The General Multimodal Network Equilibrium Problem with Elastic Balanced Demand

The general multimodal network equilibrium problem with elastic balanced demand is studied. This problem is a combination of trip distribution, modal split and trip assignment problems. The problem is approached from an asymmetric network equilibrium point of view with side constraints. The balances for travel demand are taken as side constraints. These balances do not guarantee that the problem’s solution will satisfy the user equilibrium conditions. It is shown that the obtained solution is equilibrium traffic pattern in terms of the generalized travel costs which is constructed with the use of dual variables for demand balance constraints. The economical interpretation of dual variables from the city infrastructure extension point of view is proposed. By calculating of the dual values we know whether or not a city area is suitable for growing. It is established that if the travel costs are co-coercive then the set of shortest routes in terms of generalized travel costs is the same for every solution of the studied problem.