Motivation

Understanding vehicular moving behaviors provides the fundamental rationales for planning, designing, controlling and managing the road systems.

In order to avoid the time- and money-consuming field observations, numerical implementation can be used as an efficient instead for providing precious reference and guidance. Therefore, along with the rapid progress of digital technology since early fifties, numerous traffic simulation models have been plentifully proposed.

Generally, existing traffic models can be roughly separated into three branches; depending on the level of detail or resolution of traffic been derived—macroscopic, microscopic and mesoscopic models. The coarsest ones are the macroscopic models which include the traffic flow models and fluid-dynamical models. Traffic flow models analyze the relationships between speed, density and volume (May, 1990). Fluid-dynamical models, on the other hand, analogize vehicular flow to fluids and assume that aggregate behavior of drivers is dominated by the surrounding traffic conditions. Lighthill and Whitham (1955) and Richard (1956) developed the most prominent one-order fluid-dynamical models. Subsequently, high-order fluid-dynamical models were developed by other researchers; for example, Payne (1971), Liu et al (1998) and Zhang (1998).

The microscopic traffic flow models, in contrast, describe the interaction between individual vehicle and other vehicles. Car-following models are the most pertinent models to explicate the one-dimensional movements in a longitudinal lane such that the following vehicle adjusts its speed to maintain desirable or safe distance headway to the lead vehicle. Stimulus-response models are perhaps the most prominent models developed in the 1950s and 1960s by the General Motors (GM) research group, because the same principles is still being applied and/or extended nowadays by scholars worldwide, for example, that by May (1990), Brackstone and McDonald (1999), Lan and Yeh (2001), etc.

The third branch, the mesoscopic models, serves as the linkage to fill the gap between the aggregate level approach of macroscopic models and the

individual viewpoint in the microscopic ones. Mesoscopic models aim to describe the behavior of small groups of vehicles. Examples of these models are the cluster models, gas-kinetic models and the cell transmission models.

Prigogine & Herman (1971) proposed the kinetic equation of vehicular traffic and summarized the possible alternate forms of the relaxation term.

Hoogendoorn and Bovy (1999) proposed a traffic flow model describing multilane heterogeneous (i.e. unconstrained and constrained) traffic flow.

Various kinetic models were subsequently proposed by many researchers, such as Paveri-Fontana (1975), Phillips (1979), and more recently Nelson (1995), and Nelson and Sopasakis (1998). Daganzo (1993, 1994) proposed the cell transmission model (CTM model for short) and since then have been popularly utilized for traffic simulation.

Recently, various CA models that can be categorized as one branch from the microscopic perspective have been developed to describe the phenomena of real traffic flows with complex dynamic behaviors, owing to their capacity for reflecting complicated traffic patterns via comparatively concise numerical algorithms. Nagel and Schreckenberg (1992) proposed their famous pioneer model (referred as for NaSch model hereinafter) to reproduce the basic features of real traffic. In their model, the road is divided into squared cells of length 7.5 meters. Each cell can either be empty or occupied by at most one car (i.e., the size of a car is viewed as one cell). Space, speed, acceleration and even time are treated as discrete variables. The state of the road at one certain instant is derived from one time-step ahead by applying acceleration, braking, randomization and driving rules for all cars at the same instant (i.e., parallel dynamics). Obviously, such a coarse description is an extreme simplification of real world conditions; therefore, a considerable number of modified NaSch models has been developed in the past decade. For instance, Nagel (1996, 1998) employed the concept of stochastic CA and treated each particle with randomized-integer speed between zero and maximum speed. Rickert et al (1996) examined a simple two-lane CA model and pointed out some important parameters that define the shape of the fundamental diagram (flow-density);

Chowdhury et al (1997) generalized the NaSch model by introducing a particle-hopping model for two-lane traffic with two different vehicle speeds (fast and slow); Barlović et al (1998), in contrast to the constant randomization in the NaSch model, introduced a velocity-dependent randomization (VDR) parameter. Although the VDR model is a simple generalization of the NaSch

model, it is capable of revealing some complex traffic dynamics, i.e., the existence of wide phase separated jams and metastable free-flow states. Nagel et al (1998) further proposed different CA rules to govern vehicular lane-change behavior. More Recently, Boris Kerner (2002, 2004), a German traffic physician, introduced a three-phase traffic theory that consists of free flow, synchronized flow, and wide-moving jam phases. The latter two phases exist in congested states in which downstream front of the synchronized flow phase is often fixed at a bottleneck while the wide-moving jam will propagate through the position where bottleneck locates. To explore the emergence of such traffic patterns, Kerner and partners tried to describe the complex spatiotemporal behaviors based on empirical freeway traffic analysis. (Kerner et al, 2004)

Over the years, most conventional CA models were developed for depicting the traffic phenomena on freeways. However, most of times these models were limited to the simulation of pure traffic scenarios in which vehicles have identical size. Few has been devoted to the analysis of urban traffic such as mixed traffic that is comprised by vehicles in various sizes; such as heavy vehicles (e.g., bus, truck), light vehicles (car) and of course, smaller two-wheel ones (motorcycle, bicycle). It is evidenced that the coarse cell system in existing CA models makes it extremely impossible to reflect various vehicle sizes and the slight speed variation of vehicles on urban streets. Thus inevitably refined cell system must be established beforehand if one ever tries to successfully simulate the urban traffic.

In addition to the refined cell system, some unique behaviors must also be scrupulously considered in places where both cars and motorcycles are introduced. Unlike heavy or light vehicles that normally move within a specific longitudinal lane and sometimes change lanes for overtaking or turning, motorcycles do not move in a specified lane. As the result, conventional flow models may not satisfactorily elucidate the motorcycles’ moving behaviors.

Because motorcycles are the most popular transportation mode in Taiwan as well as in some other Asian countries, it is important to gain better insights of the motorcycles’ moving behaviors, from both academic and practical perspectives.