In recent years, the transport simulation of large road networks has become far more rapid and detailed, and many exciting developments in this field have emerged. Transport simulation has broadened from the simulation of automobiles to include pedestrian and rail elements. Advances in transport simulation and the evolving Intelligent Transport System (ITS) are leading to new applications, such as the linking of driving simulators with traffic simulation to give a more realistic environment of driver behaviour surrounding the subject vehicles.
THE ROLE OF MACROSCOPIC MODELING IN THE SIMULATION, SURVEILLANCE AND CONTROL OF MOTORWAY NETWORK TRAFFIC
Dynamic and macroscopic discretized analytic state-space models of motorway network traffic are more than mere simulation tools; they can be used as a valuable basis for the employment of powerful methods for surveillance and control, such as a Kalman Filter, various Automatic Control methodologies and gradient-based optimization. In the motorway traffic context, this leads to a transparent, convenient and efficient handling of various significant tasks, including dynamic traffic assignment, traffic state estimation and prediction, real-time parameter estimation, incident alarm, travel-time and congestion estimation and prediction, optimal coordinated ramp metering, system-optimal or user-optimal route guidance and integrated traffic control.
Mathematical modeling is the imitation of the relevant aspects of a process by use of appropriate mathematical equations and further logical relationships. When fed with sufficient initial and boundary conditions as well as control inputs and further exogenous variables, a dynamic model may produce the evolution of the process state over time. If the modeling equations are appropriately implemented in a computer, the resulting simulator can be employed as a cost-effective and convenient tool for multiple uses, such as, in the case of traffic flow, planning of new extended transportation infrastructure; testing the efficiency of various traffic control measures, strategies and systems; comparison of alternatives etc.
Two basic modeling approaches have been pursued in the area of traffic flow; microscopic modeling, which describes the longitudinal (car-following) and lateral (lane-changing) movement of individual vehicles; and macroscopic modeling, which addresses traffic as a particular fluid with aggregate variables (density, mean speed, flow). Both approaches can be contrasted with respect to a number of aspects:
• Simulation: The traffic flow simulation market is dominated by the microscopic approach, possibly due to its direct similarity with the perceived real process as compared to the abstract, mathematically more challenging macroscopic description.
• Computational effort is far lower in macroscopic approaches.
• Beyond simulation, macroscopic models of whole traffic networks can be expressed in an analytic form that opens the way for the use of a multitude of powerful available surveillance and control methods such as a Kalman Filter, Automatic Control methods, gradient-based optimization etc.
• Accuracy depends on the employed validation procedures that are easier to apply in the low-resolution macroscopic models.
• Specific considerations may be more easily and directly incorporated in microscopic models.
Over the decades, various dynamic macroscopic models, mostly in the form of Partial Differential Equations (PDE), of related research efforts have been proposed by Hoogendoorn and Bovy (2001). As the conservation equation is the only exact relationship in traffic flow modeling, it is included in all approaches. In addition, first-order models involve a static speed-density relationship while second-order models address the mean speed dynamics with potentially more realism. Although the technical literature on macroscopic traffic flow modeling is vast and increasing in an accelerated pace, rigorous model validation exercises using real traffic data are surprisingly sparse. Given the largely empirical character of the proposed models, the lack of validation efforts is a shortcoming that cannot be sufficiently emphasized.
Another issue connected to macroscopic models is the space-time discretization of the related PDE in order to enable their numerical solution in digital computers. In numerous cases, sophisticated numerical schemes are employed for a reliable and accurate numerical approximation of the PDE. These approaches, however, typically result in complex computational schemes that require a high computational effort and, moreover, do not lead to analytical discretized models; in other words, these approaches employ a significant effort to approximate the PDE that are all but exact. An alternative, more practicable, approach is to discretize the original empirical PDE by use of simple schemes leading to analytical state-space models that can then be readily validated; implemented in a computer with low computational effort; used as a valuable basis for the analytical derivation of various surveillance and control tools. The main disadvantage of these approaches resides in the fact that any theoretical investigations and results obtained for the PDE are not directly transferable to the discretized model.
