Transport User Benefits Calculation with the “rule of a Half” for Travel Demand Models with Constraints

The importance of user benefits in transport projects assessments is well-known by transport planners and economists. Generally they have the greatest impact on the result of costbenefit analysis. It is common practice to adopt the consumer surplus measure for calculating transport user benefits. Normally the well-known “Rule of a Half”, as a practical approximation for the integral of the demand curve, is used to determine the change of consumer surplus. In this paper we enter into the question of whether the Rule of a Half is valid in the case of travel demand models with multiple constraints. Such models are often used for travel demand modeling of large-scale areas. The most discussed and well-known model in transport modeling field is the doubly constrained gravity model. Beside this model with inelastic constraints there are also more flexible models with elastic constraints. The theoretical analysis in this paper provides a mathematical proof for the validity of the concept of the Rule of a Half for travel demand models with multiple elastic and inelastic constraints. In this case the Rule of a Half is also a correct approximation of the change of consumer surplus.