3.2 A Hybrid Systematic Simulation Tool
To explore system behavior, this study constructs a systematic simulation model to determine the causal relationship among fundamental factors in urban transportation system.
The proposed decision support model for simulating the effects of resource allocation policies on transport diversity can help planners decide when and how to invest transportation infrastructure and services.
3.2.1 Resource Allocation
Transportation systems consist of infrastructure, modes, and stakeholders. Different transport stakeholders with diverse demands have different needs for transportation infrastructure and services resulting in a diversity of needs. In fact, in transportation planning, transport policy-makers must simultaneously consider the trade-off between differences in the supply of transport infrastructure or modes, as well as the various needs of stakeholders. Feng and Hsieh (2009) suggested the concept of transport diversity, defined as different levels of satisfaction within stakeholder needs and measured using the variations in achievement among needs, to assess the performance of urban transportation system. Two approaches to improving transport diversity are goal setting (demand side) and resource management (supply side). If demand side parameters, such as classifications and expected goal values, are given, the critical issue for decision-makers is how to allocate finite available resources to realize greater transport diversity referring to more equitable achievement of stakeholder needs.
Resource management can improve transportation system performance by increasing resource quantity, capacity and utilization. Resource utilization is the main tool used to influence transportation performance, while the quantity and related capacity of resources are finite and either expensive or difficult to increase. Additionally, decision-makers can impact resource utilization via the strategies used to allocate resources among policies. Applying inappropriate investments to given stakeholder needs causes bias that reduces equity and wastes resources which could otherwise be utilized more efficiently (Shohet and Perelstein, 2004). Consequently, the efficient and effective allocation of limited resources among policies offers a realistic management opportunity for improving transportation performance.
Kuhn and Madanat (2006) proposed optimization models to deal with asset allocation of
the magnitude of maintenance and rehabilitation. Furthermore, Bigotte and Antunes (2007) compared the exact model and the heuristic methods, such as Genetic Algorithms (GA), Tabu Search, and a specialized local search heuristic, to illustrate the social infrastructure allocation.
Wang et al., (2007) proposed a GA model for equipment investment and allocation in portfolio planning. Moreover, Chu and Durango-Cohen (2008) introduced a time-series model named ARMAX to support the allocation of resources to preserve infrastructure facilities.
Withanachchi et al., (2007) assessed the impact of resource allocation on public health service provision according to the discussion of relationship among mortality rate, capital-stock, labor-stock and the patient characteristics. With data from the German economy, Conrad (2000) provided a comprehensive discussion of transportation resource allocation based on detailed microeconomic model. Resource allocation is often based primarily on the societal benefits of transportation infrastructure and service investment.
Resource allocation policies impact system performance. Gorman (2008) aimed that appropriately designed infrastructure allocation can decrease the cost and improves the quality of life since resource allocation policies direct influence on safety, environment and delays.
However, few studies have explored resource allocation policies because of the difficulty of designing, implementing, and quantifying system relationships due to associated uncertainty, feedback interaction, and complexity (Nguyen and Ogunlana, 2005; Kang and Jae, 2005). The design of resource allocation policies is complicated by iteration and delays in implementing allocation decisions (Udwadia et al., 2003). Iteration creates closed work flow in which interactive or interdependent relationships between parameters can be traced and checked for optional change requirement (Yeh et al., 2006).
3.2.2 Systematic Approaches
Resource allocation for systems in which diverse variables are linked by rich interactions offers various macro benefits (Simon, 1996). The interactions among system elements are crucial for understanding and managing the behavior and performance of transportation systems. However, effectively explaining and controlling system evolution over time is difficult (Lee et al., 2007). To overcome the weakness of traditional techniques, including the inability of traditional tools to explain compounding effects, as well as the inability to handle uncertainty, feedback loops, and iterative processes (Nguyen and Ogunlana, 2005), systems approaches, combining servo-mechanism thinking with simulation for systems analysis (Sterman, 2000), have been introduced to model complex and uncertain behavior and performance of systems (Alberts et al., 2004). Simulated outputs are inadequate for optimizing policy decisions but are considered useful for discussing allocation policies and performances. System dynamics, one of the primary established tools for system analysis, can address rationality in system management (Lane, 2000). Quantitative methods are adopted in
system dynamics; for example, the travel speed shown in Figure 3-1(A) is calculated precisely as trip distance divided by travel time. This method enables decision-makers to understand the influence on transport diversity of specific policies and external characteristics, such as population, income and strategy delays.
