  We present a conceptual framework for the dynamic traffic resources
allocation problem in a situation of elastic demand among customers. We
introduce an activity-based model to express customers' successive actions and
transfers in order to capture the essential aspect of transfers as a derived
demand. We focus on the decision-making of customers, in that they only use a
mobility service when their space-time prism constraints represent the worst
case. Under the setting with such elastic demand, we characterize a class of
dynamic traffic resources allocation mechanisms that strictly keep space-time
prism constraints of users and capacity constraints of traffic resources.
Within the class of mechanisms, we show the optimal mechanism that maximizes
discounted social welfare and show an exact solution algorithm for both, myopic
and non-myopic settings, using the zero-suppressed binary decision diagram. We
also present approximation algorithms that are still included in the class of
mechanisms. In numerical studies, we showed that our proposed algorithm works
effectively in settings with high rejection rates, meaning that this algorithm
can be used to focus on the behavior of latent customers who have not used
mobility services so far. The proposed non-myopic algorithm is suitable to
design services for limited small number of customers, for example a
car-sharing services for prescribed members, while the proposed myopic
algorithm is suitable for designing services for a large unspecified number of
customers, for example, a ride-sharing service in a large city.
