impedances. The highway modeling network describes, among many other things, length and speed of the various facilities contained in the network. Based on the length and speed of each section in the network, a travel time for each section is determined. Then, this network is "skimmed" to find the minimum time path or the interzonal travel time between every pair of origin and destination zones.
Travel time within a zone or intrazonal travel time is estimated using the nearest neighbor method, which uses half of the travel time to the nearest zone as the intrazonal impedance. Time spent outside the vehicle at the beginning or end of the trip is known as terminal time. In the KYOVA area, time penalties imposed on the bridges are shown in Table 4.3 and are applied in the trip distribution phase only. The intrazonal, terminal, and bridge penalty times are added to zone-to-zone intrazonal driving time matrix to produce travel time for each zone-to-zone interchange. This total travel time for each zone-to -zone interchange is known as trip impedance. During the development and validation of the gravity model, additional adjustment s were made to the impedances to obtain a better fit to the 1966 observed data.
INTRAZONAL TRIPS
Intrazonal trips represent trips made totally within a zone. They are assumed to travel on the local streets and are not assigned to roadway network during trip assignment phase. Intrazonal travel times are shown, as described earlier.
The number of intrazonal trips at HIATS are determined by applying the gravity model. However, other methods of intrazonal and intrazonal trip separation exist. One such
method assumes that a fixed percentage of the trips purpose will be intrazonal regardless of zone size.
It is noticed that when the value of friction factor for a given impedance is decreased, then trip length is reduced and intrazonal volumes are increased. This is means that less volume will be assigned to the highway network links. On other hand, if the friction factor is increased, trip length is increased and intrazonal volumes are decreased, thus, increasing the traffic volume on the highway network links.
CALIBRATION AND VALIDATION
Due to the lack of any recent household travel surveys for Huntington-Ironton metropolitan area, no efforts were spent to calibrate the trip distribution model. Instead, the empirically developed friction factors shown in Table 4.1 previously, are used as input into the trip generation model. These friction factor values are the results of the calibration process conducted on the 1974 trip distribution model (reference 9). Reasonableness checks are performed, however, on the results of 1990 trip distribution model to determine the model's performance validity.
One validity check is the average person travel. The model average person work travel trip time is estimated to be 14.11 minutes ( 13.2 minutes in 1972 survey) while CTPP value is calculated to be 17.70 minutes. It is reported that the CTPP trip time values should be considered with a lot of caution and an error margin as high as 5 minutes can be safely assumed in connection with CTPP reported values. Reference listed 1990 mean work travel times for 39 metropolitan areas with one million inhabitants or more. It is reported that the highest travel time of 31.1 minutes occurred in New York and lowest of 19.7 minutes in Rochester. Also reference identified states with the maximum and minimum mean work travel times in 1990. It is reported that the maximum of 27.80 minutes occurred in the state of New York and minimum of 11.90 minutes occurred in the state of North Dakota. The Huntington - Ironton Metropolitan area average work travel time (14.11 minutes) is in between the maximum and minimum reported mean travel time and below the lowest travel time reported of the 39 metropolitan areas of 1 million inhabitants or more.
Another validity check is to compare the trip length frequency distribution plots generated by the model against observed trip length frequency distribution plots. The home based work trip frequency distribution plot is the only available observed data. The source of this observed data is the 2000 CTPP part 3 Table 3-7.
Efforts were made to relate the CTPP trip table with the CTPP trip length table to allow the transfer of the trip interchange information to the trip length table and be able to calculate the trip length frequency distribution. However, the results were not encouraging. The relating and matching process was able to account for only 24% of the total trips. Thus, given this poor Matching rate, the inaccuracy of the CTPP reported travel time data, it was decided to forego this check. This decision was also recommended by WVDOH and ODOT technical staff. When time permits, however, an alternate work trip length frequency distribution validity check can be pursued in cooperation with ODOT and WVDOH. This alternate check will use the CTPP trip table and gravity model skim tree results.
Comparing the daily work trip (person-trip) interchanges from the 1990 CTPP with those of the trip distribution model helps to determine the validity of the model. It is worth mentioning here that the CTPP data were collected based on a 20.1%sample. Thus, the CTPP trip interchanges might not reflect the actual trip interchanges on daily basis. Table 4.4 shows the 1990 daily work trip (origin-destination)interchanges from both CTPP and gravity model.
Overall, the total number of trips reported in CTPP is 295,014? While that estimates from gravity model is 279,235 person work trips per day. It is determined that this is a pretty good indication that the model, overall, is performing adequately. Closer inspection of table 4.4 reveals that only 5.38% difference exists between the CTPP and the model reported values on the trips destined to urban places of the study area. In fact, the trips destined to urban regions of the study area represent the majority (66.6%) of the total work trips of the study area.
OUTPUT OF THE TRIP DISTRIBUTION MODEL
As described earlier in this chapter, the trip distribution model provides information on zone to zone travel (trip interchanges or trip table). A summary of trip interchanges "from" and to major area types for each of the internal trip purposes is provided in total trip are external. In 1971 the split was 85.5%(internal) and 13.5% (external). The vehicle travel time for work trips (11.99 minutes) is the highest among all of the internal vehicle trips while the external -external truck trips are the highest (35.42 minutes) among all external vehicle trips. The difference between the work person travel time (16.11) and the vehicle travel time (11.99) is due to the terminal time associated with the two ends of a trip. Overall, the difference of 3.15 minutes seems to be reasonable for work terminal time in our transportation study area.
Using the productions and attractions of each TAZ, the highway skim file and the friction factors for five trip purposes, the gravity model function is used to create the HBW, HBNW, NHBW and External-Internal trip tables.
The reasonableness of a trip distribution model can be determined by reviewing the average trip lengths by trip purpose that result from the model .
These trip length are reasonable in comparison with areas of similar size and make-up as the Huntington metropolitan area.
After the person-trips were distributed among all of the different zones, it was then necessary to convert the person-trips into vehicle trips. This was done by applying auto-occupancy factors to the person trip totals to yield vehicles trips. Separate occupancy factors were used for the different trip purposes and reflect local operating conditions.
