#### DMCA

## FACILITATING NO-NOTICE EVACUATION THROUGH OPTIMAL PICK-UP LOCATION SELECTION (2009)

### BibTeX

@MISC{Liu09facilitatingno-notice,

author = {Sirui Liu and Pamela Murray-Tuite},

title = {FACILITATING NO-NOTICE EVACUATION THROUGH OPTIMAL PICK-UP LOCATION SELECTION },

year = {2009}

}

### OpenURL

### Abstract

Under no-notice disasters, dependents in facilities such as schools and daycare centers usually wait for their families to pick them up. This family pickup behavior could increase individual evacuation time and cause extra delay to other vehicles in the network. Relocating the dependents to other pickup sites may facilitate no-notice evacuation. This study developed an optimization model to determine optimal pickup locations, assuming that all evacuating families have personal vehicles; the objective is to maximize the number of evacuees who can successfully pick up dependents and then escape from the dangerous zones within a safe evacuation time threshold. The optimization model was based on anticipated travel time output from the simulation model (VISSIM in this study); iteration between the two models was performed. The methodology was applied to a case study based on a simplified version of Chicago Heights, Illinois. The case study involved three facilities with 492 dependents and three safe time thresholds (i.e., 30, 45 and 60 minutes). Improvements in total travel time, average speed, total delay time and average delay time per vehicle and increases in the number of successful evacuations of dependents were used to evaluate the performance of the relocation strategy. This study also examined the sensitivity of the strategy to parents' arrival time, number of dependents, and safe time. Finally, relocation sites were recommended based on the results of all scenarios. The results found that the relocation strategy was sensitive to safe evacuation time and number of pickup evacuees (pickup evacuees refer to those persons with a need to pick up their dependents inside the dangerous zones). The relocation strategy was prominently effective when safe evacuation time fell into a moderate range or the number of pickup evacuees was fairly high. Application of the proposed methodology to a certain area can assist local decision-makers to take effective measures during no-notice evacuation and the relocation sites could be part of local evacuation management plans. Abstract Under no-notice disasters, dependents in facilities such as schools and daycare centers usually wait for their families to pick them up. This family pickup behavior could increase individual evacuation time and cause extra delay to other vehicles in the network. Relocating the dependents to other pickup sites may facilitate no-notice evacuation. This study developed an optimization model to determine optimal pickup locations, assuming that all evacuating families have personal vehicles; the objective is to maximize the number of evacuees who can successfully pick up dependents and then escape from the dangerous zones within a safe evacuation time threshold. The optimization model was based on anticipated travel time output from the simulation model (VISSIM in this study); iteration between the two models was performed. The methodology was applied to a case study based on a simplified version of Chicago Heights, Illinois. The case study involved three facilities with 492 dependents and three safe time thresholds (i.e., 30, 45 and 60 minutes). Improvements in total travel time, average speed, total delay time and average delay time per vehicle and increases in the number of successful evacuations of dependents were used to evaluate the performance of the relocation strategy. This study also examined the sensitivity of the strategy to parents' arrival time, number of dependents, and safe time. Finally, relocation sites were recommended based on the results of all scenarios. The results found that the relocation strategy was sensitive to safe evacuation time and number of pickup evacuees (pickup evacuees refer to those persons with a need to pick up their dependents inside the dangerous zones). The relocation strategy was prominently effective when safe evacuation time fell into a moderate range or the number of pickup evacuees was fairly high. Application of the proposed methodology to a certain area can assist local decision-makers to take effective measures during no-notice evacuation and the relocation sites could be part of local evacuation management plans. 