It has been recently proposed and tested that traffic in large urban regions (neighbourhoods) can be modelled dynamically at an aggregate level, if the neighbourhoods are uniformly congested. By exploiting the insights and the properties of a macroscopic fundamental diagram (MW), we describe the rush hour dynamically in case of multi-region cities that are not uniformly congested. A cruising-for-parking model is developed that considers the dynamics of different types of vehicles, while travelling towards their destinations or cruising. This model describes the physics of hypercongestion caused by the phenomenon, it shows that cruising-for-parking affects all the users of the system, even those with destinations outside the limited parking region and it provides tools to estimate the direct costs of all users, as these expressed by additional vehicle-hours travelled. Also, it describes the rush hour dynamically while vehicles searching for a spot (properly recognizing that delays are greater when flows are lower, unlike existing economic models). (C) 2015 Elsevier Ltd. All rights reserved.