HYBRID TRAFFIC SIMULATION MODELS: VEHICLE LOADING AT MESO-MICRO BOUNDARIES
Traffic simulation models, especially microscopic ones, are becoming increasingly popular and are being used to address a wide range of problems, from planning to operations. However, for applications with large-scale networks, microscopic models are impractical because of input data and calibration requirements. Hybrid models that combine simulation models at different levels of detail have the potential to address these practical issues. This chapter presents a framework for implementing mesomicro hybrid models which facilitates a consistent representation of traffic dynamics. Furthermore, the chapter carries out a detailed examination of an important element impacting the consistent representation of traffic dynamics, i.e., the loading of vehicles from the mesoto the micro-model. A new loading method is presented demonstrating a superior performance as compared to existing approaches. The method is useful not only in the context of hybrid models, but also for microscopic models on their own. A case study illustrates the importance of the method in improving the fidelity of both hybrid and pure microscopic models.
While microscopic traffic simulation is becoming ever more popular, especially in the evaluation of advanced traffic management systems and intelligent transportation systems (ITS), the amount of effort needed for model calibration and for the preparation of input data often inhibits its use on large networks. Recently, hybrid mesoscopic-microscopic models have appeared (Burghout, 2004; Burghout et al., 2005; Shi and Ziliaskopoulos, 2006; Yang and Morgan, 2006) allowing a detailed microscopic simulation of specific areas of interest, while simulating the remaining areas in lesser detail on a mesoscopic level. Since mesoscopic simulation has a more aggregated representation of the roadway and the vehicle interactions, it requires much less effort in calibration and preparation of input data (especially coding of the road network). In addition, a number of hybrid macroscopic-microscopic models have recently appeared.
The development and implementation of hybrid models that combine traffic simulation models at different levels of detail require the resolution of a number of issues, some of them related to the interaction of the two models at their boundaries. Among these issues, the consistency in traffic dynamics at the mesoand micro-network boundaries is particularly important.
The objective of this chapter is twofold:
(a) to present a general framework for the implementation of hybrid simulation models satisfying the various integration requirements;
(b) to detailed discuss an important aspect that has serious implications for the validity of simulation models in general and hybrid models in particular. This aspect is the mechanism used to load vehicles arriving from the mesoscopic area into the microscopic area, which affects the consistency of traffic dynamics at the meso-micro boundaries.
HYBRID MODELING FRAMEWORK
The main requirements that the integration of micro/meso models needs to satisfy in order to develop reliable hybrid models include:
• Consistency in network representation. One of the most basic conditions is the general consistency of the two models in their representation of the road network, especially at the boundaries between the two models. A consistent network representation has important implications for capacity determination, and hence impacts traffic dynamics at the boundaries between the models. Furthermore, it impacts the links included in each model and hence, the consistency with respect to route choice as discussed below.
• Consistency in route choice representation. One of the most important conditions is the consistency of the two models in their representation of paths, and route choice alternatives. The route choice needs to be consistent across the models to ensure that vehicles will make the same decision given the same route choice situation (pre-trip or en-route), regardless of if they are in the microor the meso-model. This also means that the representation of the alternative paths needs to be consistent throughout the hybrid model, as do the travel times (link costs).
• Consistency of traffic dynamics at meso-micro boundaries. Besides the consistency of network representation, the consistency of traffic dynamics at the boundaries between the mesoand micro-submodels needs to be ensured. In other words, the traffic dynamics upstream and downstream of the boundaries must be consistent. For instance, when a queue forms downstream of the boundary point, and grows until it reaches the boundary, it should continue in the other submodel, upstream the boundary, similarly to how it would have done if the boundary had not been there.
• Consistency in traffic performance for meso and micro submodels. The two submodels need to be consistent with each other with regard to the results they produce. Ideally, for the facilities that can be simulated sufficiently well by both models, the results in terms of common outputs such as travel times, flows, speeds, densities, etc, should be similar. This implies the need for a consistent calibration of the two models.
• Transparent communication and data exchanges. The submodels exchange large amounts of data conveying vehicle characteristics and downstream traffic conditions. This requires an efficient synchronization and communication paradigm and a design that minimizes the amount and frequency of data exchange. Otherwise, the communication overhead may become very large. On the other hand, aggregation and disaggregation of information at the boundaries may introduce complications and should therefore be avoided.