In the following contents, the definitions of WTW and SA are made for the following analyses. The previous literature is reviewed to address the issues and to aid to conclude principles for modeling and experiment design. The parameters used in agent-based modeling are also illustrated in this chapter.
2.1 Walking accessibility and mobility measures
In term of transportation, “accessibility” can be defined as: The means by which an individual can accomplish some economic or social activity through access to that activity (Meyer and Miller, 2001). Howard (1902) initially set walking accessibility measure as a half mile; Perry (1929) used a quarter mile (5-minute walk) as the radius of a neighborhood unit; and in Sweden it was set as a range of about 300~500m (Lynch and Hack, 1984). The characteristics of the pedestrian, e.g., trip purpose, gender, and age, and urban context may alter the acceptable distances (Clifton and Krizek, 2004). For example, Pushkarev and Zupan(1975) compared the cumulative distribution of walking distances for a trip at two Manhattan buildings. They found that trips to eat had the shortest walking distance and that shopping trips had the longest ones among five purposes (eat, work, pleasure, business and shop). However, to-date few studies have explored the variation in walking distance and its implication for pedestrians.
A useful method to express the variability of walking distance is the statistical distribution.
As mentioned earlier, Pushkarev and Zupan(1975) applied this method to analyze walking distances. Seneviratne (1985) observed the distribution of walking distances by conducting a survey in the central business district of Calgary, Canada. It is worth noting that Seneviratne (1985) derived the critical distance of 243m (796 ft), at the maximum rate of change of the distribution function as the more reasonable estimate for the average walking distance of 250m (819 ft). This advanced application of statistical frequency for estimating walking distance inspired our later analysis.
“Mobility” can be defined as: The ability and knowledge to travel from one location to another in a reasonable amount of time and for acceptable costs (Meyer and Miller, 2001).
For pedestrian, mobility indicator can be mean walking speed and acceleration. For example, Henderson stated that the desired speeds can be represented as a Gaussian distribution at 1.34±0.26 m/s (mean±standard deviation) (Henderson, 1971). Willis et al. calculated their observations and found that the data are distributed normally at about 1.47±0.299 m/s
10
(Willis et al., 2004). Imms and Edholm found that the mean speed of the elderly (60-99 years old) is about 0.74±0.29 m/s (Imms and Edholm, 1981). Rouphail et al. (2000) stated that if the elderly constitute more than 20 percent of the total pedestrians, the average walking speed would decrease to 0.9144 m/s (3.0 ft/s).
In short, walking mobility is the important characteristic that reflects age and health conditions. Studies have focused on accessibility and mobility measures, but the difference in mobility is rarely taken into account in public space design. This issue will be highlighted in the coming decades, because population rapidly ages in the most of developed countries.
2.2 Definitions of willingness to walk
This research defines willingness to walk (WTW) as a quantity that represents how much effort pedestrians are willing to spend to arrive at their destination. The following are some pertinent characteristics of WTW. First, WTW is associated with individual characteristics and the purpose of the trip (Clifton and Krizek, 2004). Second, the estimate of WTW varies depends on the estimator. A planner may estimate WTW from a different perspective than a user who must decide if s/he should make the trip or not. The discrepancy between these two estimates usually results in the planner’s estimate not fitting that of the average user (usually too far for the user), and consequently the facility shows a low usage (Fruin, 1971).
Third, WTW can be estimated using various measures. It has been estimated with distance and time (Howard, 1902; Perry, 1929). However, walking time is more suited to a self-reporting survey, because respondents can recognize time spent, but not distance traveled. Other studies looked at WTW in terms of how often people intend to walk. For example, Untermann (1984) proposed a negative exponential distribution to illustrate the relationship between frequency and walking distance, where about 70% of the people are willing to walk 500 feet, about 40% are willing to walk 1000 feet and only about 10% are willing to walk half a mile. A similar opinion can be found in Fruin(1971) and Gehl(2001).
In addition, variations in walking distance or time spent walking are also important when assessing the need for improving street amenities. Nevertheless, this issue is rarely discussed in the literature.
2.3 Street amenities
The attributes of PEQ often include safety, comfort, attractiveness, and convenience and are associated with several street amenities (or elements), as summarized in Table 1(Fruin, 1971;
Mitra-Sarka, 1994; Untermann, 1984). A higher level of street amenity will increase street space quality and give pedestrians a better walking experience. For example, a street with
11
good lighting will reduce “fear”, a significant factor leading to a higher HR. Thus, energy will be expended at a lesser rate. If a pedestrian is used to expending a certain amount of WEE, his/her distance can be extended by improving the PEQ of the street.
