Chapter 2: Model Description

Exhibit 1 shows the overall structure of the model. On the Web implementation of the model (go to the separate report, Mass Evacuation Transportation Model: User Manual), the user specifies a number of different inputs. Based on the specified inputs, the model determines where patients need to be transported and estimates how long it will take for the available vehicles to transport them to the receiving facilities. The output includes the total evacuation time, the number of round trips required for each vehicle type, and a graph of evacuation progress by patient type.

2.1. Inputs

Before the model can be run, several inputs describing the available resources, the facilities involved in the evacuation, and the scenario-specific inputs must be provided. The following describes each in detail.

2.1.1 Vehicle Inputs

The number and capacity of vehicles are considered to be the primary resources determining the eventual total evacuation time. In order to calculate evacuation time, the user must input the following information:

• Vehicle Type: The model assumes buses, wheelchair vans, BLS vehicles and ALS vehicles are used in the evacuation. If public transit buses and private coaches are both used to transport ambulatory patients, only one vehicle "type" should be entered using the average characteristics for both. Thus, vehicle types are roughly organized by the type of patient they are able to transport and do not reflect the specific models or ownership of the vehicles.
• Number of Available Vehicles: This number is the total number of vehicles of a single type that can be used for the evacuation. It may be that only a subset of the total emergency vehicle fleet could be used. If that is the case, then only those units that will be available during the evacuation should be specified.
• Capacity: This is the number of patients a particular vehicle is capable of transporting in one trip. The capacity number should not include the driver. The number should reflect a reasonable capacity under emergency conditions. Thus, a BLS ambulance might be able to accept two patients under emergency conditions even if one is recommended for normal use.
• Per Patient Load Time: The loading time is considered in the model. The loading time will obviously be shorter if the scenario assumes that patients are already in the hospital lobby or a nearby staging area (e.g., a parking lot) rather than still in their hospital room. The unloading time at the receiving facilities is assumed to be equal to the specified loading time.

2.1.2 Facility Inputs

For any facility, the following information needs to be input:

• Name: The name of the facility (e.g., "Westshore Hospital").
• Capacity and occupancy rate: For evacuating facilities, the capacity and occupancy together determine the total number of persons to be evacuated from the facility. For receiving facilities, these two numbers determine the number of persons that the facility can receive during the evacuation, although the user can also specify a surge capacity.
• Patient mix: The patient mix is the percent of patients or evacuees that can be transported by each vehicle type. For example, a hospital may have some ambulatory patients that could be transported on buses, some wheelchair bound patients who do not require additional care in wheelchair vans, some bedridden patients who need BLS transport, and ICU patients that require ALS transport. Patients are thus grouped by acuity rather than the specific diagnosis, and are prioritized to ensure that the most severely ill patients travel the least distance. The percentages must sum to a total of 100 percent. Facility patient mix of course varies daily, but an estimate must be input in order to estimate the evacuation time.
• Location: In order to calculate the transportation times, the location of each facility must be input. This location should be entered as a latitude and longitude. Transportation times are calculated based upon driving time and traffic conditions. For further information on the calculation of travel times, go to Section 2.2.1.
• Receiving/evacuation: The user must identify whether this is a receiving or an evacuating facility. Evacuees who cannot be transported to receiving facilities, because of capacity constraints, are transported to the "overflow facility" (go to Section 2.1.3).

2.1.3 Scenario-Specific Inputs

Additional inputs are necessary to characterize the scenario, including how many additional patients a facility can accommodate and whether the traffic routes are impaired. The scenario-specific inputs include those assumptions that are most likely to change from one run to the next. In order to view several evacuation time estimates, one can vary the following scenario-specific inputs:

