Population Capacity Threats to Urban Area Resiliency: Observations on Chaotic Transportation Network Behavior

This paper is an endeavor to picture excessive population threats to the resiliency of a large metropolitan area. By employing an existing evolutionary model of traffic flow on a small expository network, we show how chaotic situations occur at certain demand and supply parameter values, and try to address the questions: How may one determine city population capacity for its transportation network, what happens if the city passes this limit, or how may one return the city to a stable situation when it runs into unstable or chaotic situations. Under certain assumptions, the paper designs a simulation experiment to revisit the phenomenon discovered by Greenshields in 1934, but for a transportation network in a large city. A flow simulation shows that very small changes in the demand and supply of the network result in large variations in the throughput of the network, such that the time series of the latter values to an external observer are chaotic (with positive Lyapunov exponent). The limit to the resiliency of the city from the standpoint of its transportation network capacity is, then, estimated by a value for the city’s population. It is then argued how to take the network out of this situation.