3 The primary purpose of a no-notice evacuation is to save people's lives Evacuation time In a short-notice case, people can choose whether to evacuate or not, and when to evacuate In a no-notice scenario, almost everyone in the impacted area evacuates at the time of the disaster occurrence Origin evacuation place In a "short notice" evacuation case, evacuees often start from their homes together with their families. In a "no-notice" scenario, evacuees start evacuation from wherever they are at that time, (i.e., schools, work places, entertainment place, etc.) most likely by themselves. Family gathering process Families gather together before they start to evacuate. Families gather together during or after the evacuation When a no-notice disaster occurs during the daytime, household members may be scattered throughout the road network. Household dependents in facilities such as schools and daycare centers may wait for their families to pick them up; this family pickup behavior could increase individual evacuation time and cause extra delay for other vehicles in the network. When a large amount of vehicles rush into certain places to pick up dependents within a short period of time, bottlenecks could easily be formed for those locations whose entries/exits cannot accommodate heavy traffic. Facilities' current locations may not be well designed for the emergency case and limited entry/exit by itself could be a bottleneck. Relocating facilities' dependents to appropriate sites would eliminate unnecessary bottlenecks and smooth road traffic. Therefore, this study addresses selecting appropriate pickup locations to facilitate no-notice evacuation. A school is a typical facility having a number of carless dependents who need to be picked up. Most school districts have developed an emergency plan, which in summary, requests three kinds of action, i.e., shelter in place, lockdown, and off-site evacuation. According to the Office of the Superintendent, Arlington High School, Massachusetts 7 (2006), shelter-in-place is used when a danger happens outside the school, such as a chemical spill; lock-down is used when a danger is inside the school and makes evacuation impractical; off-site evacuation is used in an extreme emergency situation, and an evacuation location such as another school, church, Boys & Girls Club, Town Hall or ice skating rink, are prearranged for each individual school. This school's existing emergency plans demonstrate that moving dependents to other sites is a feasible strategy. Moreover, some previous studies have involved this issue; for example, Sinuany-Stern and Stern (1993) studied relocating carless people under an emergency situation, where carless households are assumed to move to a certain point first and are then picked up by organized transportation and transported to the shelter, and the households are assumed to use shortcuts and not interfere with road traffic. This study develops a mathematical model to determine optimal pickup locations for facilities; the objective is to maximize the number of evacuees who can successfully pick up dependents and escape from the dangerous zones afterwards. The model is tested for a given network based on the City of Chicago Heights, Illinois. This report is organized as follows. Chapter 1 describes the background and purpose of this study. Chapter 2 reviews the previous studies on evacuation modeling and the location problem. Chapter 3 formulates the optimization model and explains the methodologies adopted in this study. Chapter 4 describes basic information of the case study in Chicago Heights, such as the network, demand, assumptions and scenarios, and presents the results and the sensitivity analysis. Chapter 5 concludes the study and discusses the future directions. Chapter 2 Literature Review This chapter mainly reviews the previous studies on evacuation modeling. Numerous studies on evacuation planning and modeling were conducted since the 1980s, driven by tragic events such as the Three Mile Island nuclear reactor incident in 1979, September 11 terrorist attacks in 2001, and Hurricanes Katrina and Rita in 2005. Those studies generally focused on estimating evacuation time and determining optimal evacuation routes and optimal shelter locations, using operations research methods and simulation models. Evacuation studies, according to scopes and features of impacted areas, fall into five general categories: regions, neighborhoods, buildings, ships, and airplanes Regional Evacuation Regional (urban) evacuation models can be classified into aggregate models and disaggregate models. An aggregate model investigates a group of vehicles as a whole, while a disaggregate model evaluates each individual driver's behavior. An aggregate model overlooks the difference of individual driver's behavior among the population. The model developed in this study is a disaggregate model that relies on microsimulation. Aggregate Evacuation Modeling Most evacuation models were developed on an aggregate level and simulation-based (macroscopic), such as NETVAC, DYNEV, MASSVAC, and TEVACS; most of these models were dealing with hurricanes or nuclear plant incidents, as both are among the most frequent and severe disasters in the United Stated. Few previous works exist regarding regional evacuation models on the micro simulation level In general, most of the aforementioned models are capable of estimating network clearance time and identifying evacuation bottlenecks of the network. Most of these simulators assume that the evacuation process has reached equilibrium, thereby estimating evacuation