Braess’ Paradox in Evacuation Planning
Link to study: http://cdn.intechopen.com/pdfs-wm/37898.pdf
Moynihan and Fonseca’s (2012) research study explains the concept of Braess’ Paradox as seen in real life situations of storm and hurricane evacuations. As discussed in class, Braess’ Paradox refers to a condition where adding new resources to a transportation network can sometimes decrease the efficiency of the overall system (Easley & Kleinberg, 2010). In the case of a storm evacuation, the traffic moves inland from the coast. In this situation, it is ideal to minimize time taken by each traveler to move away from the coast, considering the potential risk to human life. Based on the study, Hurricane Floyd led to major traffic bottlenecks throughout the evacuation routes, thus increasing the potential threat to life due to the high risk of the hurricane hitting the massive crowd at once. The idea here is to find the optimal set of coastal-inland routes within the existing roadway systems of the affected regions. Factors like population size of specific coastal areas, proximity to evacuation route origins, etc. need to be considered to build an evacuation plan that minimizes travel time and maximizes vehicle exit rate.
As discussed in lecture, the equilibrium traffic is achieved when all travelers adopt strategies that minimize travel time, to the point where no traveler has an incentive to switch routes. Adding a new express highway tends to draw each traveler on that route, given their self-interest to reach their destinations faster. During an evacuation situation, self-interest (to save your own life) is a big factor that compels people to try taking the fastest route, not realizing that their decisions increase the overall travel time. The simplified diagrams (Easley & Kleinberg, 2010) below can further explain the event in terms of Braess’ Paradox:
Figure 1A: Traffic flow from coastal area A to inland B via highway C-D Figure 1B: Traffic flow from A to B via routes A-C-B & A-D-B (Source: http://www.cs.cornell.edu/home/kleinber/networks-book/networks-book-ch08.pdf)
During an evacuation, let’s suppose there is an influx of 4000 from coastal area A moving towards inland B. Keeping their safety in mind, each traveler would take the 0-minute CD route in an attempt to get to the inland before the storm. The travel time in this case (Figure 1A) would be 80 minutes (4000/100+0+4000/100). If route CD is blocked (Figure 1B), the travelers would divide between routes ACB and ADB, thus reaching an equilibrium time of 65 minutes (2000/100+45).
Figure 2: Traffic control using temporary barriers during contraflow operations (Source: http://cdn.intechopen.com/pdfs-wm/37898.pdf)
As explained in the study, the aforementioned concept has been applied to evacuation plans of many Southeastern states of the US. They are using the model of “contraflow” (as shown in Figure 2), which involves blocking access to certain routes and reversing traffic flow on other ones. Figure 2 is a real life example of how the indicated road was blocked to allow the entire traffic flow to be reversed to go towards the inland of Alabama during an evacuation. Based on Braess’ Paradox, this plan can accommodate the movement of a larger number of travelers from the impact zone with a more efficient overall evacuation flow.