• Surge capacity: The surge capacity input represents the percentage over normal capacity that a receiving facility could accommodate in an emergency. It is shown as a percentage because large facilities can typically accommodate many more individuals than smaller facilities. This factor is an important factor in determining evacuation times. If surge capacity within a city's facilities is only 5 percent, then the vast majority of evacuees might need to be transported to other cities, incurring hours of time for each trip and potentially increasing the evacuation time from hours to days. By contrast, a surge capacity of 15 percent could accommodate many more individuals within the system, thus reducing total evacuation times.
• Traffic congestion: It is expected that traffic congestion during an evacuation will be significantly higher than normal. The travel time estimator (go to Section 2.2) calculates an average driving time for normal traffic. This congestion multiplier allows planners to add additional time to each trip as a multiple of the travel time under normal traffic conditions. The travel time estimator also takes into consideration the population density of the metropolitan area where the facilities are located. The model is pre-loaded with population densities of all the Metropolitan Statistical Areas (MSAs).
• Location of overflow receiving facility: The model includes an "overflow" receiving facility that is used in the event that the specified receiving facilities do not have capacity to accept the patients from all the evacuating facilities. In reality, the overflow facility may represent an airport where patients are taken to be transported out of State. The user specifies the travel time to the overflow facility from evacuating facilities.

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2.2 Model Calculations

The model works by transferring patients between evacuating facilities and receiving facilities including overflow facilities. The model assumes a priority to how patients are moved, which is based on patient acuity—e.g., those requiring advanced ALS ambulance are transferred to the nearest facilities in order to avoid lengthy transfers for the sickest patients.

In order to calculate the estimated time required to evacuate all the patients from evacuating facilities, the model performs the following steps:

• Calculates travel time between all facility-facility pairs
• Assigns evacuees from evacuating facilities to receiving facilities based on patient priority
• Iteratively assigns vehicles to transport as available and tabulates total travel time and total number of trips per vehicle type.

These processes are described in more detail below.

2.2.1 Calculation of Travel Time

In order to appropriately determine the shortest evacuation time, travel time between all facility pairs is needed. In developing the model, we considered a number of options for handling travel time. One option we considered was to require inter-facility travel time as a user input, but when the number of facilities increases the number of travel times increases geometrically. With as few as a few dozen facilities, entering inter-facility travel time would simply be too burdensome to the user. Another option considered was to link the model to a Web-based real-time drive time calculator, such as Google Maps. We elected not to use this approach because we wanted to avoid linking the model to a service that, while currently free, may not be in the near future. In addition, this approach would have locked the model to a particular third-party vendor.

The project team instead developed an alternative approach that estimates inter-facility travel time based on the user-specified facility locations. Abt Associates teamed with the firm GIS Dynamics to create a database of driving times in 25 of the largest 50 metropolitan statistical areas (MSAs) in the United States, selected to represent a wide geographic diversity. In each of these MSAs, 16 geographically dispersed hospitals were selected as representative points and GIS Dynamics created a matrix representing the 120 unique travel times between each hospital-hospital pair. This database of 3000 travel time pairs was used to build our travel time model.

In order to determine whether geographical barriers contributed significantly to travel time, project staff categorized the 25 cities into those with or without significant geographical barriers (e.g., requiring travel via bridges) and those with and without grid-based road systems. Additional information on total population, population density, and land and water area was also collected for the analysis. All available variables (grid-based, bridge-dependent, population, land area, etc) were analyzed for potential contributions to regional variations in travel time.

Several model types were evaluated to determine whether a linear model or another model was the best form. A good fit was found with a spline model, which is characterized by two regions each with its own linear regression. It was found that within-city travel rates were slower than travel at the greatest distances within an MSA. This is likely due to highway travel once you travel greater than 50 miles from a city center. The city-specific variables of population, land area, and others did not affect travel times for large distances, highway travel being equivalent from one region to the next. However, the population density did have a very appreciable effect on shorter distances

A new travel time model was developed with these results in mind. A density-driven rate is applied to shorter distances while a lower non-density-dependent rate is applied to longer distances. The model is also constrained such that both regressions arrive at the same join point for each city. The new model was compared against the existing New York travel time database (obtained during project staff's collaboration with the City—go to Section 3) and the data for the 25 cities to ensure that residual times were as low as possible. This model now allows travel distances to be calculated for any location in the United States based upon a limited number of parameters.

2.2.2 Assignment of Patient Destinations

Before travel time can be calculated, evacuees must first be assigned a destination. This is done based on patient priority. Patient priority determines which patients (labeled by vehicle type) should be moved the least distance. Patients are then assigned by priority from facilities which are evacuating to the nearest receiving facility that can accommodate them. Receiving facilities are considered to be able to accommodate them up to their capacity (if occupancy rate is below 100%) and additionally up to the surge capacity percentage.

