1.1 Background
Cellular automaton (CA), a newly developed microscopic traffic stream modeling approach, is a powerful tool to describe the phenomena of real traffic flows characterized with complex dynamic behaviors. Different CA models have been developed to describe the basic phenomena of real traffic flows characterized with complex dynamic behaviors over the past two decade. Nagel and Schreckenberg (1992) proposed a minimal model (hereafter NaSch model) of vehicular traffic on idealized single-lane highways to reproduce the basic features of real traffic. In NaSch model, the road is divided into cells of length 7.5 meters.
Each cell can either be empty or occupied by at most one car. The space, speed, acceleration and even the time are treated as discrete variables. The state of the road at any time-step can be obtained from that at any one time-step ahead by applying acceleration, braking, randomization, and driving rules for all cars at the same time (parallel dynamics). Obviously, such a description is an extreme simplification of the real world conditions. Therefore, a considerable number of modified NaSch CA models have been extended.
For instance, Rickert et al. (1996) examined a simple two-lane CA model and pointed out important parameters defining 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) introduced a velocity-dependent randomization (VDR) parameter, in contrast to the constant randomization in the NaSch model. The VDR model is a simple generalization of the NaSch model leading to a completely different jam dynamics, i.e., the existence of wide phase separated jams and metastable free-flow states. Wang et al. (2000) introduced Fukui-Ishibashi (FI) model to investigate the asymptotic self-organization phenomena of one-dimensional traffic flow. From the point of view of practical applications, modeling vehicular traffic on multi-lane highways are more relevant than that on idealized single-lane highways, which are, nevertheless, interesting from the point of fundamental understanding of true non-equilibrium phenomena in driven-diffusive lattice gases (Chowdhury et al., 2000). Rickert et al. (1996) examined a simple two-lane CA model and pointed out
(1998) proposed a simple lane-change model — if vehicles are fulfilled both incentive criterion and safety criteria, they will change the positions to the available adjacent lane(s).
Using CA simulations to explore the formation of traffic patterns, including the vehicular trajectories, flow-occupancy fundamental diagrams, spatiotemporal traffic features associated with stationary and moving bottlenecks, among others, is a challenging task. But it can provide with more insightful information to help understand the formation of traffic phenomena so as to evaluate the effectiveness of any promising control or management tactics. Many scientists have been searching for the fundamental principles governing the dynamics of traffic flow. Treiterer (1975) used a series of aerial photography to analysis phantom jams, which may be induced due to spontaneous velocity fluctuations or lane changes. Hermann and Kerner (1998) applied CA technique and self-organization process to explore the formation of traffic congestion. Knospe et al. (1999) dealt with the effect of slow cars in two-lane systems and found that even few slow cars can initiate the formation of platoons at low densities. Wolf (1999) employed a modified NaSch model to address the metastable states at the jamming transition in detail. Research to improve the behavior of CA models by finer discretization of cells was carried out by Knospe et al.
(2000). Pottmeier et al. (2002) studied the impact of localized defect in a CA model for traffic flow exhibiting metastable states and phase separation. Kerner (2002; 2002; 2004) introduced a three-phase traffic theory which consists of free flow, synchronized flow and wide moving jam phases. The later two phases exist in congested states where downstream front of the synchronized flow phase is often fixed at a bottleneck but the wide moving jam will propagate through the spatial locations of the bottleneck. To explore the emergence of such traffic patterns, Kerner and partners have shown complex spatiotemporal behaviors based on empirical freeway traffic analysis. (e.g., Kerner et al., 1996, 1998, 2002, 2004).
Bham and Benekohal (2004) developed a high fidelity traffic simulation model based on CA and car-following concepts, which had been satisfactorily validated at the macroscopic and microscopic levels using two sets of field data.
Most of the aforementioned conventional traffic flow models are based on the assumption of the homogeneity of traffic flow. In addition, recent CA models are mainly developed assuming identical vehicle parameters. These models can be used to simulate the interactions of individual vehicles in traffic vehicular system; however, they cannot demonstrate the real vehicle traffic conditions due to the lack of consideration of the driver heterogeneity in individual characteristics and driving behaviors. Except for Lan and
Chang’s works (2003, 2005), few have devoted to mixed traffic flows, composed of different vehicle types. In reality, mixed traffic is prevailing around the world either in developed or under developing countries. For instance, bicycles, motorcycles, rickshaws or tricycles, cars, vans, mini-buses, regular buses and even articulated buses are ubiquitous in urban streets. Cars, coaches, trucks, trailers and even twin-trucks are very popular in freeways. Some of such different-dimensioned vehicles, with different in length and width, may share the same lane while moving (e.g., a motorcycle and a car can move together in one single lane that is used by a bus). Moreover, these vehicles also move with different parameters (e.g., different acceleration/deceleration rate, desired speed and different safe driver speeds). There are heterogeneous behaviors across drivers (e.g., aggressive or timid driver) with very different characteristics. For the purpose of planning, design and operational control, it is always important to capture the traffic flow features so that more realistic traffic flow models can be developed to better represent the prevailing traffic situations.
