Presentation on theme: "Modal split to be estimated on an interzonal basis."— Presentation transcript:
1Modal split to be estimated on an interzonal basis. Modal ChoiceModal 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, incomeModal characteristics: travel time (combination of access/egress time, waiting time, line haul time), frequencyCarjiTransitOther
2Logit ModelDisaggregate level of analysis – the trip maker as the unit of analysisChoice riders vs. CaptivesModelling travellers with a choiceProbability 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, weInfer % of travellers for each mode
3Logit Model (cont.) % auto captive % Transit 50% % transit captive U(transit)-U(auto)-ve+ve
4Logit Model (Continued) Multinomial vs. Bimodal logit modelExample of bimodal case: transit vs autoPt = Probability that transit is chosenPtUt = Impedance of transitUa = Impedance of autoe = base of log = 2.718Pa = Probability that automobile is chosenPt + Pa = 1.00eUt=eUt + eUa
5Logit 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 = constantX(1) = modal access + egress time (min)X(2) = waiting time (min)X(3) = line haul time (min)X(4) = out-of-pocket cost (cents)=
6Logit Model (Continued) From trip distribution model, for a future year Tij= 1000 person trips/dayFuture year service attributes:X(1) X(2) X(3) X(4)AutoBusam modal constants: auto: -012, transit=-0.56Find modal split.Solution: First compute U valuesU (auto) = U(bus) =
7Logit Model Example (Continued) Pauto = 0.78Pbus = 0.221.00Therefore modal shares from zone i to zone j:Auto users = 0.78x1000 = 780 tripsBus users = 0.22x = 220 trips1000 trips
8Multinomial Logit Model Pm =eUmΣ for all m’(eUm)Where Pm = probability that mode m is chosenUm = utility of mode m (defined earlier)e = base of logarithmsm’ = index over all modes included in the choice setNote: if only two modes are involved, the multinomial logit simplifies to the binary logit model.
9Multinomial 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 TWhere C = out of pocket cost (dollars), and T = travel time (minutes). βm values areBus transit 0.00Rail transit 0.20AutoFor 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.
10Multinomial Logit Model Solution:Utility functions: U = βm C TU (automobile) = (3.00) (12) = 0.78U(rail) = U(bus) =Modal probabilities by using multinomial logit model:Pm = eUm/[Sum of eUm’]By using the above, we findP(auto) = P(rail) = P(bus) =Expected demand (auto) = 900(0.7501) = for rail = 114 and for bus = 111.Total = = 900 check.