Choice of mode
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Choice of Mode. David Levinson. The Onion. A study by the American Public Transportation Association reveals that 98 percent of Americans support the use of mass transit by others.” They reported on a campaign supposedly kicked off by APTA "Take The Bus... I'll Be Glad You Did.".

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Choice of mode

Choice of Mode

David Levinson


The onion

The Onion

  • A study by the American Public Transportation Association reveals that 98 percent of Americans support the use of mass transit by others.” They reported on a campaign supposedly kicked off by APTA "Take The Bus... I'll Be Glad You Did."


Moral suasion

Moral Suasion


Richardson arms race model

Richardson Arms Race Model

  • Lewis Frye Richardson, a Quaker physicist, suggested that an arms race can be understood as an interaction between two states with three motives. 

  • Grievances between states cause them to acquire arms to use against one another. 

  • States fear each other and so acquire arms to defend themselves against the others’ weapons. 

  • Because weapons are costly, their expense creates fatigue that decreases future purchases. 


Example

Example

  • ArmsRace.xls


How does this relate to transport land use

How Does This Relate To Transport/Land Use

  • Arms Races

  • Bicycle vs. Car

  • Bus vs. Car

  • SUV vs. Car

  • Communities fighting for development,

  • Communities building infrastructure (competitive advantage/disadvantage)


Caveat planner

Caveat Planner

  • Richardson’s (or any abstract) model is obviously a simplification. We can relax assumptions and make it more realistic (e.g. (dis)economies of scale associated with arms … does fatigue per unit of armament increase or decrease with total level of armaments?)


Prisoner s dilemma

Prisoner’s Dilemma


Repeated prisoner s dilemma

Repeated Prisoner’s Dilemma

  • If 2 players, and game repeated indefinitely, the incentive is to cooperate.

  • However if the end is known, the incentive is to defect on the previous turn.

  • Also, if there are multiple players, cooperation becomes much more difficult to achieve


Modal arms races payoffs are time try to minimize

Modal Arms Races (payoffs are time, try to minimize)


Travel time as mode share changes

Travel Time as Mode Share Changes


Model 1

Model 1

  • Here we assumed the following:

  • MA = Auto Mode Share

  • MB = Bus Mode Share = 1 – Auto Mode Share

  • TA= Auto Travel Time

  • TB = Bus Travel Time


Or note total time drops as car use rises

OR (Note Total Time Drops as Car Use Rises)


Model 2

Model 2

  • D = Schedule Delay


Implications

Implications

  • Driving is always faster than riding the bus.

  • Total travel time would be minimized if everyone rode the bus. Buses could operated frequently and more directly.

  • However, in the absence of cooperation, the rational outcome is for everyone to drive.

  • Cooperation is difficult to achieve in multi-player games.


Cooperation

Cooperation

  • How can cooperation be achieved?


Beijing cars vs bikes

Beijing: Cars vs. Bikes


Individual rationality

Individual Rationality

  • Assumption: Individuals will do what is in their own long term interest.

  • This can’t always be measured.

  • Max U = f( time, money, socioeconomics, demographics, etc.)


Mode choice

Mode Choice


Objective of mode choice

Objective of Mode Choice

  • AGGREGATE: Estimate the number of trips from each zone to each zone by purpose that take mode m.

  • DISAGGREGATE: Estimate the probability that a particular trip (purpose, time, zone-zone) by a specific individual will take mode m.

  • Typically forecasters use a “discrete choice” model, that predicts distinct (or discrete or qualitative) choices (bus vs. car) rather than continuous ones (3.4 trips vs. 3.6).

  • Logit is the most popular version of mode choice model.


Daniel mcfadden

Daniel McFadden

  • In addition to being my Econometrics Professor in grad school, University of Minnesota graduate Daniel McFadden won the Nobel Prize in Economics for developing the Logit model for transportation mode choice

  • In particular, his application of Logit to forecasting for the BART rail system in the San Francisco Bay Area) was noted.

  • Urban Travel Demand: A Behavioral Analysis by Tom Domencich and Daniel L. McFadden North-Holland Publishing Co., 1975. Reprinted 1996.

  • http://emlab.berkeley.edu/users/mcfadden/travel.html


The logit model

Pm - probability of taking mode m

Umij- Utility of mode m between OD pair ij for an individual (or a representative traveler)

Umij = f(Cij,…)

The Logit Model


What affects choice of mode

What Affects Choice of Mode?

