The Crowd Before the Storin 291 The Crowd Before the storm Jonathan David Charlesworth Finale Nankai doshi Joseph edgar gonzalez The Governors School renamed August 2001: Maggie L. Walker Governor's School for government and international studies Richmond. va Advisor: John A Barnes Introduction pplying safety regulations and flow-density equations, we find the maxi- mum rate of flow througl ugh a lane of ro bad is 1, 500 cars/h, occurring when cars travel at 27.6 mp We construct a computer simulation that tracks the exit of cars through South Carolina's evacuation network. We attempt to optimize the network by reversing opposing lanes on various roads and altering the time that each city should begin evacuating, using a modified genetic algorithm The best solution-the one that evacuates the most people in 24 h--involves reversing all the opposing lanes on evacuation routes. Increasing the holding capacity of Columbia is only marginally helpful. Georgia and Florida traffic on I-95 is only mildly detrimental, but allowing people to take their boats and campers greatly decreases the number of people that can be evacuated Background on Evacuation Plans After the 1999evacuation, the South Carolina Department of Transportation (SCDOT)designated evacuation routes for all major coastal areas, including 14 different ways to leave the coast from 32 regions. The routes take evacuees past I-95 and I-20. Although officers direct traffic at intersections, traffic on road not inin the plan may have long waits to get onto roads in the plan. Moreover, the South Carolina Emergency Preparedness Division(SCEPD) does not call The LIMAP Journal 22(3)(2001)291-299. Copyright 2001 by COMAP, Inc. All rights reserved Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice. Abstracting with credit is perod. To copy otherwise, tted, but copyrights for components of this work owned by others than COMAP must be honor to republish, to post on servers, or to redistribute to lists requires prior permission from COMAP
The Crowd Before the Storm 291 The Crowd Before the Storm Jonathan David Charlesworth Finale Pankaj Doshi Joseph Edgar Gonzalez The Governorís School renamed August 2001: Maggie L. Walker Governorís School for Government and International Studies Richmond, VA Advisor: John A. Barnes Introduction Applying safety regulations and flow-density equations, we find the maximum rate of flow through a lane of road is 1,500 cars/h, occurring when cars travel at 27.6 mph. We construct a computer simulation that tracks the exit of cars through South Carolinaís evacuation network. We attempt to optimize the network by reversing opposing lanes on various roads and altering the time that each city should begin evacuating, using a modified genetic algorithm. The best solutionóthe one that evacuates the most people in 24 hóinvolves reversing all the opposing lanes on evacuation routes. Increasing the holding capacity of Columbia is only marginally helpful. Georgia and Florida traffic on I-95 is only mildly detrimental, but allowing people to take their boats and campers greatly decreases the number of people that can be evacuated. Background on Evacuation Plans After the 1999 evacuation, the South Carolina Department of Transportation (SCDOT) designated evacuation routes for all major coastal areas, including 14 different ways to leave the coast from 32 regions. The routes take evacuees past I-95 and I-20. Although officers direct traffic at intersections, traffic on roads not in in the plan may have long waits to get onto roads in the plan. Moreover, the South Carolina Emergency Preparedness Division (SCEPD) does not call The UMAP Journal 22 (3) (2001) 291ñ299. c Copyright 2001 by COMAP, Inc. All rights reserved. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice. Abstracting with credit is permitted, but copyrights for components of this work owned by others than COMAP must be honored. To copy otherwise, to republish, to post on servers, or to redistribute to lists requires prior permission from COMAP