Table 1 Attributes of pedestrian environment quality and their corresponding street amenities (source: Mitra-Sarkar, 1994; Untermann, 1984).
Attributes Description Amenities
Safety Prevent conflicts and crime from vehicles or other activities through separation or
protection
Sidewalk, lighting, signage
Comfort Provide pedestrians protection from inclement weather by means of air and temperature control, protection from wind, rain etc.
Roadside trees, benches, arcade, pavement
Attractiveness Attract pedestrians by the aesthetic
arrangement of urban space, colorful design and visual diversity
Shop windows, retail activities, public art
Convenience Reduce travel distance, enhance continuity of travel, and ensure good intermodal connection
Distance, pedestrian bridge, underground
passages/walkways
There are seven physical attributes to represent SA: right of way, lighting, planting, street furniture, pavement, retailing, and fountains, as shown in Table 1. Although other attributes have been mentioned in previous studies, it is those selected that form a basic street space and significantly affect users’ behavior (Alexander, 1974; Appleyard and Lintell, 1972;
Booth, 1983; Fukahori and Kubota, 2003; Gehl, 2001; Harris and Dines, 1997).
2.4 Variation to willingness to walk
Environmental factors will affect the WTW. Weather is a critical factor (Pushkarev and Zupan, 1975; Zacharias, 2001), but so is the design of the pedestrian environment. In turn, a higher WTW can be considered as an effect of improved amenities from improvement projects. Studies have found that the average acceptable walking distance can be readily be extended by creating a pleasant environment in the urban space (Lövemark, 1972;
Untermann, 1984), as shown in Figure 4. It should be noted however that the environmental effect has limits. The upward trend tends to peak at the greatest distance people are willing
12
to walk. In addition, the downward trend has a boundary as well, such as a bad street space where most pedestrians will not walk regardless of how short the distance is.
Figure 4 The trade-off between walking distance and the quality of pedestrian environment. μ is denoted as “environment impedance” the inverse of pedestrian environment quality.
2.5 Physiological effects
In the following, I argue that energy can be another measure of WTW. Energy expenditure is an important aspect of physiology. To measure WTW with energy, I must look toward the fields of exercise physiology and psychophysiology linking psychological perception and physiological response. The energy expenditure studies in exercise physiology have focused on specific groups (such as soldiers, people of a certain age group etc.), moving status (such as the walking speed), and the working environment (such as a moving platform to simulate ship motion) (Bastien et al., 2005; Demczuk, 1998; Heus et al., 1998; Rose et al., 1991).
Methods to record EE often include the doubly labeled water technique, pedometers, oxygen consumption (VO2), carbon production (VCO2) and heart rate (HR). Among those, HR indicates the rate of oxygen consumption which relates linearly with HR (McArdle et al., 2007, pp. 206). It shows a close estimation and provides an affordable way to obtain reasonably accurate data in freely moving subjects (Spurr et al., 1988). Thus, this research uses HR to measure WEE.
Another question is how PEQ affects WEE through psychological perception. According to studies of psychophysiology, the effect from psychological perception can be observed by physiological measures, such as HR (Andreassi, 2007). HR indicates the arousal of the sympathetic nervous system (SNS). When a person walks on a street s/he perceives the PEQ,
13
and this perception produces a specific emotion. This emotion causes an arousal of the SNS.
Psychophysiology studies found that a negative mood state (such as fear) significantly increases a person’s HR, thereby increasing energy expenditure at the same time. In contrast, a positive emotion, such as a pleasant feeling, will result in lowering the HR (Levenson et al., 1990). Since a good street environment results in pedestrians having a positive emotion, they spend less energy while walking.
2.6 Agent-based model in the dynamic pedestrian research
An ABM involves both the model and the simulator to observe the effect on the system of the interaction between agents as well as the interaction between agents and the environment (O’Sullivan and Haklay, 2000). The ABPM is one of the ABMs for pedestrians.
Its strength lies in the use of fine-scale data and the “bottom-up” prediction (Bonabeau, 2002). Traditionally, the transportation models used the data scale to study pedestrians, but they focused more on O-D pair analysis and used a higher scale than the scale for walking (Batty, 2001). The traditional prediction models are aggregative and built with “top-down”
thinking, while the emerging notion of prediction turns to the “bottom-up” thinking, where observed events are collected and to allow the development of superior systems. Thus, pedestrian movements can be simulated to predict a more global structure from the local action and reflect the actual characteristics of the local environment (Batty, 2005).
One issue when building an ABPM is how to choose a suitable scale for the spatial data.
