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Innovations in Travel Demand Modeling, Volume 2: Papers (2008)

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Suggested Citation:"T57054 txt_036.pdf." National Academies of Sciences, Engineering, and Medicine. 2008. Innovations in Travel Demand Modeling, Volume 2: Papers. Washington, DC: The National Academies Press. doi: 10.17226/13678.
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The only nontrivial transformation that requires explanation is the aggregation of non- transit- exponentiated utility, for which the following notation is introduced: i = 1, 2, . . . , I = choice alternatives; n = 1, 2, . . . , N = individual records to be aggre- gated within the group; Vin = known individual utilities; Pn(i) = known individual probabilities; Wn = person trips (1, for individual tours; party size, for joint tours); Vi = unknown aggregate utilities; and W = total person trips for the group. The purpose of utility aggregation is to find a utility expression that will exactly replicate (a) aggregate mode shares and (b) total composite utility across all individ- ual records and consequently replicate a UB calculation. The aggregate mode shares for the group of records can be readily calculated as follows: (1) The first condition (replication of aggregate shares) leads to the following expression: (2) where C denotes a utility scale constant that has to be determined. The second condition (replication of the composite utility) leads to the following expression (for simplicity it is assumed that the choice model is a simple multinomial logit model and the composite utility is calculated as a simple one- level log sum): (3) Equation 4 results from an equivalent transformation of Equation 3: (4) By substituting the expression for aggregate utilities from Equation 2 to Equation 4, the necessary formula for the utility scale C is obtained: (5) By combining Equations 2 and 5, it is possible to obtain the expression for aggregate exponentiated utilities that would exactly reproduce the target market shares and user benefits: (6) Equation 6 has a simple intuitive interpretation. The aggregate exponentiated utility of each mode is propor- tional to a product of two factors. The first one is equal to the aggregate mode share and reflects the improve- ment of each mode in comparison with the other (com- peting) modes. The second one is equal to the weighted geometric average of the individual (exponentiated) log sums; this component is sensitive to the overall improve- ment of all modes. This aggregation calculation should be implemented separately for the base scenario and the build scenario and for each group of aggregated records. In the same way that this aggregation can be applied for mode utili- ties, it can be applied for the composite nontransit utility as well as it can be generalized for any nested structure by using a full mode choice log sum for each record LSn. The aggregate exponentiated nontransit utility can be calculated as follows: (7) where SOV = single- occupancy vehicle, HOV = high- occupancy vechicle, NM = nonmotorized vehicle, and SB = school bus. The described methodology of UB calculation has been applied for the analysis of the recent LRT project in Columbus, Ohio, and approved by FTA. The results are provided in a companion paper. V P i Ci = ( )⎡⎣ ⎤⎦ +ln P i W P i W n n n N ( ) = × ( ) = ∑ 1 exp V P SOV P HOV P NM P SBNT ( ) = ( ) + ( ) + ( ) + ( ) ⎡ ⎣ ⎢⎢ ⎤ ⎦ ⎥⎥ exp× ( )⎡⎣ ⎤⎦ = ∏ LSn W W n N n 1 exp exp exp V P i C P i V i in i I ( ) = ( ) × ( ) = ( ) × ( )⎡ ⎣ ⎢⎢ ⎤ = ∑ 1 ⎦ ⎥⎥ = ∏ W W n N n 1 exp exp exp exp V C P i C V i i I i I in ( ) = ( ) × ( ) = ( ) = = = ∑ ∑ 1 1 ( )⎡ ⎣ ⎢⎢ ⎤ ⎦ ⎥⎥ == ∑∏ i I W W n N n 11 exp exp ln expV W W Vi i I n n N in i I( ) = × ( )⎡ ⎣ ⎢ = = = ∑ ∑ ∑ 1 1 1⎢ ⎤ ⎦ ⎥⎥ ⎧ ⎨⎪ ⎩⎪ ⎫ ⎬⎪ ⎭⎪ = ( )⎡ ⎣ ⎢⎢ ⎤ ⎦ ⎥⎥ == ∑ exp Vin i I W W n n 11 N∏ W V W Vi i I n n N in× ( )⎡⎣⎢⎢ ⎤ ⎦ ⎥⎥ = × ( ) = = ∑ ∑ln exp ln exp 1 1 i I = ∑⎡⎣⎢⎢ ⎤ ⎦ ⎥⎥1 36 INNOVATIONS IN TRAVEL DEMAND MODELING, VOLUME 2

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TRB Conference Proceedings 42, Innovations in Travel Demand Modeling, Volume 2: Papers includes the papers that were presented at a May 21-23, 2006, conference that examined advances in travel demand modeling, explored the opportunities and the challenges associated with the implementation of advanced travel models, and reviewed the skills and training necessary to apply new modeling techniques. TRB Conference Proceedings 42, Innovations in Travel Demand Modeling, Volume 1: Session Summaries is available online.

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