Travel-Demand Models
4.3 Examples of Trip-based Demand Models
where the EMPU are expressed as:
sm/d=E max
k′ (Vk′/dm+τk′/dm) sd=E max
m′
(Vm′/d+sm′/d+τm′/d)
and the models that represent the various steps may have any functional form pro- vided that they can be obtained from the assumptions of random utility models.
182 4 Travel-Demand Models trip purposes: workers in the various economic sectors for home-based work trips, students of different levels for home-based school trips, and the family for home- based other purpose trips. The main limitation of classification table models is that trip frequencies and demand levels are not expressed as functions of socioeconomic variables other than those used to define the classes. In addition, limitations in data availability and the difficulty of forecasting the future number of users for detailed user classes generally keep the number of classes relatively small, even when a more detailed breakdown might be appropriate.
Trip rate regressionmodels are more sophisticated. These models express the trip ratemi[osh]for a user of classiand for purposesas a function, typically linear, of variables corresponding to the user class and the zone of origin:
mi[osh] =
j
βjXij o (4.3.2)
The attributesXj oare usually the mean values of socioeconomic variables such as income, number of cars owned, and so on, but they may also include level-of- service attributes such as zonal accessibility, defined by the inclusive variableYxin (4.3.5) or by some other variable. The name trip rate regression is derived from the statistical model, linear regression, which is used to specify the variablesXj and to estimate the coefficientsβj.
In early applications, model (4.3.2) was specified at the level of traffic zones.
Thus, its explanatory variables represented attributes of an entire zone (e.g., popu- lation, employment, number of shops, etc.) More recently, these models have been applied at a more disaggregate level, typically households and individuals. The ap- plication of model (4.3.2) at a disaggregate level, however, can lead to problems because some combinations of variable values and coefficients may result in nega- tive trip rates. Hence it is better to use logit or other random utility specifications for disaggregate trip rate models.
Random Utility Models Behavioral models are generally applied to represent trips that are not regularly made. In a random utility framework, the trip ratemi[osh]
can be expressed as
mi[osh] =
x
xpi[x/osh](SE,T) (4.3.3)
wherepi[x/osh](SE,T)represents the probability that a user in zoneoundertakes xtrips for purposesin periodh. Alternatively, the trip ratemi[osh]can be obtained as the product of the outputs of two models: a trip production model that covers a longer time period, for example, the whole dayg, and a departure time choice model:
mi[osh] =
x
xpi[x/osg](SE,T)·
yh
yhpi[yh/osx](SE,T)
Purpose Type of user Trip rate H-W Worker in the Industrial sector 1.024
Worker in the Service sector 1.084 Worker in the Private Services sector 1.245 Worker in the Public Services sector 0.931
H-Sc Primary school student 0.84
Lower secondary school student 0.87 Upper secondary school student 0.86 Vocational secondary school student 0.88
H-Sndg Family 0.25
H-Sdg Family 0.11
H-Ps Family 0.16
H-Sr Family 0.27
H-Acc Family 0.11
H-oth Family 0.13
Trip purpose code Trip purpose
H-W Home–work
H-Sc Home–school
H-Sndg Shopping for nondurable goods H-Sdg Shopping for durable goods
H-Ps Personal services
H-Sr Social–recreational
H-Acc Accompanying others H-Oth Other purposes Fig. 4.4 Daily urban trip production rates
whereyh represents the number of trips undertaken in period hout of all trips x made over the whole periodg[yh=0,1, . . . , x].
Specification of the full model requires definition of the alternatives, of the choice set and of the model that predicts choices from this set.
Definition of Choice Alternatives As stated, the choice alternatives in this case consist of different numbers of trips undertaken in periodh.
Definition of Choice Set The choice set depends on the reference period. Ifhis a short period (i.e., the peak hour), so that the probability of undertaking more than one trip can be ignored, the choice set generally consists of two alternatives: one trip and no trip(x=0,1). For the sake of simplicity, the choice set is intentionally bounded (x=0,1,2 or more) for larger periods.
Functional Form The binary and multinomial logit are the random utility models most frequently used to predict the trip frequency choicepi[x/osh]in (4.3.3). If his so short that the probability of making more than one trip during the period is negligible, a binary logit model can be applied to the alternatives of undertaking the trip or not. Otherwise, a multinomial logit model gives the probabilitypi[x/osh]of
184 4 Travel-Demand Models undertakingxtrips, withxequal to 0,1,2, . . . , nor more trips:
pi[x/osh] = exp(Vxi/θo)
j=0,...,nexp(Vji/θo) (4.3.4) Systematic utility functions include variables that represent the need or the pos- sibility of carrying out activities connected with the purpose being modeled. These variables may relate either to the household or the individual. Household-level vari- ables include, for example, total income and household size, whereas individual- level variables include occupational status, gender, family role, age, and so on. Other variables often used in the systematic utility of trip frequency models relate to the origin area, and especially itsaccessibilitywith respect to the possible destinations for the trip purpose. Accessibility can be expressed by the EMPU corresponding to the destination choice model, for example, the logsumYx given by the following expression for a logit distribution model,
Yx=ln
d′
exp[Vd′/θd+δdYd′] (4.3.5) Figure4.5gives an example of a trip frequency model for the morning peak pe- riod in an urban area. A model of this type should be considered a method for quan- titative analysis of the determinants of urban mobility11 rather than an operational tool. Applying it to predict travel demand in an entire urban area would require a considerable amount of information. However, the same is not true of all behavioral models: operational trip frequency models are sometimes used to develop forecasts for large study areas; the intercity trip frequency models described in Sect.4.3.4are examples of this type of model.
Clearly, random utility models (4.3.3), or family or individual regression models (4.3.2) require more information12than the trip rate model (4.3.1). The latter, how- ever, has the shortcoming of not being sensitive to variables other than those that define the user classes.
11Analysis of the model coefficients may suggest factors that influence urban trip-making for pur- poses other than commuting and study. For example, the results shown in Fig.4.5suggest that the frequency of activities (and trips) increases with income level. Greater accessibility of the resi- dence zone with respect to the location of commercial activities increases shopping trip frequency, but is not significant for business and personal service trips. There is a greater tendency for women and unemployed persons to undertake trips; young people tend to have less mobility, in the time period considered, especially for shopping; there is a substitution effect with other members of the family for shopping (positive coefficient for the TOF variable), whereas there is a complementarity effect for other purposes (negative TOF coefficient). Carrying out other activities (coefficient of the TOP variable) reduces the time available to engage in the activity (trip purpose) considered and so on. Note, also, that the accessibility coefficient, in accordance with the behavioral interpretation of the model, should turn out to be within the interval(0,1).
12The sample enumeration aggregation technique, described in Sect. 3.7, should therefore be used for more sophisticated model specifications.