The accelerated deployment of smart cities has led to a proliferation of diverse services operating simultaneously within urban environments. However, this growth presents the challenge of scalability issues, due to the varied resources used per service and the difficulty in analyzing wide-ranging network flows, since most traffic is not classified by their service. We present a path toward a smart city sensitive to criticality by: (1) showcasing con- tributions to evolve an infrastructure with the internet-of-things (IoT) and edge computing to accommodate traffic differentiation and service criticality; and (2) proposing a distributed network protocol, Rank, that is capable of dynamically allocating various types of resources along paths between nodes in the network infrastructure, so that new services could be added on demand. Our results show that it is possible to transform a smart city into a criticality-sensitive one by adopting a traffic classification with little to no impact on packet forwarding and time synchronization through hierarchical elements with respect to a GNSS source, where Rank conveniently solves the dynamics of variable traffic with low overhead.