Demand Travel and Traffic Forecasting
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Background
To date, we learned to solve the following two types of traffic problems
Given traffic demand, analyze the transportation system performance for a given system configuration Given traffic demand, design the transportation system to achieve a certain level of service
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How about these problems?
Walmart is building a supercenter in Davis, how many parking spots does it need to provide for it shopping customers? There have been built new homes in West Village in Davis, how many lane miles is needed to accommodate traffic in this new neighborhood? What is traffic impact of West Village on Russell blvd. and highway 113?
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Example: transportation demand analysis for Davis
Baseline:
0 houses
Design:
Residential Development: 1500 Houses
Baseline:
0 Emp
Design:
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Baseline:
1500 Emp 25,000 Students
Design:
1500 Emp 30,000 Students
Example: transportation demand analysis for Davis in 2010
(3500 students/1166 units) (2750 faculty, staff/700 units) 5000 Daily Person Trips (Productions) (10,000 sq ft office/service) 3200 Daily Person Trips (Attractions)
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Example: transportation demand analysis for Davis in 2010
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Travel demand and traffic forecasting
Travel volumes will change over time due to: economy individual travel preferences travelers' recreational/social activities modification of a roadway network road construction Analysts must develop and use methodological approaches for forecasting changes in traffic volumes.
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Traffic Demand
How do we know present or past traffic demand?
By counting traffic volume (manually or automatically e.g. inductive loop detectors) at specific locations By conducting surveys (e.g., household survey asking detailed travel questions)
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Background
In the short run, traffic demand may change in response to changes in: operating conditions (e.g., bus frequency, natural or man made disasters) transportation system (e.g., maintenance and construction activities, new bus service line) In the long run, traffic demand may change in response to changes in: socioecomonic conditions (e.g. population growth)
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land use patterns (e.g., new residential development, new shopping malls) transportation system (e.g., new light rail)
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What is travel demand analysis ?
Socioeconomic conditions
Land use pattern
Transportation system configuration Travel demand and forecasting
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Transportation system performance
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Popular Traffic Detectors
Traveler socioeconomics and activity patterns
The "four-step" travel demand modeling process
Trip generation Trip distribution Mode choice Route choice System evaluation (LOS etc)
The number of trips made Origins and destinations The mode used The route followed
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Trip generation: sample trips
Trips 1, 2 are made in AM peak. Trips 5 is made in PM peak. Trips 3,4,6,7 are made in non commuting peak periods.
DROP CHILD
LUNCH Trip 1 Trip 2 Trip 3 Trip 4
HOME
Trip 5
WORK
Trip 7
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Trip 6
Primary Tour
SHOP Secondary Tour
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Trip Generation
Aggregation of decision making units Predicting trip generation behavior is simplified by considering a household travelers (group) instead of individual travelers Segmentation of trips by type: Working Shopping Social/recreational (vacation, visiting friends, sports, ...)
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Trip Generation Model
Linear form in which the number of vehicle-based trips is a function of various socioeconomic and distributional (residential and commercial) characteristics.
Ti = b0 + b1 z1i + b2 z 2i + L + bk z ki
Ti : number of vehicle-based trips of a given type in some specific time period made by household i bk : coefficient estimated from traveler survey data and corresponding to variable k (estimated by the method of least squares) zki : variable k (income, employment in neighborhood, number of household members, etc.) of house hold i
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Example
Number of vehicle-based shopping trips daily per household = 0.10 + (0.005 HouseholdSize) + (0.00002 AnnualHouseHoldIncome) - (0.20 * NoOfShopsInNeighborhood) There are 2 retail shops in the neighborhood.
HouseHold Household Type Size 1 2
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Annual Income $20K $30K $45K
Vehicle-Based Shopping Trips
1 2 3
3
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Probabilistic Trip Generation Model
Linear regression is easier to use but will produce fractions of trips for a given period of time (not realistic!). Probability of making number of trips may be more appropriate:
e P (Ti ) = Ti !
- i
Ti i
i = e
BZ i
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Ti : number of vehicle-based trips of a given type made in some specific time period made by household i, a whole integer P(Ti) : probability of household i making exactly Ti trips i : Poisson parameter, mean number of trips made by household i (can also be a fractional number). B : vector of estimable coefficients, and Zi : vector of variables determining average trip generation of house hold i.
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Example
Poisson regression is estimated for the example presented earlier. The estimated coefficients are:
BZi = -0.30 + (0.08 * HouseholdSize) + (0.000002 * AnnualHouseHoldIncome) - (0.10 * NoOfShopsInNeighborhood)
There are 2 retail shops in the neighborhood. What is the probability of making no trip in a day?
HouseHold Household Type Size 1
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Annual Income $20K $30K $45K
Number of trips
Probability of making no trip
1 2 3
2 3
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Mode and Destination Choice
Once number of trips generated per unit time is known, traveler mode and destination should be determined.