The types of spatial data in an ABPM can be categorized as discrete or continuous. Cellular automata (CA) is a widely-used discrete type ABPM and its successful application can be found in Batty (2005). Continuous spatial data can be found in studies using Cartesian coordinate system, like Helbing et al. (1995) or in flow analyses. The former marks space and location in a grid and may be too rough to observe any local congestions or the performance of the design. Therefore, continuous data is preferred in the present study.
Agents, the environment and rules are the three components of the ABPM simulator (Epstein and Axtell, 1995). An agent of a pedestrian is coded by giving it human dimensions and behavioral characteristics, such as walking speed, body depth, shoulder width and personal space (Fruin, 1971). The range of these characteristics is large. Measures also vary across social factors and culture, and thus behavior characteristics should be surveyed to ensure they fit the local environment (Hall, 1966).
Environment in an ABPM refers to the artificial world for space and facilities. Recently, bottlenecks, room and channel have been simulated to observe the effects of geometrical
14
form (e.g., funnel), behavioral characteristics (e.g., visual perception) and collective behavior (e.g., lane formation) (Helbing et al., 2001; Turner and Penn, 2002; Isobe et al., 2004). It was found that the geometrical form of the design significantly affects a system’s performance. This finding indicates that congestion can be improved.
The behavior of agents is governed by a set of rules or a strategy. Maximizing utility and minimizing cost are often applied to analyze route choice (Antonini et al., 2006;
Hoogendoorn and Bovy, 2005). Other objectives like minimum energy expenditure or keeping a desired speed, can be developed as strategies (Hsu and Tsai, 2010). Rules and strategies must be designed to fit the environment, because agents act for specific purposes.
In this study, pedestrians pass each other in corridors by changing direction in order to bypass slow-walking pedestrians. This strategy can maximize spaciousness and it is discussed in the next section.
Applying an ABPM for a pedestrian corridor design is rarely found in the literature. The most relevant issue is the analysis by Helbing et al. (Helbing et al., 2005). They applied their “social force model” to the analysis of improving walkways, bottlenecks and intersections. They found that a series of columnar objects, e.g., a railing or a row of trees, in the middle of a road can stabilize a lane or a tunnel where impatient pedestrians try to overtake one another but are obstructed by the opposite stream. They also found that a funnel-shaped design can improve a pushy crowd. However, they did not offer any suggestions for dealing with the substantial difference in mobility, nor did they take the effect of reducing the effective width of the corridor into account.
2.7 Summary
In this chapter, I have reviewed the literature of WTW. This thesis integrated the statements from the published studies to make the rigorous definition to illustrate its relationship with street amenities. The previous studies mostly agree that better SA can enhance WTW within a range, but we need empirical evidences to conduct the following analyses. That is because only when the linearity between SA and WTW is ensured, the analyses and prediction can be conducted with Pandolf et al. and discrete choice models I used.
The characteristics of ABM are also reviewed to aid the following study. I first highlighted the advantage of ABM for the dynamic characteristics of pedestrians. The components of ABM generally include rule, scale and parameters. The third is important for the following ABM simulations, because the corridor is designed to reflect a population aging society. By these parameters, the following simulations can be conducted close to the real world. This
15
idea may not be new; in particular ABM recently receives much attention. However, its application for space design by comparing the mobility performances may be a new creation.
16
Walking primarily costs the pedestrian time and physical effort (Pushkarev and Zupan, 1975), and a typical measurement of physical effort is energy expenditure (EE) (McArdle et al., 2007). Let’s introduce a “work” type equation, (1), to illustrate the process of EE:
t dt amount of energy s/he consumed is about ew. If street environments can be categorized by street types, then equation (1) can be rewritten as: walking at a constant velocity v for a period of time t on a type p street; and μp is the friction on a type p street. If we sum the energy consumption for each type of street, then we get the total energy consumption ew. It is evident that there is a trade-off for the pedestrian between s and μ under a given EE, as shown in Figure 3.Pandolf et al. (1977) illustrated a WEE model from a physiological perspective:
/
( )(1.5 0.35 ) where W is the metabolic rate or energy expenditure per second (J/s, watts) ; m is the body weight (kg); l is the load carried (kg); v is the velocity (m/s); G is the grade (%); and n is the terrain factor or friction. To determine the total amount of WEE, the metabolic rate needs to be multiplied by the walking time t:t W
ew (4) where the unit of ew is in joule(J). Hall et al. (2004) compared the published energy expenditure models, and found that the prediction of Pandolf et al.’s model (1977) is very