Travel and Transportation © Allen C. Goodman, 2009

Monocentric Models Look at model of the type we’ve used. Second constraint is a time constraint, where time can be used either for working or commuting. Assume that commuting has only time costs. If we optimize with respect to u, we get: Marginal valuation of travel time

If you look back at Ralph model… You get the same thing. It tells you how many people live where. Remembering that in the monocentric model, everyone worked downtown, you could come up with an average length of commute (in miles or in hours). It also said that as incomes rise people will always move further out. Let’s see.

Let’s see Redefine λ 2 /λ 1 as ψ Differentiate with respect to income y and substitute in the boxed term from a few slides ago. This gives : Must be + for stability.

… and First term is income elasticity of housing demand. Second term is income elasticity of valuation of time. If [1] > [2]  people move further out. If [2] > [1]  people move closer in.

This is obviously not a good model for serious prediction It assumes that everyone works downtown. No cross commuting. All commuting goes along radii to the downtown area. No one ever commutes outward. People talk about distance or time, but since time is so hard to measure, they almost always use distance.

Trying to explain 1.Where they start trips. 2.Where they go. 3.When they travel. 4.Mode of travel (including mixed modes). 5.Time components. 6.Money components. 7.McFadden won his Nobel for his work in this area.

Fundamental Model - MNL Be very careful. There are two (2) models out there that can be confused. 1.One set of parameters, many alternatives, such as origins, destinations, time costs, money costs, etc.  one set of coefficients. 2.One set of characteristics, many (k) alternatives  k -1 vectors of coefficients. 3.Mathematically, they’re identical, but they can be confusing.

Consider modeling how people get to work Simple Example Home Work Drive ? ($ cost, time cost, reliability, income, etc.) Bus ? ($ cost, time cost, reliability, income, etc.) Walk ? ($ cost, time cost, reliability, income, etc.) Choice (z 1, z 2, z 3, z 4, etc..)

Logit Model So, we compare the characteristics of the mode taken, with the mode(s) not taken. Probabilities add up to 1. This form was tractable at a time when various forms of probit models were not, and is still much better understood than the probit models.

Properties Depends ONLY on values of characteristics 1 and 2 – not on any others. This is either good or bad, but it is a limitation.

What does it give you? If one of the z variables is travel time another is travel cost, then ratios of the coefficients will give valuations of travel time. Generally, somewhere between 35 to 50 percent of the wage rate, although the percentage seems to rise as income rises. Walking and waiting time are valued much higher than in-vehicle time – a universal finding conventionally summarized as 2 to 2-1/2 times as high.

Walking and waiting time Key features in the disutility of public transit as opposed to cars. –Flexibility of timing. –Carrying capacity. –Multi-trip planning

Using transportation demand Must model the current, rather than some hypothetical environment. What we use depends on what we have. In addition, current land use patterns are not exogenous. Expanding mass transit can even exacerbate highway congestion because the induced development, even if relatively transit-oriented, still generates many automobile trips. For example, the Bay Area Rapid Transit system in San Francisco is credited with causing Walnut Creek, an outlying station, to develop into a major center of office employment – but despite its good transit access, 95 percent of commuting trips to this center are by automobile

BART is a good example Walnut Creek BART doesn’t go to Marin County. BART misses large parts of the city of SF. BART gets you nowhere near San Jose.