Posted by Damien Pierce, Software Engineer, and John Anderson, Senior Research Director, Google Research
Some cities or communities develop an evacuation plan to be used in case of an emergency. There are a number of reasons why city officials might enact their plan, a primary one being a natural disaster, such as a tornado, flood, or wildfire. An evacuation plan can help the community more effectively respond to an emergency, and so could help save lives. However, it can be difficult for a city to evaluate such a plan because it is not practical to have an entire town or city rehearse a full blown evacuation. For example, Mill Valley, a city in northern California, created a wildfire evacuation plan but lacked an estimate for how long the evacuation would take.
Today we describe a case study in which we teamed up with the city of Mill Valley to test and improve their evacuation plan. We outline our approach in our paper, “Mill Valley Evacuation Study”. We started by using a traffic simulator to model a citywide evacuation. The research goal was to provide the city with detailed estimates for how long it would take to evacuate the city, and, by studying the egress pattern, to find modifications to make the plan more effective. While our prior work on this subject provided an estimate for the evacuation time and showed how the time could be reduced if certain road changes were implemented, it turns out the recommendations in that paper — such as changing the number of outgoing lanes on an arterial — were not feasible. The current round of research improves upon the initial study by more accurately modeling the number and starting locations of vehicles, by using a more realistic map, and by working closely with city officials to ensure that recommended changes to the plan are deemed viable.
Geography and methodology
Mill Valley is in Marin County, California, north of San Francisco. Many of the residences are located on the steep hillsides of several valleys surrounded by dense redwood forests.
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| Aerial views of Mill Valley, courtesy of the City of Mill Valley. |
Many of those residences are in areas that have only one exit direction, toward the town center. From there the best evacuation route is toward Highway 101, which is in the flat part of the city and is the most likely area to be far from potential wildfires. Some neighborhoods have other routes that lead away from both the city and Highway 101, but those routes pass through hilly forested areas, which could be dangerous or impassable during a wildfire. So, the evacuation plan directs all vehicles west of Highway 101 to head east, to the highway (see map below). The neighborhoods east of Highway 101 are not included in the simulation because they are away from areas with a high fire hazard rating, and are close to the highway.
Mill Valley has about 11,400 households west of Highway 101. Most Mill Valley households have two vehicles. Evacuation times scale with the number of vehicles, so it is in the common interest to minimize the number of vehicles used during an evacuation. To that end, Mill Valley has a public awareness campaign aimed at having each household evacuate in one vehicle. While no one knows how many vehicles would be used during an evacuation, it is safe to assume it is on average between one and two per household. The basic evacuation problem, then, is how to efficiently get between 11 and 23 thousand vehicles from the various residences onto one of the three sets of Highway 101 on-ramps.
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| The simulated part of Mill Valley west of Highway 101 is inside the blue border. Highway 101 is shown in green. The red squares indicate the three sets of Highway 101 on-ramps. The pink area has the highest fire hazard rating. |
The current work uses the same general methodology as the previous research, namely, running the open source SUMO agent-based traffic simulator on a map of Mill Valley. The traffic simulator models traffic by simulating each vehicle individually. The detailed behaviors of vehicles are dictated by a car-following model. Each vehicle is given a point and time at which to start and an initial route. The routes of most vehicles are updated throughout the simulation, depending on conditions. To consider potential changes in driver behavior under the high stress conditions of an evacuation, the effects of the “aggressiveness” of each car is also investigated, but in our case the impacts are minimal. Some simplifying assumptions are that vehicles originate at residential addresses and the roads and highways are initially empty. These assumptions correspond approximately to conditions that could be encountered if an evacuation happens in the middle of the night. The main inputs in the simulation are the road network, the household locations, the average number of vehicles per household, and a departure temporal distribution. We have to make assumptions about the departure distribution. After discussing with the city officials, we chose a distribution such that most vehicles depart within an hour.
Four bottlenecks
Mill Valley has three sets of Highway 101 on-ramps: northern, middle, and southern. All the vehicles must use one of these sets of on-ramps to reach their destination (either the northernmost or southernmost segment of Highway 101 included in our map). Given that we are only concerned with the majority of Mill Valley that lies west of the highway, there are two lanes that approach the northern on-ramps, and one lane that approaches each of the middle and southern on-ramps. Since every vehicle has to pass over one of these four lanes to reach the highway, they are the bottlenecks. Given the geography and existing infrastructure, adding more lanes is infeasible. The aim of this research, then, is to try to modify traffic patterns to maximize the rate of traffic on each of the four lanes.
