Jammin'with Floyd 301 Jammin’ with Floyd: A Traffic Flow Analysis of South Carolina hurricane evacuation Christopher hanusa Ari Nieh Matthew schneider Harvey mudd college Claremont, CA Advisor: Ran libeskind-Hadas Introduction We analyze the 1999 Hurricane Floyd evacuation with a traffic-flow model explaining the extreme congestion on 1-26. Then we look at the new South Carolina Hurricane Evacuation Plan, whichincludes lanereversals. We analyze their effect; they would significantly benefit traffic leaving Charleston. With lane reversals, the maximum number of vehicles passing any point on 1-26 is 6,000 cars/h We develop two plans to evacuate the South Carolina coast: the first b geographic location, the second by license-plate parity We explore the use of temporary shelters; we find that 1-26 has sufficient capacity for oversized vehicles; and we determine the effects of evacuees from orgia and Flori Traffic flow mode The following definitions and model are taken directly from Mannering and Kilareski [1990, 168-182 The primary dependent variable is level of service(LOS), or amount of congestion, of a roadway. There are six different LOS conditions, A through E, with a being the least congested and F being the most congested. We focus on che distinction between levels e and F The UIMAP Journal 22(3)(2001)301-310. @Copyright 2001 by COMAP, Inc. All rights 1 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
Jamminí with Floyd 301 Jamminí with Floyd: A Traffic Flow Analysis of South Carolina Hurricane Evacuation Christopher Hanusa Ari Nieh Matthew Schnaider Harvey Mudd College Claremont, CA Advisor: Ran Libeskind-Hadas Introduction We analyze the 1999 Hurricane Floyd evacuation with a traffic-flow model, explaining the extreme congestion on I-26. Then we look at the new South Carolina Hurricane Evacuation Plan, which includes lane reversals. We analyze their effect; they would significantly benefit traffic leaving Charleston. With lane reversals, the maximum number of vehicles passing any point on I-26 is 6,000 cars/h. We develop two plans to evacuate the South Carolina coast: the first by geographic location, the second by license-plate parity. We explore the use of temporary shelters; we find that I-26 has sufficient capacity for oversized vehicles; and we determine the effects of evacuees from Georgia and Florida. Traffic Flow Model The following definitions and model are taken directly from Mannering and Kilareski [1990, 168ñ182]. The primary dependent variable is level of service (LOS), or amount of congestion, of a roadway. There are six different LOS conditions, A through F, with A being the least congested and F being the most congested. We focus on the distinction between levels E and F. The UMAP Journal 22 (3) (2001) 301ñ310. 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
302 The UMAP Journal 22.3 (2001) Level of Service E represents operating conditions at or near capacity level. All speeds are reduced to a low but relatively uniform value, normally between 30 and 46 mpl Level of Service F is used to define forced or breakdown flow, with speeds of less than 30 mph. This condition exists wherever the amount of traffic approaching a point exceeds the amount that can traverse that point. Queues form behind such locations If we enter LOS F, the roadway has exceeded its capacity and the usefulness of the evacuation has broken down. An evacuation strategy that results in a highway reaching LOS F is unacceptable For a given highway, we can determine the maximum number of vehicles that can flow through a particular section while maintaining a desired level of service. To make this more concrete, we define the characteristic quantity iaxIImlIn service flow Definition. Maximum Service Flow(MSFi) for agivenlevel of service i, assuming ideal roadway conditions, is the maximum possible rate of flow for a peak 15- min period, expanded to an hourly volume and expressed in passenger cars per hour per lane(pcphpl). To calculate the msF of a highway for a given LOS,we multiply the roads capacity under ideal conditions by the volume-to-capacity ratio for the desired LOS. More formally, MSFi=ci=, where c, is the capacity under ideal conditions for a freeway with Design Speed j, and (o/c)i is the maximum volume-to-capacity ratio associated with LOS i. For highways with 60-and 70-mph design speeds, c; is 2,000 pcphpl [Transportation Research Board 1985]. Since LOS E is considered to be"at capacity, "(U/cE=1.0. The design speed of a road is based mostly on the importance and grade of the road; roads that are major and have shallower grades have higher design speeds. The elevation profile along I-26 shows that South Carolina is flat enough to warrant the highest design speed An immediate consequence of (1)is that to maintain MSFe or better(which we consider necessary for a successful evacuation), the number of passenger cars per hour per lane must not exceed 2,000 for any highway. For it to be useful in model calculations, we need to convert the maximum service flow to a quantity that conveys information about a particular roadway This quantity is known as the service flow rate of a roadway. Definition. The service flow rate for level of service i, denoted SFi, is the actual maximal flow that can be achieved given a roadway and its unique set of prevailing conditions. The service flow rate is calculated SFi= MSFi Nfo fHv fp in terms of the adjustment factors