292 The UMAP Journal 22.3 (2001) for any traffic type limitations (i.e, all campers, RVs, and cars with boats are allowed)[ South Carolina Department of Public Safety 19991 Assumptions Assumptions About Hurricanes e There is exactly one hurricane on the east coast of the united States at the time of the evacuation The hurricane, like Floyd, moves along the South Carolina coast. Most Atlantic hurricanes that reach the United States follow a northeasterly path along the coast Vaccaro 2000 Assumptions about Traffic Flow All cities act as points. The smaller streets within a city do not affect flow in and out of a cit The capacity of a city is the sum of its hotel rooms and the number of cars that can fit on the citys roads The flow between intersections is constant density of traffic between intersections is constant Charlotte and Gastonia in North Carolina; Spartanburg, Greenville, and An derson in South Carolina; and Augusta, Georgia are infinite drains, meaning that we do not route people beyond them. Flow out of these cities should not create traffic jams. The cities are also large and therefore should be able to accommodate most if not all incoming evacuees After the order to evacuate is issued, vehicles immediately fill the roads Traffic regulators attempt to maintain the ideal density, using South Car olina's GiS system All motorized vehicles are 16 ft long. This takes into account the percent age of motorcycles, compact cars, sedans, trucks, boats, and RVs and their On average, three people travel in one vehicle The traffic that enters I-95 from Georgia or Florida stays on i-95 and travels through South Carolina
292 The UMAP Journal 22.3 (2001) for any traffic type limitations (i.e., all campers, RVs, and cars with boats are allowed) [South Carolina Department of Public Safety 1999]. Assumptions Assumptions About Hurricanes • There is exactly one hurricane on the East Coast of the United States at the time of the evacuation. • The hurricane, like Floyd, moves along the South Carolina coast. Most Atlantic hurricanes that reach the United States follow a northeasterly path along the coast [Vaccaro 2000]. Assumptions About Traffic Flow • All cities act as points. The smaller streets within a city do not affect flow in and out of a city. • The capacity of a city is the sum of its hotel rooms and the number of cars that can fit on the cityís roads. • The flow between intersections is constant. • Density of traffic between intersections is constant. • Charlotte and Gastonia in North Carolina; Spartanburg, Greenville, and Anderson in South Carolina; and Augusta, Georgia are infinite drains, meaning that we do not route people beyond them. Flow out of these cities should not create traffic jams. The cities are also large and therefore should be able to accommodate most if not all incoming evacuees. • After the order to evacuate is issued, vehicles immediately fill the roads. • Traffic regulators attempt to maintain the ideal density, using South Carolinaís GIS system. • All motorized vehicles are 16 ft long. This takes into account the percentage of motorcycles, compact cars, sedans, trucks, boats, and RVs and their lengths. • On average, three people travel in one vehicle. • The traffic that enters I-95 from Georgia or Florida stays on I-95 and travels through South Carolina
The Croud Before the StorIn 293 Assumptions About People All people on the coast follow evacuation regulations immediately. Drivers obey the speed limit and keep a safe following distance Flow-Density Relationship Flow is the number of vehicles passing a point on the road per unit time The flow q on a road depends on the velocity v and density k of vehicles on the q= ku (1) Empirical studies suggest that velocity and density are related by [ayakrishnan etal.1996]: k where k, is the density of a road in a traffic jam, a is a parameter dependent on the road and vehicle conditions, and uf, free velocity, is speed at which a vehicle would travel if their were no other vehicles on the road. Generally, the free velocity is the speed limit of the road We substitute(2)into (1) to obtain flow as a function of density This equation is linearin the free velocity. To find the ideal density that produces the fastest flow, we take the first derivative of the flow with respect to density and set it equal to zero k k ki kj Solving for k, we find the ideal density ki k k Assuming that all roads behave similarly, we find a numerical value for the ideal density. Jam density is generally between 185 and 250 vehicles/mile [Haynie 2000; we use the average value of 218 vehicles/mile. By fitting(2) to Kockelman' s flow-density data for various cars, road conditions, and driver types in Kockelman [1998, we find that a has an average value of 3(Figure 1) Therefore, the ideal density is 54 vehicles per mile
