Conclusions

1. Our first finding is that the applicability of the common adopted formula for estimating 1-D vehicular average speed (q=kv, enclosed as Equation (2-4)) should be carefully re-scrutinized. Equation (2-4) was originally developed by scholars in the field of fluid mechanics upon the fact that fluid flow is continuous. However, traffic flow by nature is no longer continuous but in essence a congregation of discrete particles (vehicles). Besides, by definition the 1-D local traffic flow-q(x) is a time-based parameter measured at fixed point whereas the local traffic density-k(t) is a space-based traffic parameter

for an certain instant. So Equation (2-4) may be valid under some very restricted conditions, i.e., homogeneous state in which each vehicle equips with identical features (e.g., same headway and identical speed, etc), or in the limit as both the space and time measurement intervals approach zero. If neither of those situations holds, then use of the formula to calculate speed can give misleading results, which would not agree with empirical measurements. This issue is worthy for further survey because Equation (2-4) has often been uncritically applied to situations that exceed its validity.

2. This study endeavors in the development of one novel CA model which is capable of simulating various urban traffic contexts. CA modeling can be categorized as one branch of microscopic approach that interrelationship of individual vehicle movements interacted with other vehicles are described.

There are several obvious advantages for selecting CA model for traffic simulations. First, the rule set that describes the update of each vehicle is minimal. Next, the update schedule, being completely parallel, is simple, too.

Besides, it is capable of reproducing important entities prevailed in real traffic, e.g., density-flow relation and the traffic jam in congested traffic.

The most important and subtle reason is the computation explicitness. It means that data is directly updated and iterations for converging to some predefined residue are never required. The beneficial aspect of using explicit computation is that it minimizes the simulation time and thereby increases likelihood for real-time simulation. Besides, the developed CA model also enjoys an additional advantage—flexibility. Owing the refined grid system devised, the proposed CA model is capable of handling different traffic scenarios and complex mixed traffic that comprised by various vehicle types.

3. Our most important finding is that this study substantiates the criticality of grid system utilized in CA simulation, which in essence represents the resolution (i.e., the degree of detail or the acceptable approximation of traffic phenomena one expects to analyze) may be achieved. The coupled low resolution of existing CA models strictly circumvents their applicability.

Aside from their popularity in the past, there is continuous criticism for the significantly limited application of existing CA models to freeway traffic and the deficiency to uncover delicate vehicular behavior from microscopic

viewpoint. This may mainly suffers from the comparatively coarse grid system implemented by most existing CA models, in which each lane is only allowed to be occupied by a single vehicle laterally. It is obvious that such coarse grid system is difficult to implement for mixed traffic simulations where vehicles have different sizes (length and width) and/or possess distinct behavior. The coarse grid system also stands as the crucial barrier for implementing existing CA models into urban traffic simulation in which usually low speed limits prevail and oftentimes vehicles move with slight speed variations. As a matter of fact, few efforts are available hitherto to evaluate the impact of different vehicular width through CA simulation.

Consequently, it is comprehensible that a refiner grid system will be the crucial prerequisite for expanding the application of CA modeling to mixed traffic prevailed in urban streets.

4. To contend with such restriction, in this study we first propose a refined 3-D grid system that considers time and both vehicular length and width. As the onset the concept of “common unit” (CU), “cell” and “site” are defined to serve as the universal basis, the basic unit for describing different vehicle sizes and for roadways, respectively. The size of site and cell can be selected in accordance with the scenarios simulated as well as the resolution of simulation required. The sole restriction is that the size of both basic site and basic cell should be identical, i.e., to be the common unit. Besides, to cope with this 3-D grid system, we also extend the 2-D traffic parameters that proposed by Daganzo (1997) to be 3-dimensional. The spatiotemporal traffic flow (q(S) and ρ(S)) are therefore defined. Our following simulations evidence the superiority of the proposed novel CA model since that it successfully liberates the above-mentioned restriction and is able to handle the violate traffic phenomena in real world. Based upon the enhanced resolution and the increased flexibility of the proposed CA model, analysis of different traffic contexts, such as such as the mixed traffic comprised by vehicles of various sizes and sophisticated traffic phenomena in urban area, can be performed successfully.

