Highway Engineering

Based on these definitions of utility, the probability that a trip maker will

select one mode option,m, is equal to the probability that this option’s utility

is greater than the utility of all other options. The probability of a commuter

choosing mode m (bus, car, train) can thus be represented by the following multi-

nomial logit choice model:

(2.15)

where

Pm=probability that mode mis chosen

m¢=index over all modes included in chosen set

Details of the derivation of Equation 2.15 are provided in McFadden (1981).

Where only two modes are involved, the above formula simplifies to the fol-

lowing binary logit model:

(2.16)

P

(^1) euu

1

1 21

=

+ ()-

P

e

m e

um

= um

()

 ()¢

32 Highway Engineering

Example 2.5 – Use of multi-nomial logit model for estimation of modal split

Use a logit model to determine the probabilities of a group of 5000 work

commuters choosing between three modes of travel during the morning peak

hour:


 Private car


 Bus


 Light rail.

The utility functions for the three modes are estimated using the following

equations:

UC =2.4 -0.2C-0.03T

UB =0.0 -0.2C-0.03T

ULR=0.4 -0.2C-0.03T

where

C=cost (£)

T=travel time (minutes)

For all workers:

 The cost of driving is £4.00 with a travel time of 20 minutes


 The bus fare is £0.50 with a travel time of 40 minutes


 The rail fare is £0.80 with a travel time of 25 minutes.

Contd