302 The UMAP Journal 22.3 (2001) • Level of Service E represents operating conditions at or near capacity level. All speeds are reduced to a low but relatively uniform value, normally between 30 and 46 mph. • Level of Service F is used to define forced or breakdown flow, with speeds of less than 30 mph. This condition exists wherever the amount of traffic approaching a point exceeds the amount that can traverse that point. Queues form behind such locations. If we enter LOS F, the roadway has exceeded its capacity and the usefulness of the evacuation has broken down. An evacuation strategy that results in a highway reaching LOS F is unacceptable. For a given highway, we can determine the maximum number of vehicles that can flow through a particular section while maintaining a desired level of service. To make this more concrete, we define the characteristic quantity maximum service flow. Definition. Maximum Service Flow(MSFi) for a given level of service i, assuming ideal roadway conditions, is the maximum possible rate of flow for a peak 15- min period, expanded to an hourly volume and expressed in passenger cars per hour per lane (pcphpl). To calculate the MSF of a highway for a given LOS, we multiply the roadís capacity under ideal conditions by the volume-to-capacity ratio for the desired LOS. More formally, MSFi = cj v c i , (1) where cj is the capacity under ideal conditions for a freeway with Design Speed j, and (v/c)i is the maximum volume-to-capacity ratio associated with LOS i. For highways with 60- and 70-mph design speeds, cj is 2,000 pcphpl [Transportation Research Board 1985]. Since LOS E is considered to be ìat capacity,î (v/c)E = 1.0. The design speed of a road is based mostly on the importance and grade of the road; roads that are major and have shallower grades have higher design speeds. The elevation profile along I-26 shows that South Carolina is flat enough to warrant the highest design speed. An immediate consequence of (1) is that to maintain MSFE or better (which we consider necessary for a successful evacuation), the number of passenger cars per hour per lane must not exceed 2,000 for any highway. For it to be useful in model calculations, we need to convert the maximum service flow to a quantity that conveys information about a particular roadway. This quantity is known as the service flow rate of a roadway. Definition. The service flow rate for level of service i, denoted SFi, is the actual maximal flow that can be achieved given a roadway and its unique set of prevailing conditions. The service flow rate is calculated as SFi = MSFiNfwfHVfp, (2) in terms of the adjustment factors:
Jammin with Floyd 303 N: the number of lanes fu: the adjustment for nonideal lane widths and lateral clearances, fHv: effect of nonpassenger vehicles, and fp: the adjustment for nonideal driver populations We assume that the lanes on I-26 and other high wavs are l deal (i.e. fu=1):at least 12 ft wide with obstructions at least 6 ft from traveled pavement [Manner- ing and Kilareski 1990]. To account for driver unfamiliarity with reversed lanes and stress of evacuation, we set fp=0.7 for reversed lanes and fp =0.8 for normal lanes, in accordance with Mannering and Kilareski [ 1990]. The model also employs an adjustment factor, denoted fHv, for reduction of flow due to heavy vehicles such as trucks, buses, RVs, and trailers. Later we discuss the effects of heavy vehicles on traffic flow. Strengths and Weaknesses This model is easy to implement, the mathematics behind it is quite sim ple, and it is backed by the National Transportation Board. We establish its reliability by using it to predict traffic flow patterns in the 1999 evacuation We assume that the number of lanes does not change, which requires that here are no lane restrictions throughout the length of the freeway and no lanes are added or taken away by construction. The major weakness of our model is that it fails to take into account the erratic behavior of people under the strain of a natural disaster. The simplicity of our model also limits its usefulness. It can be applied only to normal highway situations, not to a network of roads Improving Evacuation Flow Gathering data from a various sources, we estimate the number of vehi cles used in the 1999 evacuation. According to Dow and Cutter [2000, 65% of households that were surveyed chose to evacuate. About 70% of households used one vehicle or fewer, leaving 30% of households taking two vehicles. Of the evacuees, 25% used 1-26 during the evacuation. Based on population esti- mates[County Population Estimates.. 1999] and average number of people per household [Estimates of Housing Units . 19981, and assuming a rela- tively uniform distribution of people per household, we calculate the number of vehicles used during the evacuation (Table 1)