A B
C
Trip distance
Travel speed
System Dynamics (quantitative method)
Safety
Cognitive Maps (qualitative method)
Travel time
Driver behavior
Trips
Travel cost Accessibility
Sensitivity Model (semi-quantitative method)
FIGURE 3-1 Torn system approaches
However, the precise relationships between factors might be unavailable owing to the complexity of systems (Stylios and Groumpos, 2000; Chan and Huang, 2004). Cognitive maps are introduced to solve the problems of qualitative factors and linkages. System dynamics modeling emphasizes process, data and exact cause-effect relationships, whereas cognitive maps imply that decision-makers make sense of reality and decide what they should do to forecast how the world would be more preferable in the future (Eden and Ackermann, 2004). For instance, the impacts of driver behavior and travel speed on safety, shown in Figure 3-1(B), are identified via the qualitative cognition of experienced experts. Cognitive maps are employed to resolve conflicts, establish brainstorming, and assist negotiation (Pidd, 1996). Moreover, Kwahk and Kim (1999) identified the characteristics of cognitive maps as:
understanding causal relationships, promoting the identification of opportunities and threats, and facilitating system thinking. A major difficulty of cognitive maps lies in determining relationship intensity with a qualitative feature reflecting the cognitive condition of individuals, something which cannot be directly measured. Some researchers indicated relationships using weighted connections, i.e. simple additive weighting (SAW) and analytic hierarchy process (AHP) (Georgopoulos et al., 2003; Kwahk and Kim, 1999). Carbonara and Scozzi (2006) suggested that a collective map representing the consensus of all the stakeholders should be created by analyzing the maps of participants in a decision-making group. Besides, Kang et al. (2004) proposed that the relationships could be derived via a statistical approach.
The most severe challenge of the cognitive maps refers to the algorithm of multiplying
an input vector with an adjacency matrix. This implies that the relationships between all factors are linear and addible while the impact intensions are constant. The sensitivity model developed by Vester and von Hesler (1982) is thus employed, which includes system thinking, fuzziness, and simulation of semi-quantitative data. The sensitivity model focuses on pattern recognition and feedback mechanism rather than mono-causal relationship and enabling analysis of complex systems possible via fuzzy logic, which provides a systematic method in which systems can be understood without detailed precision but accurate ordinal parameters (Chan and Huang, 2004). The relationship between variables is identified as the adjustment factors provided by the Transportation Research Board (2000). For example, variation in trip patterns over time, indicated in Figure 3-1(C), is influenced by the levels of cost, accessibility, safety and speed via a semi-quantitative connection. Consequently, to obtain different kinds of relationships that fit real world situation, a hybrid model integrating system dynamics, cognitive maps, and sensitivity model is described in the future.
3.2.3 Decision Support Model
A decision support model is developed to help decision-makers understand system behavior and make investment decisions in relation to urban transportation systems. The decision support model is suitable for any spatial scale considered a holistic system of transportation planning regardless of individual stakeholder needs. The Taipei metropolitan area, the largest in Taiwan, provides the empirical study to discuss the managerial implications of the model. Moreover, owing to the dynamic interactions between the various transportation system elements, systems seem to be misinterpreted by excessive insistence on a specific sector without consideration of the inter-relationships. Therefore, the simplified interactions in the urban transportation system are represented in Figure 3-2. The model comprises various variables and equations and is first divided into four subsystems, namely MRT, bus, passenger car and motorcycle. These subsystems are interrelated via shared parameters, for instance, congestion, safety, and so on. A feedback system is then constructed with all of the variables and connections. Furthermore, the subsystems of pedestrians and bicycles, paratransit (taxi and demand response transportation) as well as parking and the land use patterns are assumed as the external environment.
FIGURE 3-2 Simplified interaction in the urban transportation system.
The structure of the MRT subsystem (Figure 3-3) describes both the supply of MRT infrastructure and the needs of MRT users. The crowd phenomenon and subsidy strategy involve two balancing feedback loops, whereas MRT line construction reduces crowd size.
On the other hand, there are several growing feedback loops involved in stakeholder needs.
The common management instruments for attracting people from other modes, such as infrastructure investment, pricing and subsidy, are taken into account in the subsystem.