time based on determined equilibrium traffic flow. However, under abnormal situations such as evacuation, equilibrium of road traffic is hard to achieve due to the practical reason that no historical experience exists for evacuees to choose routes and minimize their evacuation time; this is contrary to normal situations recurring almost every day, in which travelers can learn from past experience to choose routes 9 with minimum travel time Disaggregate Evacuation Modeling The previously mentioned models are aggregate as they do not consider an individual's behavior while modeling the evacuation progress. Stern and Sinuany-Stern (1989) first incorporated some behavior-related parameters, including diffusion time of evacuation instruction and individuals' preparation time, in a microscopic simulation model for an urban evacuation. Later Sinuany-Stern and Stern (1993) developed the SLAM Network Evacuation Model (SNEM) based on this behavioral-based model to test the effects of traffic factors (e.g. household size, car ownership and intersection traversing time) and route choice parameters on network clearance time. Sinuany-Stern and Stern's work assumes that household members are together when a disaster occurs; therefore it takes households as entities, instead of individual household members. In reality, family members could be scattered at different places under nonotice evacuation. Murray-Tuite and Mahmassani Neighborhood Evacuation Less attention was paid to the subject of neighborhood-scale evacuation under an emergency during the last twenty years, compared to region-scale evacuation or building evacuation No-notice Evacuation Recently, more and more focus is placed on no-notice evacuation. As a no-notice disaster requires quick response, real time estimation tools are important, for which computation time is a critical issue. Chiu et al. Shelter Location Many other previous studies focused on different specific aspects of an emergency evacuation. One is that the location of shelters may influence network clearance time significantly under hurricane evacuation. Facility Location Problem This study involves relocating dependents at facilities to make an evacuation efficient, so we here provide an overview of basic facility location problems. The facility location problem is a critical issue for strategic planning of a wide range of enterprises, e.g., a retailer chooses where to locate a store or a city planner selects locations of fire stations based on a set of rules (Owen and Diskin, 1998). Basic location problems, such as the P-median, P-center, set covering and maximal covering problems, are reviewed by Owen and Diskin (1998). The P-median problem is to locate P facilities in order to minimize the total travel cost between demands and facilities; the P-Center problem, also called the minmax problem, is to locate P facilities so as to minimize the maximum travel cost between a demand and its nearest facility; the set covering problem is to locate the minimum number of facilities that will serve all demands within a specified time; the maximal covering problem is to place P facilities with the goal to maximize the amount of demand covered within an acceptable distance between demands and facilities (Owen and Diskin, 1998). The P-Center, set covering and maximal covering problems can all be applied to locate emergency 11 medical services (EMS); the P-center and maximal covering problems are used to locate a given number of EMS, and the set covering problem is used to determine the least number of EMS to cover all population of a certain area. The above mentioned basic location problems do not account for location costs, which limits their application to practical problems. The fixed charge facility location problems are thus introduced with a fixed cost for each potential location site, and categorized as uncapacitated and capacitated according to whether facility capacities are incorporated or not (Owen and Diskin, 1998). The fixed charge facility location problems determine the number of facilities located endogenously, rather than pre-specified as in median and center problems. However, without considering varying costs associated with flows between facilities and demands, fixed charge problems still cannot solve such a problem as locating a warehouse, which is a general case in industry and needs to find the best shipments between facilities and customers. Hence, the location-allocation problems incorporate flow allocation between demands and facilities into a basic location problem (usually a median problem or a fixed charge problem) (Owen and Diskin, 1998). The location problem presented in this study is essentially a P-center problem that locates students to minimize the maximum of a pickup travel time. The flow allocation is not the case of this study as it is predetermined which parent picks up which child. The previous works provide valuable contributions to the emergency evacuation field, however most of them omit family gathering behavior under no-notice evacuation