Jamminí with Floyd 303 N: the number of lanes, fw: the adjustment for nonideal lane widths and lateral clearances, fHV: effect of nonpassenger vehicles, and fp: the adjustment for nonideal driver populations. We assume that the lanes on I-26 and other highways are ideal (i.e., fw = 1): at least 12 ft wide with obstructions at least 6 ft from traveled pavement [Mannering and Kilareski 1990]. To account for driver unfamiliarity with reversed lanes and stress of evacuation, we set fp = 0.7 for reversed lanes and fp = 0.8 for normal lanes, in accordance with Mannering and Kilareski [1990]. The model also employs an adjustment factor, denoted fHV, for reduction of flow due to heavy vehicles such as trucks, buses, RVs, and trailers. Later we discuss the effects of heavy vehicles on traffic flow. Strengths and Weaknesses This model is easy to implement, the mathematics behind it is quite simple, and it is backed by the National Transportation Board. We establish its reliability by using it to predict traffic flow patterns in the 1999 evacuation. We assume that the number of lanes does not change, which requires that there are no lane restrictions throughout the length of the freeway and no lanes are added or taken away by construction. The major weakness of our model is that it fails to take into account the erratic behavior of people under the strain of a natural disaster. The simplicity of our model also limits its usefulness. It can be applied only to normal highway situations, not to a network of roads. Improving Evacuation Flow Gathering data from a various sources, we estimate the number of vehicles used in the 1999 evacuation. According to Dow and Cutter [2000], 65% of households that were surveyed chose to evacuate. About 70% of households used one vehicle or fewer, leaving 30% of households taking two vehicles. Of the evacuees, 25% used I-26 during the evacuation. Based on population estimates [County Population Estimates ... 1999] and average number of people per household [Estimates of Housing Units ... 1998], and assuming a relatively uniform distribution of people per household, we calculate the number of vehicles used during the evacuation (Table 1)
304 The UMAP Journal 22.3 (2001) Evacuation participation estimates for Hurricane Floyd, in thousands on Evacuees Evacuating Vehicles Vehicles Households Central 59 Northern Total 632 245 319 61 Reversing lanes According to our model, the capacity of a highway is directly proportional to the number of lanes. This implies that lane reversal would nearly double he capacity of I-26 Approximately 319,000 vehicles were used to evacuate the coastal counties of South carolina. Of evacuees surveyed by Dow and Cutter [2000, 16. 3% evacuated between noon and 3 P. M. on Sept. 14. Assuming independence between the above factors in the hours between 9 A.M. and noon 1-26 must have been clogged by an attempted influx of about 3, 300 vehicles/h. Even if evenly distributed, this was more than the 3, 200 vehicles/h that the two Columbia-bound lanes of 1-26 could take under evacuation conditions. The result was LOS F-a large traffic jam. Our model predicts that this jam would have lingered for hours, even after the influx of vehicles had died down What if the coastal-bound lanes of [-26 were reversed? With corrections for nonideal conditions, our model predicts an SFE of 6,000 pcphpl. Therefore, reversing the lanes of 1-26 has the potential to increase service flow rate by a factor of 1.6 Simultaneous evacuation Strategies By Hurricane Path Hurricanes sweep from south to north. Because a hurricane commonly travels at a speed of less than 30 mph, the southernmost counties of South Carolina would be affected at least two hours before the northernmost ones However, analysis indicates that a staggered evacuation strategy would not improve the speed of the evacuation. The evacuation routes are largely par- allel to one another and rarely intersect. Thus, the evacuation of each county should affect only the traffic on evacuation routes of nearby counties. There fore, postponing evacuation of counties farther from the hurricane would be