Evacuation plan
When we started this research, Mill Valley had a preliminary evacuation plan. It included modifying traffic patterns — disabling traffic lights and changing traffic rules — on a few road segments, as well as specifying the resources (traffic officers, signage) necessary to implement the changes. As an example, a two-way road may be changed to a one-way road to double the number of outgoing lanes. Temporarily changing the direction of traffic is called contraflow.
The plot below shows the simulated fraction of vehicles that have departed or reached their destinations versus time, for 1, 1.5, and 2 vehicles per household (left to right). The dashed line on the far left shows the fraction that have departed. The solid black lines show the preliminary evacuation plan results and the dotted lines indicate the normal road network (baseline) results. The preliminary evacuation plan significantly speeds up the evacuation.
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| The cumulative fraction of vehicles vs. time in hours. The demand curve is shown in the dashed line on the far left. The solid lines show the preliminary evacuation plan curves for 1, 1.5 and 2 vehicles per household (left to right). The dotted lines show the same for the baseline case. |
We can understand how effective the preliminary evacuation plan is by measuring the rates at the bottlenecks. The below plots show the rate of traffic on each of the four lanes leading to the highway on-ramps for the case of 1.5 vehicles per household for both the baseline case (the normal road rules; shown shaded in gray) and the preliminary evacuation plan (shown outlined in black). The average rate per lane varies greatly in the different cases. It is clear that, while the evacuation plan leads to increased evacuation rates, there is room for improvement. In particular, the middle on-ramps are quite underutilized.
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| The rates of traffic on the four lanes leading to Highway 101 on-ramps for both the baseline case (normal road rules; shown shaded in gray) and the preliminary evacuation plan (shown outlined in black). |
Final evacuation plan
After studying the map and investigating different alternatives, we, working together with city officials, found a minimal set of new road changes that substantially lower the evacuation time compared to the preliminary evacuation plan (shown below). We call this the final evacuation plan. It extends the contraflow section of the preliminary plan 1000 feet further west, to a main intersection. Crucially, this allows for one of the (normally) two outgoing lanes to be dedicated to routing traffic to the middle on-ramps. It also creates two outgoing lanes from that main intersection clear through to the northern on-ramps, over ¾ of a mile to the east.
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| A map of the main changes in the final evacuation plan. The red line shows that traffic heading north on Camino Alto gets diverted to the middle Highway 101 on-ramps. The blue line shows traffic in the northern lane of E Blithedale Ave gets routed on the new contraflow section. |
The rate per lane plots comparing the preliminary and final evacuation plans are shown below for 1.5 vehicles per household. The simulation indicates that the final plan increases the average rate of traffic on the lane leading to the middle on-ramps from about 4 vehicles per minute to about 18. It also increases the through rate of the northern on-ramps by over 60%.
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| The rates of traffic on the four lanes leading to Highway 101 on-ramps for both the preliminary case (shown shaded in gray) and the final evacuation plan (shown outlined in black). |
The below plot shows the cumulative fraction of vehicles vs. time, comparing the cases of 1, 1.5 and 2 vehicles per household for the preliminary and final evacuation plans. The speedup is quite significant, on the scale of hours. For example, with 1.5 vehicles per household, it took 5.3 hours to evacuate the city using the preliminary evacuation plan, and only 3.5 hours using the final plan.
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| The cumulative fraction of vehicles vs. time in hours. The demand curve is shown in the dashed line on the far left. The solid lines show the final evacuation plan curves for 1, 1.5 and 2 vehicles per household (left to right). The dotted lines show the same for the preliminary evacuation plan. |
Conclusion
Evacuation plans can be crucial in quickly getting many people to safety in emergency situations. While some cities have traffic evacuation plans in place, it can be difficult for officials to learn how well the plan works or whether it can be improved. Google Research helped Mill Valley test and evaluate their evacuation plan by running traffic simulations. We found that, while the preliminary plan did speed up the evacuation time, some minor changes to the plan significantly expedited evacuation. We worked closely with the city during this research, and Mill Valley has adopted the final plan. We were able to provide the city with more simulation details, including results for evacuating the city one area at a time. Full details can be found in the paper.
Detailed recommendations for a particular evacuation plan are necessarily specific to the area under study. So, the specific road network changes we found for Mill Valley are not directly applicable for other cities. However, we used only public data (road network from OpenStreetMap; household information from census data) and an open source simulator (SUMO), so any city or agency could use the methodology used in our paper to obtain results for their area.
Acknowledgements
We thank former Mayor John McCauley and City of Mill Valley personnel Tom Welch, Lindsay Haynes, Danielle Staude, Rick Navarro and Alan Piombo for numerous discussions and feedback, and Carla Bromberg for program management.
