1. Modal Choice Car j i 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 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 0 U(transit)-U(auto) -ve +ve

4. 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 Logit Model (Continued) eUt = eUt + eUa

5. 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) Logit Model (Continued) =

6. 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 5 0 20 100 Bus 10 15 40 50 am modal constants: auto: -012, transit=-0.56 Find modal split. Solution: First compute U values U (auto) = -0.745 U(bus) = -1.990 Logit Model (Continued)

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 1000 = 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 - 0.50C - 0.01T Where C = out of pocket cost (dollars), and T = travel time (minutes). βm values are Bus transit 0.00 Rail transit 0.20 Auto 2.40 For a particular origin-destination pair, the cost of an auto trip, which takes 12 minutes is $3.00. 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 - 0.50C - 0.01T U (automobile) = 2.40 - 0.50(3.00) - 0.01(12) = 0.78 U(rail) = -1.00 U(bus) = -1.025 Modal probabilities by using multinomial logit model: Pm = eUm/[Sum of eUm’] By using the above, we find P(auto) = 0.7501 P(rail) = 0.1265 P(bus) = 0.1234 Expected demand (auto) = 900(0.7501) = 675 for rail = 114 and for bus = 111. Total = 675+114+111 = 900 check.