Traffic Modelling

Within traffic engineering, there are four primary steps involved in traffic modelling: travel demand; trip distribution; modal split; and traffic assignment. Common methods used to model each of these steps as well as considerations that should be made in the context of modelling evacuations specifically are detailed below.¹⁵

Travel Demand

Traffic demand modelling is used to determine the traffic load on the transportation network. In the case of an evacuation, this relates to the number of people who will evacuate (trip generation) and when the evacuees will depart from their initial location (departure timing). For trip generation, the area/region that needs to evacuate must be determined followed by the number of people within that area who will evacuate (as opposed to staying-and-defending or sheltering-in-place). This determines the number of trips that will depart from an origin (a house, a neighbourhood, a city, etc.) and end up at a destination (generally represented using an origin-destination (OD) matrix). There are several different ways that trip generation can be determined, including descriptive models (regression analysis, cross-classification/category analysis, etc.) and random utility models.¹⁶

15 In the field of evacuation modelling, some steps have been researched more than others which will impact the level of understanding of these steps and the ability to accurately model them.

16 As trip generation is not something that needs to be determined via these means for the model of the case study conducted as part of this thesis, the details of these sub-models are not provided here. However, such details can be found in Ronchi et al. (2017) [25].

98 Evacuation participation and evacuation departure timing are generally modelled in one of two ways, sequentially or simultaneously [46]. The sequential approach separates trip generation and departure timing into two separate steps. Once the area to be evacuated is identified, the share of the people in that area who will evacuate is determined via descriptive or random utility modelling. The departure timing is then determined, often using varying forms of response curves (instantaneous departure, uniform distribution, Rayleigh distribution, Poisson distribution, Weibull distribution, sigmoid curve, etc.) which identify the percentage of departures in each time interval [46]. While a sequential modelling approach is used most often (due to its relative mathematical simplicity and less site-specific data requirements [172]), one of its main drawbacks is that there is no real behavioural basis on which to justify the response curves [46]. In contrast, a simultaneous travel demand model uses a repeat binary logit model to determine the share of people who will choose to evacuate and leave at that time or will postpone the evacuation decision.

This process is repeated multiple times at set intervals. The choice made at each interval is determined based on the differential utility associated with evacuating which is based on the prevailing conditions [46]. The factors discussed in Chapter 2 are examples of factors that could be chosen by modellers to impact the decision to evacuate.

Comparisons between the sequential and simultaneous modelling approaches have shown that the latter more closely represents observed evacuation travel demand behaviour as its flexibility allows it to estimate how evacuees respond dynamically to changes in hazard and road conditions as well as evacuation orders [46]. However, simultaneous models require more calibration and data. As such, the method chosen for a WUI evacuation model will depend on the purpose of a comprehensive evacuation model (real-time use, planning, etc.) and the corresponding time and data limitations.

99 Trip Distribution

Trip distribution modelling is used to represent how trips (or tours) are distributed throughout the transportation network, both spatially and temporally. This involves determining evacuees’ destinations and whether there will be sub-destinations within the overall evacuation.

The simplest and most popular approach to choosing evacuee destinations is to use proximity or other criteria such as destination attraction potential to assign evacuees to a destination [46]. This is generally done using gravity-based distribution, however, multinomial logit models can also be used [25], [65].

Depending on the purpose and number of trips taken by evacuees, either a trip-based or activity-based modelling approach can be used [25]. With the former approach, evacuees are modelled travelling directly from A to B (origin to destination – home to an evacuation shelter, home to relative’s house, fire station to a threatened neighbourhood, etc.). With an activity-based approach, intermediate activities are represented (travelling from office to school to home to evacuation shelter, etc.) and therefore tours, or chains of trips, are modelled. The approach chosen should therefore reflect the evacuation scenario that is being modelled (ex. evacuating during the middle of the night vs. mid-afternoon), keeping in mind the amount of time and computing power necessary to run the simulation.

Modal Split

Modal split determines which modes of transportation will be used during the evacuation (personal vehicle, public transportation, etc.). Many factors such as the characteristics of the disaster, the distance to safety, mode availability and access, evacuee location at the time of an event, and population groups can all impact the transportation modes used during an evacuation [65]. Given the characteristics of WUI fire evacuations, private vehicles and potentially buses are

100 the modes most likely to be used [25]. In addition to the type of mode, the number of modes used by a single household is also important as it can impact the number of vehicles in the transportation network during the evacuation.

There are various ways that modal split can be modelled. The simpler models estimate the mode choice independently of the other steps (heuristic and random utility models) [25].

Alternatively, integrated modelling simulates step choices (such as distribution and mode) simultaneously. While such models have the potential to provide a more accurate modal split, there is the potential to make assumptions which simplify the modelling process depending on the evacuation scenario being modelled (given the modes most commonly used during WUI evacuations).

Traffic Assignment

Traffic assignment modelling is used to assign evacuees to routes, thereby modelling route choice decisions [46]. Two of the primary factors involved in traffic assignment are how a route is assigned (static or dynamic) and when the route is assigned (pre-trip or enroute).¹⁷ When using static assignment, steady-state network conditions are assumed and assignment is based on a user equilibrium approach [25]. In contrast, dynamic assignment assumes that the system changes over time as a result of various factors such as the number of users in the network and path choices [173]. Dynamic assignment can use either a deterministic or stochastic route choice model, depending on the nature of the variables used.

Pre-trip assignment means that a route is assigned at the origin before the trip begins. In this case, either a single path from origin to destination is determined (fully pre-trip, with no

17 Others include capacity restraints, approach used for studying supply-demand interactions, segmentation of demand based on different user classes, and elasticity of demand [25].

101 changes made during the trip), or decision strategies for enroute choices are determined [173].

With enroute assignment, trip decisions are made during the trip based on information received while travelling. In both cases, trip decisions are made by considering the cost attributes (time, distance, financial cost, etc.) of different paths from origin to destination. To simulate these choices, random utility models, specifically deterministic or stochastic (probabilistic) choice models are used. With a deterministic choice model, travellers will choose the path that has maximum average utility (a path can only be used if the cost associated with it is the lesser of all alternative paths) [173]. A stochastic route choice model assumes that the perceived utility of a path is a random variable. Therefore, it expresses the probability that users will choose each available path [173]. Given that conditions can change quickly during an evacuation, a dynamic, enroute assignment approach is generally viewed as the best option.

Modelling Scope

The scope of a model, or the level of detail that can be simulated, should be determined based on the intended purposed of the model as the type of information obtained and the computational power/time required can vary greatly. The scope effects how vehicles are represented and how interactions between vehicles (and between vehicles and the network) are represented. There are three primary scales: macroscopic, mesoscopic and microscopic.

Macroscopic models use a fluid analogy approach, looking at parameters such as volume, speed, and density within a road section and the relationships between them [25]. At the other end of the spectrum are microsimulation models which represent the individual choices of each traveller (vehicle) and the interactions between different travellers and between travellers and the environment [25]. Different parameters can be assigned to each traveller (vehicle characteristics, driver reaction time and aggressiveness, etc.) and sub-models are used to model traveller choices

102 and interactions (car-following, acceleration/deceleration, lane-changing, etc.) [25]. Mesoscopic models combine some properties of micro and macroscopic models to create an intermediate scale of modelling. Packages of vehicles are modelled as opposed to individual vehicles and traffic flow is simulated based on the interactions between packages [25].