  • Travel Time of trip

  • Travel time to access mode

  • Wait Time f(headways of transit vehicles)

  • Transfer Time

  • Fare

  • Parking Costs

  • Tolls

  • Alternative Specific Constant

  • Other Qualitative Data (Sidewalks, Bus Shelters)


Relationship of logit and gravity

Relationship of Logit and Gravity

  • The functional relationship between the modern gravity model (negative exponential form) and the logit mode choice model are very similar, enabling simultaneous choice models to be easily developed.

  • The key difference is that the gravity model is typically much more aggregate.


Typical model structure

Alternative Structures include Nests

Advantages: Nests Allow Model to Capture Relationships between modes, skirt IIA property.

Disadvantages: Increased computation, Marginal Improvement in Estimation

(WCT) walk connected transit

(ADT) auto connect transit (driver alone/park and ride)

(APT) auto connect transit (auto passenger/kiss and ride)

(AU1) auto driver (no passenger)

(AU2) auto 2 occupants

(AU3+) auto 3+ occupants

(WK/BK) walk/bike

Typical Model Structure


Independence of irrelevant alternatives

Independence of Irrelevant Alternatives

  • Property of Logit (but not all Discrete Choice models)

  • If you add a mode, it will draw from present modes in proportion to their existing shares.

  • Example: Suppose a mode were removed. Where would those travelers go. IIA says they will go to other modes in same proportion that other travelers are currently using them. However, if we eliminated Kiss and Ride, a disproportionate number may use Park and Ride or carpool. Nesting allows us to reduce this problem. However, there is an issue of the proper Nest.

  • Other alternatives include more complex models (e.g. Mixed Logit) which are more difficult to estimate.


Conclusions

Conclusions

  • Mode share must be understood as a system involving competition.

  • This competition, under certain circumstances (without subsidies for positive feedback industries, and without penalties for negative externalities), may result in socially sub-optimal results.

  • The degree to which the results are sub-optimal, and subsidies are justified, depends on (1) belief that government can actually figure out where to direct subsidy (the pork problem), (2) understanding the dynamics of the system under question.

  • Not all subsidies are warranted, though many are justfied wrongly based on this logic.


Example1

Example

  • You are given this mode choice model

  • U=-0.412 (c/w) -0.0201* t - 0.0531*t0 -0.89*D1 - 1.78 D3 - 2.15 D4.

  • Where:

    • c/w = cost of mode (cents) / wage rate (in cents per minute)

    • t = travel time in-vehicle (min)

    • t0 = travel time out-of-vehicle (min)

    • D = mode specific dummies:

      • D1 = driving,

      • D2 = bus with walk access, [base mode]

      • D3 = bus with auto access,

      • D4 = carpool


Solve for probabilities of modes

Solve for Probabilities of Modes

  • ModeChoice.xls


Problem a

Problem a

  • You are given the following mode choice model.

  • Uij = -1 Cijm + 5 DT

  • Where:

  • Cijm = travel time between i and j by mode m

  • DT = dummy variable (alternative specific constant) for transit

  • A. Using a logit model, determine the probability of a traveler driving.

  • B. Using the results from the previous problem (#2), how many car trips will there be?


Auto times transit times

Auto Times Transit Times


Solution steps

Solution Steps

  • Compute Utility for Each Mode for Each Cell

  • Compute Exponentiated Utilities for Each Cell

  • Sum Exponentiated Utilities

  • Compute Probability for Each Mode for Each Cell

  • Multiply Probability in Each Cell by Number of Trips in Each Cell


Auto utility transit utility

Auto Utility Transit Utility


Auto e utility transit e utility

Auto e^Utility Transit e^Utility


Sum e utility

Sum e^Utility


P auto p transit

P(Auto) P(Transit)


Trips total trips auto

Trips Total Trips Auto


Vehicle ownership

Vehicle Ownership

  • VEH0= 1 if Number of household vehicles = 0

    0 otherwise

  • VEH1= 1 if Number of household vehicles = 1

    0 otherwise

  • VEH2= 1 if Number of household vehicles >= 2

    0 otherwise


Discussion auto ownership

Discussion (Auto Ownership)

  • The ownership, or lack, of an automobile is a key determinant in mode choice. This variable of auto ownership is also a factor of several factors that may change over time as a result of policies and economics. For these reasons, a simple logit model can be developed to model auto ownership. The model is expressed as follows


Specification and estimation auto ownership

Specification and Estimation (Auto Ownership)

  • HHDENS : Traffic Zone Household Density

  • RAIL50 : The proportion of residences in a zone within 0.5 miles of a rail station

  • SINFAM : The proportion of single family residences in a zone

  • HHSIZE : Average Household Size in the zone


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