Trip type: Work (variety of mode, but one destination) Shopping (variety of mode and destination) Social/Recreational (variety of mode and destination)
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Mode and Destination Choice
Utility maximization of mode/destination choice:
Vim = bmk zimk + im = U im + im
k
Vim : total utility provided by mode/destination alternative m to a traveler i bmk : coefficient estimated from traveler survey data for mode/destination alternative m corresponding to mode/destination or traveler characteristic k zimk : traveler or mode/destination characteristic k (income, travel time of mode, commercial floor space at destination, ...) for mode/destination alternative m for traveler i im : unspecifiable portion of the utility mode/destination of alternative m for traveler I, which will be assumed to be random
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Mode and Destination Choice
Probabilistic logit model formulation:
U im U is
Pim =
e
s
e
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Pim : probability that traveler "i" will select alternative "m" s : notation for available alternatives
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Example
A commuting highway has 500 individuals. A mode choice model is calibrated for this group of travelers, resulting in the following utility function:
U m = m - 0.3C - 0.02T
where C is out-of-pocket cost in dollars, and T is travel time, in min. Values of are: Bus transit: 0.00; Rail transit: 0.40; Auto: 2.00 It is estimated that the cost of an auto trip, which takes 15 min, is $2.50; rail transit trips, which take 20 min, cost $1.50; bus transit takes 30 min and costs $1.00. Predict the number of trips by each mode in this highway.
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Solution
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Highway Route Choice
Travelers' route choice decisions are primarily a function of route travel times which are determined by traffic flow.
Travel Time
Linear
Free Flow Traffic Flow (veh/hr)
Free Flow
Travel Time
Non-Linear Traffic Flow (veh/hr) Capacity
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Highway Route Choice Models
To predict the number of travelers using various routes and hence the traffic on road segments of a transportation network after modal destination choices are known. Two behavioral assumptions, two route choice models: selfish routing (everyone tries to take the quickest route) User Equilibrium (UE) Altruistic routing (people choose routes in such a way that they
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cause the least delay to system) System Optimization (SO)
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User Equilibrium (UE) Model
Two Basic Assumptions:
1. Travelers select routes with shortest travel times 2. Travelers know travel times on all available routes
between their origin and destination Strong assumption: Travelers may not use all available routes, and may base travel times on perception
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Some studies say perception bias is small
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UE Problem as an Optimization Problem
The travel time between a specified origin and destination on all used routes is the same and is less than or equal to the travel time that would be experienced by a traveler on any unused route.
min S ( x ) =
n
xn
t (w)dw
n 0
q = xn
n : A specific route between a given O-D pair w : Flow variable
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tn(w) : Performance function for route n as a function of flow xn 0 for all routes are the route flows is the total flow for an O-D pair
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UE Problem as an Optimization Problem
Travel Time
1
Free Flow
2
Traffic Flow (veh/hr)
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t1 ( q ) > t 2 (0)
t 2 ( q ) > t1 (0)
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Example on User Equilibrium Model
Two routes connect a city and a suburb. During the peak-hour morning commute, a total of 4,500 vehicles travel from the suburb to the city. Route 1 has a 60-mph speed limit and is 6 miles long. Route 2 is half as long with a 45-mph speed limit. The performance functions for route 1 & 2 are as follows: Route 1 PF increases at the rate of 4 minutes for every additional 1,000 vehicles per hour. Route 2 PF increases as the square of volume of vehicles in thousands per hour. Compute UE travel times on the two routes.
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Route 1 Suburb
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City
Route 2
Example on User Equilibrium Model
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Example on User Equilibrium Model
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Example on User Equilibrium Model
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System Optimization (SO) Model
Altruistic routing:
Preferred routes are those, which minimize total system travel time.
Finding the set of flows that minimizes the following function:
min S ( x ) = xn t n ( xn )
n
q = xn
n : route between given O-D pair
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tn(xn) : travel time for a specific route xn : flow on a specific route flow for the given O-D pair
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Example on System Optimization Model
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Example on System Optimization Model
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Compare UE and SO Solutions
User equilibrium t1 = 12.4 minutes t2 = 12.4 minutes x1 = 1,600 vehicles x2 = 2,900 vehicles tixi = 55,800 veh-min System optimization t1 = 14.13 minutes t2 = 10.09 minutes x1 = 2,033 vehicles x2 = 2,467 vehicles tixi = 53,618 veh-min
Route 1
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City
Route 2
Suburb
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Traffic Forecasting in Practice
Step 1:
The geographic region being studied is segmented into nearly homogeneous areas so called "Traffic Analysis Zones" (TAZ) based on: Land use Socioeconomic Activities Number of TAZs: Smaller TAZ provides more detailed forecast but more computational cost Larger TAZ provides less detailed forecast but less computational cost
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Traffic Forecasting in Practice
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Traffic Forecasting in Practice
Step 2:
Highway network should be defined. Highway segments are linked by using nodes which are placed at the intersections or other points where highway capacity could change. Nodes permit traffic to travel from one highway segment to next. Access links are used to connect the highway network with the centroids of the TAZs.
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Traffic Forecasting in Practice
Step 2: Performance function dependent to traffic flow and capacity:
xn t n = t fn [1 + ( ) ] xcn
tn : travel time on highway segment n tfn : free-flow travel time on highway segment n xn : traffic flow on highway segment n
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xcn : capacity of highway segment n , : model parameters vary with respect to the capacity and speed limit of the highway segment
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Traffic Forecasting in Practice
Step 3: Trip generation models and mode/destination choice models are then used to determine the number of vehicles traveling between all TAZs during a specified time period.
Ti = b0 + b1 z1i + b2 z 2i + L + bk z ki
Resulting vehicle trips are used to create matrix that gives the total number of vehicle trips going between each TAZ combination.
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Traffic Forecasting in Practice
Step 3:
Destination traffic analysis zone Origin traffic analysis zone
O/D
1
2
3
4
1 2 3 4 Tij
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Traffic Forecasting in Practice
Step 4: With the vehicle origin-destination trip matrix, traffic flows on each highway segment are determined (using computer softwares), usually by assuming UE or SO models.
min S ( x ) = xn t n ( xn )
n
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min S ( x ) =
n
xn
t (w)dw
n 0
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