Intra-Period (Within-Day) Dynamic Models

Abstract

The mathematical models described in the previous chapters are based on the assumptions of intra-period stationariety. This is equivalent to assuming, as stated in Chapter 1, that all significant variables are constant, at least on average, over successive sub-intervals of a reference period long enough to allow the system to reach stationariety condition. This assumption, although acceptable for many applications, does not allow for the satisfactory simulation of some transportation systems such as heavily congested urban road networks or low frequency scheduled services. In the first case, some important phenomena cannot be reproduced by traditional intra-period static models, including demand peaks, temporary capacity variations, temporary over-saturation of supply elements, and formation and dispersion of queues. In the second case, low-frequency services (e.g. two flights per day) may call into question the assumption of intra-period uniform supply and mixed preventive-adaptive users’ choice behavior introduced in the previous chapters. To simulate these aspects, different intra-periodal or within-day dynamic models have recently been developed; these models are usually referred to in the literature as (within-day) Dynamic Traffic Assignment (DTA) models, implying that dynamic assignment models require within-day dynamic demand and supply models.