The Crowd Before the Storm 293 Assumptions About People • All people on the coast follow evacuation regulations immediately. • Drivers obey the speed limit and keep a safe following distance. Flow-Density Relationship Flow is the number of vehicles passing a point on the road per unit time. The flow q on a road depends on the velocity v and density k of vehicles on the road: q = kv. (1) Empirical studies suggest that velocity and density are related by [Jayakrishnan et al. 1996]: v = uf 1 − k kj a , (2) where kj is the density of a road in a traffic jam, a is a parameter dependent on the road and vehicle conditions, and uf , free velocity, is speed at which a vehicle would travel if their were no other vehicles on the road. Generally, the free velocity is the speed limit of the road. We substitute (2) into (1) to obtain flow as a function of density: q = kuf 1 − k kj a . (3) This equation is linear in the free velocity. Tofind the ideal density that produces the fastest flow, we take the first derivative of the flow with respect to density and set it equal to zero: uf 1 − k kj a − auf k kj 1 − k kj a−1 = 0. Solving for k, we find the ideal density ki: ki = kj a + 1. Assuming that all roads behave similarly, we find a numerical value for the ideal density. Jam density is generally between 185 and 250 vehicles/mile [Haynie 2000]; we use the average value of 218 vehicles/mile. By fitting (2) to Kockelmanís flow-density data for various cars, road conditions, and driver types in Kockelman [1998], we find that a has an average value of 3 (Figure 1). Therefore, the ideal density is 54 vehicles per mile
294 The UMAP Journal 22.3 (2001) Density (vehicles/km) Figure 1. Plot of observed counts vs. density Data from Kockelman [1998] with our curve of fit of he form (2) To account for reaction time, vehicles must be spaced at least 2 s apart NJDOT 1999. For vehicles spaced exactly 2 s apart, we can find the density of a road where all vehicles are traveling at speed v. The distance dc required by a vehicle traveling at speed v is the sum of the vehicles length and its following distance dc =l+ 3600 where the units are miles and hours. The maximum safe density of a road is the maximum number of vehicles on the road ( the length of the road divided by the space required for each vehicle) divided by the length of the road If each car is 16 ft(3.03 x 10-3 mi) long and the density is ideal, then the maximum safe velocity of the vehicles is 27. 6 mph. we nowing the ideal density and the maximum safe velocity at that density, use(1)to find the maximum flow: U=1500. The free velocity parameter is needed to find the flow at situations other than ideal. Using(2), we find that the free velocity is 65.2 mph--close to the high way speed limit, thus validating the approach for finding the free velocity. Substituting the known and derived values of free velocity, jam density, and the exponential parameter into( 3), we quantify the flow-density relationship q=62.5611k
294 The UMAP Journal 22.3 (2001) Figure 1. Plot of observed counts vs. density. Data from Kockelman [1998] with our curve of fit of the form (2). To account for reaction time, vehicles must be spaced at least 2 s apart [NJDOT 1999]. For vehicles spaced exactly 2 s apart, we can find the density of a road where all vehicles are traveling at speed v. The distance dc required by a vehicle traveling at speed v is the sum of the vehicleís length and its following distance: dc = l + 2v 3600, where the units are miles and hours. The maximum safe density of a road is the maximum number of vehicles on the road (the length of the road divided by the space required for each vehicle) divided by the length of the road: k = 1 l + 2v 3600 . If each car is 16 ft (3.03 × 10−3 mi) long and the density is ideal, then the maximum safe velocity of the vehicles is 27.6 mph. Knowing the ideal density and the maximum safe velocity at that density, we use (1) to find the maximum flow: q = kv = 1500. (4) The free velocity parameter is needed to find the flow at situations other than ideal. Using (2), we find that the free velocity is 65.2 mphóclose to the highway speed limit, thus validating the approach for finding the free velocity. Substituting the known and derived values of free velocity, jam density, and the exponential parameter into (3), we quantify the flow-density relationship: q = 62.5k 1 − k 2183