conditions. This omission could lead to optimistic estimates of evacuation time. This report explores this issue and considers the fact that parents need to pick up their carless household members during an evacuation. A strategy of relocating dependents to more accessible sites to facilitate no-notice evacuation is proposed and evaluated in this report. Chapter 3 Methodology This chapter describes the methodology adopted in this study. First, an integer optimization model is formulated to determine optimal relocation sites for facilities. The microscopic simulation model is then introduced to provide zonal travel time information for the optimization model. As the two models interact with each other, iteration between them is performed to achieve the "real" optimal point. A procedure to accomplish this iteration process is illustrated by a chart and explained step by step. This chapter also includes the methodology to generate the trip chain. Optimization Model A no-notice evacuation usually starts at the moment when a disaster is confirmed or announced, then evacuees surge onto the road network in a very short time and cause traffic to dramatically change. In this study, time-dependent road traffic is taken into consideration by discretizing the evacuation period into several time intervals and capturing the travel time for each time interval. A mathematical optimization model was developed to find optimal relocation sites for facilities such as schools and daycare centers. Unlike a short-notice evacuation that seeks reductions in total evacuation time or personal property loss, a no-notice evacuation aims at maximizing the number of evacuees successfully escaping from the dangerous zones or minimizing total fatalities or injuries within a given time threshold (Chiu et al., 2006; is an index of pickup evacuees' origin nodes; j is an index of pickup evacuees' destination nodes; k is an index of current locations of facilities; l is an index of possible relocation sites for facilities; a is an index of time interval, a th ; x kl are binary integer decision variables. x kl = 1, if we assign facility k to site l; 0 otherwise; Ф is the average number of dependents a pickup evacuee gathers at a facility. Equation (1-1) calculates that the number of successful pickup evacuees for each i, j, l; p ijl S is the number of pickup evacuees (originating from i and evacuating to j) with dependent(s) relocated to l from all facilities before the last safe time interval, ijl A . Equation (1) determines the total number of successful pickup evacuees by summating p ijl S over i, j, l. Equation (2) requires the number of dependents relocated to possible site l to be no greater than facility l's capacity. The average number of dependents for a pickup evacuee is assumed to be the same over all of the facilities. Multiple intermediate stops for a pickup trip are not considered in this study; parents who have more than one dependent in the dangerous zone are assumed to have them in one facility. Equation (3) restricts the relocation site to a walkable distance (0.5 miles) from the original site. Equation (4) guarantees that a facility is assigned to one and only one relocation site. Facilities' current locations are also treated as possible relocation sites. Equation A ijl is an input to the optimization model and based on travel time from micro-simulation. Micro-simulation provides travel time of multiple paths for each OD pair; the path with the least travel time is assumed to be selected by pickup evacuees. Equations is the duration of a time interval (sec); ) ( E is the expected value of (sec). Equation Traffic Simulation Model Microscopic simulation outputs travel time among origins, destinations, and facility/relocation sites for the optimization model. Micro-simulation was chosen instead of simulation models on other levels, because it can model the road network in great detail, has the ability to model queues, and reflects the impacts of facilities' entry/exit configuration on travel time, which is crucial for the special case here. VISSIM, part of the PTV VISION traffic analysis package, was used in this study. VISSIM is a driver behavior based, second by second microscopic traffic simulation program, and developed to model major elements of transportation systems, such as lane configuration, vehicle composition, driver behavior, traffic controls and so on VISSIM's built-in dynamic traffic assignment algorithm was used to find routes for pickup evacuees. VISSIM accomplishes dynamic assignment procedures by iterated simulation runs. For each iterated run, drivers make decisions on route choice based on road traffic situations they experienced from the previous iterations. After multiple simulation runs, the iterations end when network traffic reaches stability, defined in VISSIM as when travel times or volumes do not vary significantly between two consecutive runs Framework The road traffic situation determines optimal relocation sites; reversely, relocation sites affect road traffic. In this study, relocation