304 The UMAP Journal 22.3 (2001) Table 1. Evacuation participation estimates for Hurricane Floyd, in thousands. Population Evacuees Evacuating Vehicles Vehicles Households on I-26 Southern 187 122 47 61 ó Central 553 359 139 181 ó Northern 233 152 59 76 ó Total 973 632 245 319 61 Reversing Lanes According to our model, the capacity of a highway is directly proportional to the number of lanes. This implies that lane reversal would nearly double the capacity of I-26. Approximately 319,000 vehicles were used to evacuate the coastal counties of South Carolina. Of evacuees surveyed by Dow and Cutter [2000], 16.3% evacuated between noon and 3 p.m. on Sept. 14. Assuming independence between the above factors, in the hours between 9 a.m. and noon, I-26 must have been clogged by an attempted influx of about 3,300 vehicles/h. Even if evenly distributed, this was more than the 3,200 vehicles/h that the two Columbia-bound lanes of I-26 could take under evacuation conditions. The result was LOS Fóa large traffic jam. Our model predicts that this jam would have lingered for hours, even after the influx of vehicles had died down. What if the coastal-bound lanes of I-26 were reversed? With corrections for nonideal conditions, our model predicts an SFE of 6,000 pcphpl. Therefore, reversing the lanes of I-26 has the potential to increase service flow rate by a factor of 1.6. Simultaneous Evacuation Strategies By Hurricane Path Hurricanes sweep from south to north. Because a hurricane commonly travels at a speed of less than 30 mph, the southernmost counties of South Carolina would be affected at least two hours before the northernmost ones. However, analysis indicates that a staggered evacuation strategy would not improve the speed of the evacuation. The evacuation routes are largely parallel to one another and rarely intersect. Thus, the evacuation of each county should affect only the traffic on evacuation routes of nearby counties. Therefore, postponing evacuation of counties farther from the hurricane would be counterproductive
Jammin with Floyd 305 By County What about avoiding simultaneous evacuation of adjacent counties? We recommend evacuating Jasper, Beaufort, Charleston, Georgetown, and Horry counties in the first wave, and leaving Hampton, Colleton, Dorchester, and Berkeley until 3-6 h later, depending on the time of day. This solution would decrease the probability of traffic reaching LOS F on any highway without significantly delaying the evacuation. The nearby state of Virginia has a similar plan for evacuating county by county Virginia Hurricane.. 1991] By License Plate Number By dividing cars into two categories, depending on the parity of the last digit on their license plate, we could separate traffic into two waves without giving preference to residents of any county. Our solution would request that che even group evacuate 3-6 h after the odd group was given the evacuation order. This would spread out the hours of peak evacuation traffic, resulting in improved traffic conditions and decreased risk of LOS F being reached. A comparison of Figures 1 and 2 demonstrates the change in time distribution of evacuation when half of the drivers evacuate six hours later. Clearly, the distribution is much smoother, reducing the likelihood of reaching LOS Figure 1. Hurricane Floyd: Fraction of evacuating population vs hours after the 1999 mandatory evacuation order (Data from Dow and Cutter 2000).) Figure 2. Even/odd license plate plan: Our projected fraction of the evacuating population vs hours after the mandatory evacuation order
Jamminí with Floyd 305 By County What about avoiding simultaneous evacuation of adjacent counties? We recommend evacuating Jasper, Beaufort, Charleston, Georgetown, and Horry counties in the first wave, and leaving Hampton, Colleton, Dorchester, and Berkeley until 3ñ6 h later, depending on the time of day. This solution would decrease the probability of traffic reaching LOS F on any highway without significantly delaying the evacuation. The nearby state of Virginia has a similar plan for evacuating county by county [Virginia Hurricane ... 1991]. By License Plate Number By dividing cars into two categories, depending on the parity of the last digit on their license plate, we could separate traffic into two waves without giving preference to residents of any county. Our solution would request that the even group evacuate 3ñ6 h after the odd group was given the evacuation order. This would spread out the hours of peak evacuation traffic, resulting in improved traffic conditions and decreased risk of LOS F being reached. A comparison of Figures 1 and 2 demonstrates the change in time distribution of evacuation when half of the drivers evacuate six hours later. Clearly, the distribution is much smoother, reducing the likelihood of reaching LOS F. Figure 1. Hurricane Floyd: Fraction of evacuating population vs. hours after the 1999 mandatory evacuation order. (Data from Dow and Cutter [2000].) Figure 2. Even/odd license plate plan: Our projected fraction of the evacuating population vs. hours after the mandatory evacuation order