The feedback structures of other subsystems, shown in Figure 3-4, resemble the MRT subsystem described above. The subsystems are capable of self-adjustment because of the negative feedback loops. The negative feedbacks also make the subsystem independent from quantitative growth. Moreover, these subsystems consider that the policies suggested by European Commission (2006), including infrastructure building, road space allocation, pricing, subsidy, regulation, and tax and fees, are used to improve urban transportation systems. The model maps the cause-effect of stakeholder behaviors in transportation systems and policies employed to allocate resources. The interactions among the components represent the use of information and managerial policies to impact system progress.
MRT trips
ability to use -MRT
: a causal relationship with + (-) signs indicating a positive (negative) effect // signs on the arrows represent the delay effect
: variables reflecting stakeholder needs; : policy variables
FIGURE 3-3 Feedback structures in MRT subsystems
This study utilizes experimental approaches to examining the relationships between resource allocation policies and transportation system performance are utilized in this study.
Individual relationships are specified with simple algebraic formulations indicating the interactions among factors. Many critical inputs are obtained by data mining and expert discussion during pattern identification, model construction, and system simulation. Open participatory meetings emphasize communication, cooperation and compromise among different participants with the objective of building consensus regarding system behavior.
These experts fully understanding the information of transportation in Taipei metropolitan area, including the planners, government and scholars, are invited to build consensus. This process is relatively time consuming but provides a significant incentive for group learning.
The bus subsystem
-The car subsystem The motorcycle subsystem
travel speed
: a causal relationship with + (-) signs indicating a positive (negative) effect : variables reflecting stakeholder needs; : policy variables
FIGURE 3-4 Feedback structures in subsystems
The decision support model integrates the algorithms of system dynamics, cognitive maps and sensitivity model. Different equation types are applied to distinct interactions according to the various attribute linking different elements. For example, the MRT accessibility in Figure 3-3 is defined as the ratio of the population served by MRT and feeder buses to the total population. This is a precise quantitative relationship and represented by Eqn. 3-3, in which the service population of MRT is related to the length of MRT lines and feeder buses routes (Eqn. 3-13). This study explores the connections among the metadata from geographic information system (GIS), such as resident population served by MRT and length of MRT lines and feeder buses routes, through regression model. The analytical results reveal that a non-linear regression model, particularly a logarithm regression model (shown as Eqn. 3-14), has a better goodness of fit and the coefficient b is statistic significant at level 0.05.
∑
For example, the coefficients of the function for determining the impact of length of MRT lines on MRT service population are estimated as a=−3.775 and b=1.141. The estimated coefficients illustrate a concave downward increasing function which provides a reasonable explanation for decreasing increment of service population due to extended MRT lines. The R2 of
g
MRT(L
MRTt ) achieves 0.92.Additionally, some linear addible parameters without precise connection are simulated in the form of cognitive maps. For instance, the initial value of universal station and universal train in Figure 3-3 are evaluated via Eqn. 3-12. However, it is difficult to obtain the exact relationships among level of universal design, crowded system and the ability for user taking the MRT. The experts invited to discussion constructed consensuses on influences in Eqn.
3-15 as
β
1 =0.6,β
2 =0.75 andβ
3 =−0.8.To transfer the ability for user taking MRT to a feasible domain, this study employs a threshold function to filter insignificant values. The filtered ability for user taking MRT determined as Eqn. 3-16 is applied in following iterations.
MRT
Besides, the operation of sensitivity model is applied to formulate some interactions that acted as the adjustment coefficient. For example, Figure 3-3 shows that MRT trips are impacted by MRT accessibility, affordability, crowdedness, and ease of use, and presented as Eqn. 3-17.
∏
× −The functions of these adjustment relationships are defined such that the vertical axis is the status value of the influencing variable and the horizontal axis is the influence level of adjustment factor on affected variable. For instance, participants built consensus that MRT accessibility positively impact on MRT trips in the expert meeting, as well as the comment agreement of threshold accessibility level and influence intensity. Figure 3-5 illustrates the adjustment function which is similar to S-curve and indicates that the variation of impacts turn into slightness if MRT accessibility places on extreme values. When the status value of MRT accessibility exceeds 0.8, the increment of MRT trips is approximately constant. While the value of MRT accessibility is greater than 0.75, MRT system can positively attracts trips from other modes. The value of MRT trips diminishes exponentially when MRT accessibility is small than 0.7. Different algorithms are applied to the distinct relationships between factors in a holistic system to establish a decision support model that creates realistic and complex behavior in spite of the simplicity of the equations.
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