Towards disaggregate dynamic travel forecasting models

Moshe Ben-Akiva, Bottom Jon, Gao Song, Iaris N. Koutsopoulos, Wen Yang
2007 Tsinghua Science and Technology  
We argue that travel forecasting models should be dynamic and disaggregate in their representation of demand, supply and supply-demand interactions, and we propose a framework for such models. The proposed framework consists of disaggregate activity-based representation of travel choices of individual motorists on the demand side integrated with disaggregate dynamic modeling of network performance, through vehicle-based traffic simulation models, on the supply side. The demand model generates
more » ... dividual members of the population and assigns to them socioeconomic characteristics. The generated motorists maintain these characteristics when they are loaded on the network by the supply model. In an equilibrium setting, the framework lends itself to a fixed-point formulation to represent and resolve demand-supply interactions. The paper discusses some of the remaining development challenges and presents an example of an existing travel forecasting model system that incorporates many of the proposed elements. Introduction Transportation systems are highly complex, and for this reason planners and engineers often use computer models to analyze and design possible system improvements. Travel forecasting models are commonly used [1] [2] to predict the travel flows and conditions that result from the interaction between the demand for travel by transportation system users and the travel options that the transportation system supplies to its users. In general terms, travelers' decisions (with respect to where, when and how to travel), as they relate to the service provided by different travel options, will be referred to as demand, and the response of the transportation system (in terms of travel time, cost, reliability and other service attributes) to a given level of demand will be referred to as supply. As Figure 1 illustrates, travel forecasting models represent supply and demand and incorporate a mechanism to determine the outcome of their interactions. These models simultaneously determine both the performance of the network and the response of its users, thus enabling planners and engineers to investigate how potential interventions will affect transportation system flows and service conditions. Page 3 of 44 Figure 1 . Travel forecasting framework The conventional framework Early travel forecasting models, originally developed in the mid-1950s [3] and taking a standard form by the late 1960s, were designed to predict steady state flows and conditions over a representative analysis time interval such as a peak period; for this reason, they are called static models. Their original applications were to analyze the effects of large transportation system capacity additions, such as building new roads. Such projects can produce effects over a long period of time, and the totality of these effects must be considered in deciding whether a project is worthwhile, so the models are often used in these analyses to make long-term forecasts. Because of the inherent degree of imprecision in such forecasts, and because predictions of steady state flows and performance are sufficient to evaluate such large-scale interventions, static models are well suited to this task. These models are still very widely applied, although sometimes to problems for which they are not well suited. We will refer to travel forecasting models based on these early principles as conventional models, recognizing that particular model system implementations may incorporate some differences with respect to the standard form. Nonetheless, the term conventional is appropriate, because the overwhelming majority of travel forecasting models in use today continue to follow the general design. Conventional travel forecasting models are characterized by static, aggregate and deterministic supply and demand modules and relationships. More specifically: • Travel demand is predicted based on the aggregate characteristics of geographic areas called zones and is defined in terms of trips made directly from one zone to another without intermediate stops. Conventional demand models predict the steady-state level of demand that would be maintained over an analysis period of one or more hours in the presence of steady state network conditions. A few user classes at most are considered, with each user class being characterized by distinct travel behavior (e.g. cars and trucks). The specific relationships used to predict travel demand as a function of zone characteristics and network supply are generally analytical (closed form mathematical formulas or tables) and deterministic. • Network supply reflects the steady-state network conditions that result from a steady-state traffic flow during the analysis period. Because they are aggregate, conventional supply relationships do not consider individual vehicles; and because they are static, they do not consider the finite time required for traffic to move along a link or from one link to the next along a path. The specific relationships used to predict network conditions (e.g. Page 5 of 44 travel time or cost) as a function of flow are generally analytical and deterministic. • Supply-demand interactions are assumed to result in a steady-state equilibrium situation, where travelers acting independently would have no incentive to change their decisions. The outcome of the supply-demand interactions, in terms of traffic flows and network conditions, reflects the aggregate, static and deterministic nature of supply and demand models, and the trip-oriented definition of travel. (Even the so-called stochastic user equilibrium is in fact a deterministic concept.) Travel forecasting models can capture supply-demand interactions at various levels of time scale, and the choice of scale dictates which choices are endogenous to the forecasting model. This includes household choices, such as where to work, where to live, the number of automobiles to own, which are not themselves travel choices, but are closely related to them. (For example, residential and employment location choices determine the origins and destinations of home-based work trips.) Travel forecasting models with long-term supply-demand interactions make the above