Network topology and robustness of Physical Internet

The Physical Internet (PI) is a new paradigmatic concept for logistic systems, characterized by flexibility and efficiency through decentralization and standardization. In the PI, the delivery route of freight can be chosen flexibly from available paths at the moment, better utilizing transportation resources than traditional systems. However, the knowledge on the congestion dynamics of traffic in the PI is still limited. Here, to contribute to the understanding of the dynamical features of the PI, we examine the robustness of a network delivery system by using a simple model that extracts the essence of the problem. We performed extensive Monte Carlo simulations on various conditions on the type of algorithm, network structure, and transportation capacity, and three scenarios that mimic changes in demand: (i) locally and temporally increased traffic demand; (ii) globally and temporally increased traffic demand; and (iii) permanent change in demand pattern. We show that adaptive algorithms are more effective in networks that contain many bypass routes (e.g., the square lattice and random networks) rather than the hub-and-spoke networks. Furthermore, the square lattice and random networks were robust against the change in the demand pattern and temporal blockage (e.g., due to high demand) of delivery paths. We suggest that such preferable properties are in a trade-off relationship between the redundancy of networks and that the bypass structure is one of the important criteria for designing network logistics.