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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 i j Car Transit Other

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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

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Logit Model (cont.) 50% U(transit)-U(auto) 0 -ve+ve % Transit % auto captive % transit captive

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

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Logit Model (Continued) Example: A calibration study has resulted in the following impedance (utility) equation for any mode m: U m = a m – 0.025X(1) – 0.032X(2) – 0.015X(3) – 0.002X(4) a m = 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) =

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Logit Model (Continued) From trip distribution model, for a future year T ij = 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 a m modal constants: auto: -012, transit=-0.56 Find modal split. Solution: First compute U values U (auto) = -0.745 U(bus) = -1.990

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Logit Model Example (Continued) P auto = 0.78 P bus = 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

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Multinomial Logit Model P m = e Um Σ for all m(e Um) Where P m = probability that mode m is chosen U m = 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.

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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 = β m - 0.50C - 0.01T Where C = out of pocket cost (dollars), and T = travel time (minutes). β m 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.

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Multinomial Logit Model Solution: Utility functions: U = β m - 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: P m = e Um /[Sum of e Um ] 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.

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