choices dependent on network performances generated from the supply side. Some travel choices are of shorter term, such as whether to travel and where to travel for non-work trips, and mode choice and departure time choice for both work and non-work trips. Travel forecasting models with supply-demand interactions at this level treat long-term choices as exogenous input, while making network performance an influencing factor of these choices. Path choices are of even shorter term, and a model that captures the supply-demand interactions at this level is a traffic assignment model, which takes as input longer-term Page 6 of 44 choices (trips in a given time period by origin, destination and mode) and performs several distinct functions: it implements the supply relationships, represents travelers' path choice behaviors, and resolves the interaction between supply and the path choice component of demand; its outputs are traffic levels and network conditions. Interactions between supply and demand components other than path choice may be resolved via "feedback" of the traffic assignment model outputs to the corresponding longer-term demand sub-models, iteratively invoking the longer-term demand sub-models and the traffic assignment model until a satisfactory indication of convergence to equilibrium is attained. (The various demand sub-models together with a traffic assignment model are often called the four-step model system. This is by far the most commonly applied travel forecasting model system framework in the world.) Path choices can be further classified by time scale: those based on recurrent network conditions and those based on non-recurrent network condition, such as incidents, work zones, etc. In the former case, the result of supply and path choices is usually conveniently represented by equilibrium conditions, while in the latter case it seems implausible to talk about equilibrium. Modeling advances Conventional travel forecasting models continue to preserve these general features many decades after their original development. However, during this period research into the individual supply and demand components of travel forecasting models has resulted in considerable advances in the sophistication and capabilities of these components. The Page 7 of 44 evolution of both supply and demand models has proceeded in several directions [4] : • From static to dynamic consideration of time: models are increasingly focused on capturing the temporal aspects of traveler behavior (choice of departure time, reaction to time-dependent conditions and information) and on predicting the variations in network flows and conditions at a relatively detailed time resolution; • From aggregate to disaggregate representation of travel: models are increasingly focused on representing individual travelers and vehicles to capture the heterogeneity of their decisions and movements. This, in turn, has led to decreased reliance on analytical and closed form mathematical models, and increased use of simulation models, where traveler and vehicle behavior are implicitly represented through logic incorporated in the simulation model. Related to this, there has been increased recognition that deterministic modeling relationships may not be appropriate in all circumstances, with increased interest in accounting for model stochasticity. During this period, supply-demand interaction models have also evolved, although to a lesser extent. The principal direction of progress has been from a static to a dynamic representation of time [5] . In the mid-1970s, research began on traffic assignment models able to represent the time variations in traffic flows and conditions that result from changing levels of travel demand, changes in network capacity (reduced, for example, by a vehicle breakdown or a crash), and the finite speed of vehicles moving over the network. These are known as dynamic traffic assignment (DTA) models, and research in this area is still very active. Page 8 of 44 choice, among other travel decisions. Choices are based on the attributes of the various travel alternatives (e.g. paths) and the traveler's own characteristics, and may represent a random selection based on the choice probabilities output by the demand model. The disaggregate supply simulator represents the time-dependent movement of individual vehicles over the network in accordance with the travel choices predicted by the demand simulator. Vehicles are moved according to either macroscopic or microscopic traffic performance models. Stochasticity in vehicle movement is explicitly represented. The supply simulator produces both vehicle-and network-level measures of travel performance, such as vehicle space-time trajectories, link travel time and cost, and congestion delay. An important feature of the proposed framework is the full and seamless integration between the demand and supply modules. Full integration means that the vehicles loaded onto the network correspond directly to the population generated in the demand module, in terms of their characteristics, and travel decisions regarding path and departure time choices. In addition, the vehicles loaded on the network maintain their socioeconomic characteristics and other attributes, so that en-route decisions and response to information is consistent with these characteristics, and their pre-trip behavior. Furthermore, the full integration between demand and supply facilitates the representation of the supply/demand interactions. The supply/demand interactions module predicts equilibrium conditions based on the interactions of the disaggregate demand and supply models. The framework accommodates the interactions at all levels of time scale, from those involving long-term land use choices Page 28 of 44 (e.g. where to work, where to live), to medium-term travel choices such as mode and departure times, to short-term path choices. (Note that if land use is included in the demand model, then it should be removed from the input in Figure 2.) With disaggregate representation of supply and demand, the computation of equilibrium cannot be based on aggregate network-level properties of traffic and conditions. Fixed point formulations offer a promising way to express and solve for equilibrium in this context. These formulations can be expressed in terms of either behavior (demand) variables