To accommodate different vehicle types moving on the surface streets, Lan and Chang (2005) first developed inhomogeneous CA models to elucidate the interacting movements of cars and motorcycles in mixed traffic contexts. The car and motorcycle are represented by non-identical particle sizes that respectively occupy 2×6 and 1×2 cell units; each cell is of 1.25×1.25 meters. To accommodate different vehicle types moving on the freeways, Lan and Hsu (2005, 2006 and 2007) first introduced generalized definitions of spatiotemporal occupancy, flow and speed to precisely capture the collective behavior of traffic features.
They further introduced a common unit (CU) of 1.25×1 meters to represent a “fine cell” and a “fine site” that can satisfactorily gauge the non-identical vehicle sizes and the non-identical lane widths, respectively. The concept of CU has major advantages for CA simulations in describing the different vehicle sizes moving on non-identical lane widths existent in different roadways.
1.2 Motivation
same type moving in different speeds, accelerations, and decelerations) and/or mixed traffic contexts, which comprise different types of vehicle (e.g., light and heavy vehicles). This study, therefore, will develop CA models to look into the spatiotemporal behaviors for heterogeneous mixed traffic on freeway.
In the well-known NaSch (1992) CA model and the subsequent modified NaSch models, the road is divided into squared cells of length 7.5 meters. Obviously, such a coarse description of cells is an extreme simplification of the real world conditions. Therefore, this study motivates to refine the cells so as to capture the sizes of different vehicle types in a more realistic manner.
The slow down rule of NaSch’s model will lead to abrupt speed drops occasionally emerged during the simulations. The acceleration rule proposed by Knospe et al. (2000) and Jiang and Wu (2003) still exhibited the deficit of abrupt change in speed at the upstream front of traffic jam. This study therefore motivates to rectify the abrupt speed drops by introducing limited deceleration capabilities when vehicles are confronted with stationary obstacles, traffic jams or signalized intersections.
The refined model is developed to explore pure-homogeneous, mixed-homogeneous, pure-heterogeneous, and mixed-heterogeneous traffic. The empirical traffic flow features, such as the traffic hysteresis and capacity drop can also be reproduced by mixed traffic, even no randomization is considered.
1.3 Research Objectives
This study proposes CA models for heterogeneous traffic flow with consideration of the heterogeneity of drivers’ characteristics and driving behaviors. There are some objectives in this research:
1. Introduce a concept of “common unit (CU)” to represent a “fine cell” and a “fine site”
that can satisfactorily gauge the non-identical vehicle sizes and the non-identical lane widths, respectively. The concept of CU has major advantages for CA simulations in describing the different vehicle sizes moving on non-identical lane widths existent in different roadways.
2. Redefine the traffic variables in the spatiotemporal (3-D) domain so as to precisely capture the collective traffic behavior and to reveal the traffic features.
3. Propose basic CA rules to explore the fundamental traffic features.
4. Propose revised CA rules, including anticipation effect, slow-to-start, lane change, and interaction among vehicles to explore the fundamental traffic features.
5. Propose refined CA rules using Forbes’ car-following concept associated with a piecewise-linear movement to rectify the abrupt deceleration existent in conventional CA models.
6. Exploring the discrepancy among the different fundamental diagrams that derived from various traffic scenarios (pure-homogeneous, mixed-homogeneous, pure-heterogeneous, and mixed-heterogeneous), especially those profiles in the congested traffic flow phases.
All of the proposed CA models in this study will be limited in the freeway contexts.
1.4 Chapters Organization
Given the objectives, the research framework was illustrated in Figure 1-1. The research is organized as follows. Chapter one introduces the background of the research.
Chapter two discusses literature review. Chapter three defines the “common unit” used in this study, the global traffic variables including occupancy, speed and flow, and the local traffic variables are defined. Chapter four develops a basic CA model with applications on the fundamental diagrams and the speed distributions at specific instantaneous time-steps and at two specific locations in pure traffic contexts. Chapter five develops a revised CA model with applications on moving and fixed bottlenecks in heterogeneous mixed traffic contexts. Chapter six proposes a refined CA model to rectify the abrupt speed drop existent in most previous CA models. Chapter seven concludes this research with some future research recommended.
FIGURE 1-1 Research framework.