A Compartmental Dynamical Network Flow Model for Evacuation Planning of Cities

An evacuation due to, e.g., hurricanes, floods, or forest fires often puts severe stress on the transportation network and can create congestion or grid locks. In this paper, we present an evacuation planning solution where we model the city traffic as a compartmental model. Each compartment corresponds to one Traffic Analysis Zone (TAZ). Under normal (i.e., non-evacuation) operations, there is often a heterogeneity in the transportation network, which enables the traffic dynamics to be modelled through Macroscopic Fundamental Diagrams (MFDs). In the evacuation case, where all the traffic travels in the same direction, the typical shape of the MFD is not present. Because of this, we propose a dynamic system with a differently shaped relationship between the traffic flow and the amount of traffic present. We then utilize the model to propose two different evacuation planning strategies, a staggered release approach and an approximate model predictive control (MPC) approach. Micro-simulator studies performed for the city of Greensboro, NC, show that by using this evacuation planning methodology the total travel time needed to evacuate the city is reduced to around half without delaying the overall time it takes to evacuate.