Comparing Dynamic Traffic Assignment Approaches for Planning
R Balakrishna, D Morgan, Q Yang, Caliper, US
While static traffic assignment may be suitable for long-range forecasting, its usability for short-term analyses is rather limited. These limitations are mainly due to basic modeling assumptions: constant demand rates over long time periods of several hours such as an entire AM peak, the lack of queues resulting in volumes greater than capacity, and the implicit constraint that all trips start and end within the same (long) time interval. In the real world, however, demand patterns can change over very short time periods of a few minutes. Queues and spillbacks are also common, and trips very often begin and end in different time intervals. Short-term planning requires assignment models that can better capture these aspects of reality.
Dynamic Traffic Assignment (DTA) can be a powerful complement to the transportation planning process when time-varying network performance measures such as queue lengths and travel times are desired over very short time intervals such as 5 or 15 minutes. DTA scores over static models when demand levels and network disruptions change significantly over very short durations, as is often observed in the real world. It should be noted, however, that a DTA solution is expected to extend the standard static definition of convergence so that drivers departing within the same time interval experience similar travel times regardless of their chosen paths.
A DTA captures the interactions between time-varying travel demand and network supply. Travel demand is typically specified as a series of time-dependent origin-destination (OD) matrices or trip tables, one for each small departure time interval. Unlike in static models, trips can begin and end in different time intervals. Route choices are also more sensitive to departure times and spatio-temporal congestion patterns of a fine resolution. Network supply typically consists of link capacities, link performance functions and disruptions (if any) such as incidents and work zones. These demand and supply elements interact to predict the formation and dissipation of queues and spillbacks, leading to more accurate bottleneck analyses. Generally, such demand-supply runs must be iterated to converge to a stable solution.
DTAs can differ significantly in their implementations of the demand and supply components and the algorithms that capture their interactions. Analytical DTA models assume that traffic is analogous to fluid flow, a very aggregate treatment of vehicular traffic. At the other end of the spectrum are microscopic models that simulate the behavior and trajectories of individual vehicles in great detail. In such models, vehicles interact with each other through car-following and lane-changing maneuvers. Mesoscopic and macroscopic models fall between these two outer classes, and are also typically based on simulation techniques. In mesoscopic models, individual vehicles are moved according to link performance functions derived from the fundamental diagram (e.g. speed-density relationship) in traffic theory. Macroscopic models update vehicle speeds using volume-delay functions (VDFs) traditionally seen in static planning models. Each type of model possesses benefits and drawbacks. Microscopic models, while very realistic, can be very hard to calibrate against reality. They also tend to be stochastic so that two model runs with identical inputs may generate slightly different outputs. Mesoscopic models sacrifice some modeling accuracy in exchange for faster run times. Macroscopic and analytical models are perhaps the farthest removed from the individual vehicle, and often the fastest.
In this paper, we discuss the modeling differences among common DTA approaches and their consequences for practical applications. We empirically compare the accuracy and computational performance of analytical, mesoscopic and macroscopic DTAs and evaluate their modeling realism against microsimulation. The TransModeler traffic simulation package is ideally suited for this test, as it can handle analytical, microscopic, macroscopic and mesoscopic models on the same network. This provides the most valid platform for comparisons, since all exogenous factors would be identical across the models. The extent and role of stochasticity is also investigated. Finally, the paper tackles the calculation of congested network travel times and dynamic equilibrium using DTA, and discusses how DTA may be integrated into the traditional planning framework. Practical issues when moving from static to dynamic models are outlined, such as model calibration and the estimation of dynamic OD matrices. Case studies could include networks from the I-5 freeway corridor in California and the I-270 freeway and arterial network from Maryland.
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