In some cases the surge capacity alone will not be sufficient to accommodate all evacuees. In this case the overflow facility is used. For instance, patients who need to be transported out of the city will be transported to locations greater than, say, two hours away. This will only occur after all receiving facilities have been filled.

The program loops through vehicle types, beginning with the first vehicle type listed by the user. The program first identifies all evacuating facilities that have patients who need transport by that vehicle type. Before it considers any other patients, the program assigns patients of that priority (such as patients requiring ALS transportation) to the nearest facilities that can accept them. This assignment follows its own rule. Starting with the list of evacuating facilities that have patients requiring that vehicle type, the program searches for the nearest facility that can accept patients from that evacuating hospital. This provides a one-to-one match between the list of evacuating facilities and the nearest receiving facilities. The program then finds which of these one-on-one pairs has the shortest travel distance, and it assigns patients for movement between that pair. The number of patients thereby assigned is the lesser of the number of patients in the evacuating facility and the number of available beds in the receiving hospital. The program decreases the number of patients in the evacuating facilities and the number of available beds in the receiving facility by this number. It then repeats the entire process until it has assigned all patients who require this conveyance type. When that condition is met, the program turns to the next conveyance mode until all patients have been evacuated. Note that the program assigns transfers; it does not actually move patients at this point.

2.2.3 Iterative Modeling

Once the travel time and allocation of evacuees is determined, the evacuation time can be calculated. At the beginning of the evacuation, vehicles are assigned to evacuating facilities. They each fill to capacity or to the number of patients available (whichever is less) using the loading time per patient that is one of the user inputs. Vehicles then transport these patients to the facilities assigned using the travel time. After discharging patients (including unloading time), the vehicle then returns to the evacuating facility and is available for reloading. Based upon the destinations for each patient, total required trips for each vehicle type are tabulated including the total time required for the trips. The total evacuation time is based upon the maximum total time for any vehicle type. Thus, if ALS vehicle transport takes more time than any other vehicle, then ALS total time is used for total evacuation time.

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2.3 Outputs

2.3.1 Total Evacuation Time

The primary output of the model is the total evacuation time, or the total time from the beginning of the evacuation until the last evacuee is on a vehicle for transport to a receiving facility. This result is given in hours.

In the model, total evacuation time is defined as the elapsed time from when the first patients begin loading on vehicles at evacuating facilities to when the last patient has been loaded on a vehicle at an evacuating facility. Total evacuation time includes (1) the time to load and unload patients from transporting vehicles and (2) round-trip travel time between evacuating and receiving facilities. Total evacuation time does not include:

• The time from when the evacuation decision is made to when the actual evacuation begins.
• The travel time from vehicle staging areas to an evacuation facility at the beginning of the evacuation process.
• The travel time for the last evacuated patient from an evacuating to receiving facility. In other words, the elapsed time for evacuation ends when the last patient is loaded on the vehicle at an evacuating facility. An alternative definition (not used in the model) would end evacuation time when the last patient arrives at a receiving facility.

2.3.2 Evacuation Time by Vehicle Type

The output also includes the time required to evacuate each type of patient. The Figure: Time to Evacuate shows an illustrative graphic of evacuation time by patient type. For example, patients requiring BLS transport will require roughly 65 hours to evacuate.

Figure: Time to Evacuate

Tabular Description of Information in Time to Evacuate

Patient or Vehicle Type	Hours
ALS	22
BLS	65
Wheelchair	30
Bus	10

Because a given patient can be transported on only one vehicle type, the total evacuation time is dependent only upon the evacuation time for the vehicle type that requires the most time. This evacuation time may be long due to small capacity (necessitating frequent trips), a large population of evacuees compared with the number of available vehicles, long distance per trip, long loading time, or other characteristics. Figure: Time to Evacuate shows the total evacuation time for each of the vehicle types. This will allow a user to see the bottleneck and potentially reallocate resources to mitigate the problem.

Another model output, which is highly correlated to the evacuation time by patient type, is the number of round trips made by each vehicle during the evacuation. As discussed below, ALS and BLS ambulances each had far more round trips than wheel chair vans or buses.

Users should run a model several times under different scenario conditions to observe the sensitivity of evacuation time to such characteristics as surge capacity, loading time per vehicle, traffic congestion, and other variables. We used this approach in New York City and Los Angeles, as discussed in the Appendixes 2 and 3.

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