sites are determined by the optimization model and the network traffic is modeled using the simulation model, VISSIM. The optimization model uses travel time output from VISSIM, which assumes current facility locations as pickup points at the beginning. When the optimization model finds new relocation sites, travel time from VISSIM should be updated accordingly; as a result, these determined optimal sites may not be "real". In order to achieve "real" optimal sites, iteration between the two models is performed until convergence is reached. A procedure to accomplish this iteration process is shown in Figure 1 Flowchart of the Study In this procedure, first, the road network under normal conditions is simulated in VISSIM and normal travel times are achieved and adopted by the optimization model to be initial travel time. Then, micro simulation for emergency situations is iteratively executed with the optimization model until the termination criteria are satisfied, to determine optimal relocation sites. Facility current locations are set to be initial pickup locations; during each iteration, new relocation sites are found, and the travel time corresponding to those new sites is updated accordingly. The procedure follows the steps below: Step 0. Run VISSIM to gain travel time in a normal situation (without pickup evacuees considered). As VISSIM can only output travel time for those OD pairs with actual vehicles dispatched, we generate dummy trips for specific OD pairs to collect the travel times needed. a) Specify OD pairs we need to collect travel times for; b) Divide the simulation time period into several periods 1 ; for each period, generate one dummy vehicle for each specified OD pair, run VISSIM and capture OD travel times within that period; when all periods are completed, travel times for the simulation time period are captured; Step 1. Set current facility locations to be the initial relocation sites (i.e., kl x =1 for l=k; 0 otherwise); Step 2. Generate the pickup trip chain file based on { kl x }, and calculate ) (a ijk q accordingly; Step 3. Run VISSIM with the pickup trip chain file from Step 2 for emergency situations, and update travel times { ) (a il t } and { ) (a lj t } for l with kl x =1; Step 4. Calculate the last time interval that guarantees successful evacuation, ijl A , and obtain the number of successful evacuations S P for { kl x } based on ijl A and ) (a ijk q ; Step 5. Run the relocation optimization model based on updated { ) (a il t } and { ) (a lj t } from Step 2, and obtain new { kl x } and the objective value Z; Step 6. If the termination criterion is satisfied, output { kl x } and end the procedure; otherwise, replace { kl x } with { kl x } and repeat Step 2-6. The termination criterion is defined to be Z less than or equal to S P from the last iteration. 1 This divided time period is different with the time interval (a) defined in the optimization model. The time period is introduced here to achieve travel time in normal situations and the time interval (a) is defined to capture travel time in emergency cases, as road traffic under emergency is more dynamic than normal situations, the time period here is predetermined to be larger and broader than the time interval. In this study, a time interval is 2.5 minutes and a time period is 15 minutes. 3.4 Pickup Trip Generation Pickup trip generation includes determining: 1) the number of pickup evacuees (i.e., parents), 2) their origins and destinations, and 3) the time they arrive at the network. In this study, all dependents at facilities are assumed to be picked up by their families with private cars; no school buses or public transit are assumed to be available for pick up. Thus, pickup demand can be calculated according to the number of dependents in the facilities. This study focuses on day time evacuation, when household dependents are in facilities like schools or daycare centers and their parents are most likely at work or home. Pickup demand origins (i.e., where parents start at the moment of a disaster) follow a logical assumption by considering where the study area is located from a major business area, i.e., central business district (CBD). Pickup demand destination zones are selected by considering the spatial relations between the disaster location and pickup points. Pickup arrival time is assumed to follow the Normal distribution. Pickup demand in this study is assumed to be deterministic and does not change with road traffic. Different number of pickup demand and different arrival time distributions were tested as sensitivity analysis in Section 4.6. 