Transportation - Traffic

The proposed contribution addresses vehicular traffic on large networks. Typically what is considered is a regional sized network, such as the Ile-de-France network in which the number of daily car trips exceeded 14.5 million in 2018. In order to carry out a trip a traveler chooses his departure time and path, the result of which is called traffic assignment. The standard behavioral assumption for departure time and path choice is that the traveler minimizes his travel cost (travel time + monetary cost). The travel cost expresses the network supply, which depends on the traffic assignment.

We present the dynamical system of an $A+B\rightarrow C$ bus loop system, served by two buses $X$ and $Y$. Here, there are three bus stops $A, B$ and $C$ in a loop where $X$ picks up people from $A$ and $B$ whilst $Y$ picks up people from $B$ only. Everybody alights at $C$, and no one boards from $C$. Thus, this is referred to as a \emph{semi-express} bus system where $X$ is a normal bus whilst $Y$ is an express bus that serves $B$ directly to $C$.

Given Holling’s definition of resilience in ecology, resilience studies in engineering fields have recently begun to focus on the system’s ability to absorb, adapt, and recover. While traditional system reliability engineering has focused on the design of a system to avoid operational collapse, the more recent study of system resilience has shifted the viewpoint for system reliability and safety from “safe–fail” to “fail–safe”, suggesting a systematic management paradigm to recover from unexpected disturbances.