5. Our next effort is to rectify the common defect of existing CA models that vehicles abruptly decelerate when encountered with stationary obstacles or traffic jams. In most existing CA models though the idea of limited

acceleration is implemented; deceleration limitation has seldom been considered. Actually, most CA models simply considered a collision-free criterion explicitly by imposing arbitrarily large deceleration rates, which can be far beyond the practical braking capability under prevailing pavement and tire conditions. Despite simulations through the existing CA models show satisfactory outcome in capturing essential features of traffic flows, most existing CA simulations also revealed that, for sake of collision prevention, a vehicle can take as short as 1s to come to a complete stop, even from a full speed, apparently exceeding the vehicular deceleration ability. We concur with that existing CA model has led to satisfactory outcome if only long-term average traffic features are concerned or only macroscopic traffic phenomena or global traffic parameters are examined because the effects of locally realistic deceleration have been smoothed out.

However, if we scrutinize in detail the microscopic traffic parameters or the neighbourhood of some unexceptional scenarios, such as an accident vehicle or a work zone blocking the partial highway lanes, it is evident that the deceleration rule in existing CA models require further revisions. For this purpose we propose the piecewise-linear movement within each time-step to replace conventional particle-hopping movement adopted in most previous CA models. Upon this adjustment and coupled with refined grid system, the limited deceleration are then introduced which is essence the extension of classic car–following concept proposed by Pipes (1953) and/or Forbes (1958). The main deviation is that appropriate deceleration is determined through Newton’s kinematics rather based on a given time headway. The validation simulations show that the proposed novel CA model can fix the unrealistic deceleration behavior, and thus to be more in line with the real world vehicular movement, In addition, the proposed CA model is also capable of revealing Kerner’s three-phase traffic patterns and phase transitions among them.

6. Upon all the effort mentioned above, this study further develops a sophisticated CA model to simulate the mixed traffic comprising cars and motorcycles. Owing to the enhanced resolution of the refined cell system, slight speed variations and effects of both the vehicular length and width can be simulated. Most importantly, the frequently observed lateral movements of cars and motorcycles as well as the wide transverse crossing behavior of

motorcycles are carefully deliberated with the corresponding CA update rules thereby added. Comparisons with existing studies authenticate the validity of our sophisticated CA model while simulating the pure car traffic scenarios. The simulations show that the unique lateral movements of motorcycles that yet investigated in any existing studies, such as breaking into two moving cars and transverse crossing through two stationary cars in traffic jam, can be precisely illustrated. Our simulations reveal that maximum car flow decreases with the increase of the motorcycle density since the increased interaction among different vehicles will impair the flow efficiency. Furthermore, the simulations also underline the necessity for introducing motorcycles’ transverse crossing behaviors into the simulations of mixed traffic, especially in congested traffic.

7. This study also constructs the methodology for extracting local traffic flow rate and occupancy from the refined grid system. The derived local traffic flow and occupancy, both AA and UMA averaged, is carefully validated through the simulation of selected complex scenarios. The results show that for pure car traffic scenarios, the UMA traffic parameters are efficient in reflecting the complicated traffic phase transitions whereas the AA traffic data is consistent with the three-phase traffic theory. In addition, through the comparison between global and local traffic fundamental diagrams, it is found that in uninterrupted traffic the AA traffic data has potential to be a useful proxy to reflect the global traffic features, though only local traffic information is gathered. In contrast, in mixed traffic comprised by cars and motorcycles, the local traffic data, both AA and UMA averaged, has comparatively poorer performance to reflect the global situation. Another important finding is that the derived local car flow usually is lower in pure car traffic, but higher in mixed traffic cases, than its global counterparts.

This may be induced by the random erratic nature of motorcycles’

movement in mixed traffic. When introducing more motorcycles in mixed traffic, the local interference raised by randomly moving motorcycles will accumulate and finally leads to a lower global car flow rate. This conclusion again evidenced that introduction of motorcycles will significantly impair the car flow rate.

8. This study serves as the pioneer effort in defining the refined CA model. The proposed novel CA model successfully breaks through the inherent defect of most previous CA models and therefore effectively extends the possible applicability of CA modeling. Thus this study shed some light for the future analysis of traffic modeling. It is looked forward that via the proposed refined CA model different traffic control strategies for separate traffic context can be efficiently evaluated before practical implementation.