19 Chapter Non-pickup Evacuee Estimation A no-notice disaster usually has immediate and severe consequences. In this case, people do not have time to consider whether or not to evacuate and when to evacuate; the most likely action they will take is following the evacuation guidance if available, or following most people's actions. So it is reasonable to assume that all people within the impacted area are evacuees and start evacuating at the time the no-notice disaster occurs. In this case study, ten internal zones are created and evenly distributed within the study area, thereby selected to be non-pickup evacuees' origins by equal chance; each zone has multiple connectors to the local road network. Eight external zones are defined and treated as possible destinations. Based on the assumption that most evacuees would choose near destinations rather than the others, probabilities of each destination chosen for each origin are estimated by assuming that approximately 70% of evacuees would choose close destinations and among alternative close destinations, each is chosen evenly. Pickup Evacuee Estimation Pickup evacuees originate from where they are at the moment of disaster occurrence, which could be either outside or inside the affected area. In this study, the affected area is assumed to be a 2 mile radius from the disaster location, thus pickup evacuees are most likely located outside the area. Here we assume 80% of them are outside the dangerous zone and 20% of them are inside when the disaster occurs. Pickup evacuees' trip distributions are estimated through different procedures for those originating from outside the affected area and those from inside. For those pickup evacuees originating inside the affected area, the departure time is assumed to follow a normal distribution with a mean of 5 minutes (after disaster occurrence) and a standard deviation of 1.25 minutes. Both origin and destination choice follow a uniform distribution; precisely, origins are assumed to be evenly distributed 23 among internal zones of the network, and destinations are assumed to be evenly distributed among external zones of the network. For those pickup evacuees originating outside the affected area, it is important to determine the time they arrive at the network instead of when they actually depart. Arrival time is assumed here to follow a Normal distribution with a mean of 20 minutes and a standard deviation of 5 minutes. (Other parameters for the Normal distribution are tested in Section 4.6 -Sensitivity Analysis.) Destination choice follows a uniform distribution. Origins are determined according to the assumption that 80% of pickup evacuees who depart from outside the affected area are from the Chicago CBD direction. As mentioned in the previous chapter, the number of pickup evacuees is determined by the total number of dependents in facilities. In this case study, there are totally 547 dependents. One pickup evacuee is assumed to be responsible for 1.11 dependents on average, i.e., Ф=1.11. In addition, the time required for a parent to find and pick up his/her dependents, µ, is assumed to follow a Normal distribution with a mean of 90 seconds and a standard deviation of 20 seconds. Other Assumptions and Modeling Considerations Other assumptions and modeling considerations employed in this case study include: The VISSIM simulation includes a 600-second warm up period, which is introduced to fill in the empty network at the beginning of the simulation in order to obtain realistic results. The whole simulation period is from 10:50 a.m. to 12:00 p.m., wherein 10:50 a.m.-11:00 a.m. is the warm-up period. A no-notice disaster is assumed to occur at 11:00 a.m., and an evacuation starts immediately. Travel time is updated every 150 seconds in VISSIM. Parents may arrive at relocation sites earlier than their children and have to wait for them. This waiting time is added to calculate departure time of the trip from relocation sites to destinations in the simulation part; and not accounted for in the optimization formulation because those parents arriving earlier most likely can successfully evacuate. Dependents in facilities are assumed to walk to relocation sites through the shortest path and not interfere with road traffic. Walking speed is assumed to be 3 mph. Capacities of facilities 1-3 are assumed to be 100, 500, 200 people; the capacity of each relocation site is assumed to be 500 people. These generous assumptions of capacity are made for the purpose that the results can reflect the impacts of the road network on the relocation strategy clearly. No other transportation modes (e.g., trains, buses or school buses) are considered for evacuation. No emergency plan regarding signal timing and right of way is executed. Result Analysis VISSIM uses random seeds to reflect stochastic variation of input flow arrival times 24 Several measures of effectiveness (MOEs) are selected to reflect the performance of the relocation strategy from the perspectives of the overall network, non-pickup evacuees, and pickup evacuees. MOEs include total travel time, average speed, total delay time and average delay time per vehicle for pickup evacuees, non-pickup evacuees, background traffic and the overall network. MOEs are measured over the time period [0, T 0 ]; time 0 is defined as the time of the disaster occurrence, which is 11:00 a.m. in this case study (the warm up period is not included for the strategy evaluation). Improvement of a MOE is formulated as Equation 25