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**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

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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.) % auto captive % Transit 50% % transit captive**

U(transit)-U(auto) -ve +ve

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**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

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**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) =

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**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) =

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**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

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**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.

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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 = 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.

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**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.

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