1. Modal split to be estimated on an interzonal basis.
Modal Choice
Modal split to be estimated on an interzonal basis.
For a given trip purpose:
Modal choice = f(trip makers’ & modal characteristics)
Examples:
Trip makers characteristics: car ownership, income
Modal characteristics: travel time (combination of access/egress time, waiting time, line haul time), frequency
Car j i
Transit
Other

2. Logit Model
Disaggregate level of analysis – the trip maker as the unit of analysis
Choice riders vs. Captives
Modelling travellers with a choice
Probability of selecting a mode is a function of the impedance (I) or generalized cost (disutility but called utility U) of modes.
U for a mode = f(travel time, travel cost, etc.)
Example: U(transit) & U(automobile)
From Probability of travellers’ mode choice, we
Infer % of travellers for each mode

3. Logit Model (cont.) % auto captive % Transit 50% % transit captive
U(transit)-U(auto)
-ve
+ve

4. Logit Model (Continued)
Multinomial vs. Bimodal logit model
Example of bimodal case: transit vs auto
Pt = Probability that transit is chosen Pt
Ut = Impedance of transit
Ua = Impedance of auto
e = base of log = 2.718
Pa = Probability that automobile is chosen
Pt + Pa = 1.00
eUt =
eUt + eUa

5. Logit Model (Continued)
Example: A calibration study has resulted in the following impedance (utility) equation for any mode m:
Um = am – 0.025X(1) – 0.032X(2) – 0.015X(3) – 0.002X(4)
am = constant
X(1) = modal access + egress time (min)
X(2) = waiting time (min)
X(3) = line haul time (min)
X(4) = out-of-pocket cost (cents) =

6. Logit Model (Continued)
From trip distribution model, for a future year Tij= 1000 person trips/day
Future year service attributes:
X(1) X(2) X(3) X(4)
Auto
Bus
am modal constants: auto: -012, transit=-0.56
Find modal split.
Solution: First compute U values
U (auto) = U(bus) =

7. Logit Model Example (Continued)
Pauto = 0.78
Pbus = 0.22
1.00
Therefore modal shares from zone i to zone j:
Auto users = 0.78x1000 = 780 trips
Bus users = 0.22x = 220 trips
1000 trips

8. Multinomial Logit Model
Pm =
eUm
Σ for all m’(eUm)
Where Pm = probability that mode m is chosen
Um = utility of mode m (defined earlier)
e = base of logarithms
m’ = index over all modes included in the choice set
Note: if only two modes are involved, the multinomial logit simplifies to the binary logit model.

9. Multinomial Logit Model
Example: A travel market segment consists of 900 individuals. A multinomial logit mode choice model is calibrated for this market segment, resulting in the following utility function:
U = βm C T
Where C = out of pocket cost (dollars), and T = travel time (minutes). βm values are
Bus transit 0.00
Rail transit 0.20
Auto
For a particular origin-destination pair, the cost of an auto trip, which takes 12 minutes is $ Rail transit trips, which take 20 minutes, cost $2.00. Bus transit takes 40 minutes and costs $1.25. Predict modal travel demand.

10. Multinomial Logit Model
Solution:
Utility functions: U = βm C T
U (automobile) = (3.00) (12) = 0.78
U(rail) = U(bus) =
Modal probabilities by using multinomial logit model:
Pm = eUm/[Sum of eUm’]
By using the above, we find
P(auto) = P(rail) = P(bus) =
Expected demand (auto) = 900(0.7501) = for rail = 114 and for bus = 111.
Total = = 900 check.