b or condition (supply) variables c, e.g.: S * D(c) = c D * S(b) = b where D() designates the demand function, S() designates the supply function and * designates functional composition. In the first case, for example, a set of network conditions represent an equilibrium if, after travelers make decisions based on the conditions and the network then reacts to the decisions that were made, the resulting network conditions are the same as the initial network conditions, so that travelers have no reason to revise their decisions. A similar interpretation applies to the second case. Fixed point approaches have occasionally been applied in the past to analyze conventional travel forecasting models, but have never been among the mainstream methods applied to solve these models, in large part because computational methods that exploit the network-level properties of equilibrium flows and conditions with homogeneous users tend to be more efficient. Nonetheless, this formulation is interesting for disaggregate dynamic Page 29 of 44 travel forecasting because it captures the essential supply-demand consistency property of equilibrium, even at a disaggregate representation level. It also appears to impose the least stringent conditions on the involved functions (i.e. the supply and demand models). Moreover, as a general approach it is robust across a wide variety of equilibrium problem details such as the amount of behavioral heterogeneity and the extent of stochasticity in the demand and supply relationships. These problem details dictate the appropriate approach for solving the equilibrium fixed point problem, but many general methods are available. For example, gradient-based methods may be appropriate for deterministic problems; stochastic approximation (or averaging) methods -including both conventional algorithms such as the method of successive averages (MSA) [63][64][56][2] as well as accelerated methods such as the one due to Polyak [65] -are appropriate for problems that allow stochasticity but represent its outcome in terms of expected values (such as the so-called Stochastic User Equilibrium model); and Markov Chain Monte Carlo methods such as Gibbs sampling are appropriate for computing the equilibrium probability distributions of traffic and condition variables in fully stochastic problems [62] . With increased recognition of the value of this formulation for disaggregate dynamic problems, new research may lead to more efficient fixed point computational methods for these problems. Examples Elements of the disaggregate dynamic travel forecasting framework presented in Section 3 can be found in a number of model systems that exist or are under development, including Page 30 of 44 DynaMIT [66] , DYNASMART [36] , Dynameq [37][38][39] , METROPOLIS [40][41] , ILUTE [25] , TRANSIMS [24] , etc. We focus here on DynaMIT as an example of a model system that is built on the principles of this framework and that includes many of the requirements outlined in the previous sections. DynaMIT combines inter-related models of travel behavior (demand simulator), dynamic network performance (supply simulator), and demand/supply interactions. It captures the stochastic nature of transportation systems and can represent the functioning and effects of ITS technologies. DynaMIT is particularly useful for short-term planning applications involving work zones, special events, high occupancy vehicles and high occupancy/toll (HOV and HOT) facilities and congestion pricing. Demand Simulator. The DynaMIT demand simulator is a microscopic, disaggregate travel behavior simulator and consists of modules for demand disaggregation, disaggregate travel choice prediction and, depending on the application, O-D matrix estimation. The role of the demand disaggregation is to generate the population of drivers from given O-D matrices. As each driver is generated, it is assigned a number of socioeconomic and trip characteristics. Based on these characteristics, individual travelers make decisions, using disaggregate choice models, about path, departure time, and possibly travel mode. The path choice model is a key component and determines the paths that vehicles follow over the network, incorporating pre-trip and/or en-route information. The departure time models capture an important behavioral response to congestion, incidents or dynamic pricing. In contrast to the framework presented in this paper, the demand simulator in DynaMIT currently does not simulate activity patterns, and is an example short-term demand model. Page 31 of 44 An important component of the demand simulator is the (aggregate) estimation of dynamic O-D flows from relevant measurements (e.g. traffic counts). The O-D matrix estimation problem is one of combining and reconciling information from diverse sources and with various error characteristics. This functionality is critical for short-term planning applications. Supply Simulator. The DynaMIT supply simulator is a disaggregate, time-based, mesoscopic traffic simulator. Given a set of travelers and their departure times and paths as predicted by the demand simulator, and given the network characteristics and implemented control strategies, the supply simulator predicts the performance of the network in terms of time-dependent travel times, queue lengths, etc. The complexity of traffic dynamics in the network is captured through the integration of three classes of models: capacities associated with roadway features, incidents, and control strategies; queuing reflecting the effect of bottlenecks; and macroscopic speed-density relationships representing uninterrupted flow. The simulator is designed to operate at different levels of granularity, depending on the requirements of the application. The demand and supply simulators in DynaMIT have also moved towards full integration. The O-D estimation process is a form of population generation. The demand simulator generates the population of drivers who are assigned socioeconomic characteristics, based on their origin, and make pre-trip route and departure time decisions. These drivers are then loaded on the network accordingly. Their characteristics are maintained throughout their trip and hence, if they receive information, or encounter a Variable Message Sign (VMS) they
doi:10.1016/s1007-0214(07)70019-6 fatcat:k35gliavafetfn5pdrgbhsk55u