The Croud Before the StorIn 295 Traffic flow model Mapping the region We programmed in Java a simplified map of South Carolina that consists of 107 junctions(cities)and 154 roads. A junction is an intersection point between two or more roads. A road connects exactly two junctions. Our map includes most of the roads in by SCEpd's model and many more. Data for the number of cars, boats, and campers in each city used in the computer model can be found in the Appendix. [EDITOR'S NOTE: We omit the Appendix I Behavior of cities Each point in the program stores a citys population and regulates traffic flow into and out of the roads connected to it. First, it flows cars out of the city into each road. The desired flow out-the maximum number of vehicles that the road can take-is defined by the flow-density equation(4)for the road that the cars are entering. If the total number of vehicles that can be exited exceeds the evacuee population of the city, then the evacuees are distributed proportionally among the roads with respect to the size of the road Next, the city lets vehicles in. The roads always try to flow into the city at the ideal flow rate. The city counts the total number of cars being sent to it and compares this to its current evacuee capacity. If the evacuee capacity is less than the number of vehicles trying to enter, the city accepts a proportion of the vehicles wanting to enter, depending on the road size. A check in the program ensures that the number of vehicles taken from the road does not exceed the number of cars on the road at that time After repeating the entering and exiting steps for each road, the city recal- culates its current evacuee population, removing all the vehicles that left and adding all the vehicles that entered Behavior of roads We define each road by its origin junction, destination junction, length, and number of lanes. The number of lanes is the number of lanes in a certain direc- tion under nonemergency circumstances. For example, a road that normally has one lane north and one lane south is considered a one-lane highway. If the number of lanes on a road changes between cities, we use the smaller number of lanes. To analyze the possibility of turning both lanes to go only north or only south, our program would double the number of lanes During an evacuation, traffic never needs to flow in both directions, be- cause the net flow of a road that flowed equally in two directions would be zero. Therefore, each road has a direction defined by its origin junction and destination junction. While the origin junction is normally the point closer to
The Crowd Before the Storm 295 Traffic Flow Model Mapping the Region We programmed in Java a simplified map of South Carolina that consists of 107 junctions (cities) and 154 roads. A junction is an intersection point between two or more roads. A road connects exactly two junctions. Our map includes most of the roads in by SCEPDís model and many more. Data for the number of cars, boats, and campers in each city used in the computer model can be found in the Appendix. [EDITORíS NOTE: We omit the Appendix.] Behavior of Cities Each point in the program stores a cityís population and regulates traffic flow into and out of the roads connected to it. First, it flows cars out of the city into each road. The desired flow outóthe maximum number of vehicles that the road can takeóis defined by the flow-density equation (4) for the road that the cars are entering. If the total number of vehicles that can be exited exceeds the evacuee population of the city, then the evacuees are distributed proportionally among the roads with respect to the size of the road. Next, the city lets vehicles in. The roads always try to flow into the city at the ideal flow rate. The city counts the total number of cars being sent to it and compares this to its current evacuee capacity. If the evacuee capacity is less than the number of vehicles trying to enter, the city accepts a proportion of the vehicles wanting to enter, depending on the road size. A check in the program ensures that the number of vehicles taken from the road does not exceed the number of cars on the road at that time. After repeating the entering and exiting steps for each road, the city recalculates its current evacuee population, removing all the vehicles that left and adding all the vehicles that entered. Behavior of Roads We define each road by its origin junction, destination junction, length, and number of lanes. The number of lanes is the number of lanes in a certain direction under nonemergency circumstances. For example, a road that normally has one lane north and one lane south is considered a one-lane highway. If the number of lanes on a road changes between cities, we use the smaller number of lanes. To analyze the possibility of turning both lanes to go only north or only south, our program would double the number of lanes. During an evacuation, traffic never needs to flow in both directions, because the net flow of a road that flowed equally in two directions would be zero. Therefore, each road has a direction defined by its origin junction and destination junction. While the origin junction is normally the point closer to