Innovations in Travel Demand Modeling, Volume 1: Session Summaries (2008)

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that causes the path times to be equal. After the reason- able path set is determined, an allocation mechanism can be used to try to achieve a more exact equilibrium solu- tion over the fixed set of reasonable paths. • The Atlanta study included iteratively building a reasonable rate set and solving the dynamic user- equilibrium for that route set. After each dynamic user- equilibrium solution, routes that had previously received vehicles but no longer did were pruned from the rate set and new reasonable rates were determined. The initial simulation results included a small number of links with travel times exceeding 1 hour. A time–space diagram of vehicles arriving at specific links was plotted. After cells in the Atlanta network became saturated while vehicles continued to arrive, the cell saturation effect moved upstream. The overcongested link caused other links upstream to become oversaturated. • Preliminary results from the VISTA model for the 6:00 a.m. to 7:00 a.m. period were examined. Summary statistics for the number of links, total observed count, and total estimated flow for volume ranges, along with relative error and percent root- mean- square error, were reviewed. Scatter plots of the DTA results were also examined. Preliminary results from four iterations indi- cated a relatively good fit with observed data. • The work in Atlanta is ongoing. Efforts are focus- ing on resolving discrepancies between demand and net- work counts and examining routes between origins and destinations that could use these links but do not. Other activities are reviewing travel time data and the reason- ableness of the network times. Time- dependent ori- gin–destination estimation and the use of subareas to reduce the size of DTA are also being explored. URBAN ARTERIAL SPEED–FLOW EQUATIONS FOR TRAVEL DEMAND MODELS Richard Dowling and Alexander Skabardonis Richard Dowling discussed a recent study conducted for the Southern California Association of Governments (SCAG) to improve the accuracy of peak- period speeds predicted by the SCAG travel demand model. He described the purpose of the study, the data collection activities conducted for the study, and the analysis of the data. Volume 2 contains a paper on the topic.2 The fol- lowing points were covered in his presentation. • The objective of the study was to develop improved field- calibrated speed–flow equations for use in the SCAG travel demand model to predict the mean speed of traffic on signalized urban arterials in the Los Angeles metropolitan area. Intersection turning movement counts and GPS- equipped vehicles were used to obtain a total of 216 hourly observations of speed and traffic flow on 54 directional street segments at eight different sites in the Los Angeles metropolitan area. In addition, 45 observations were conducted on the I-10 Freeway. • The data collection method measured intersection discharge rates rather than demand. If demand is less than the discharge capacity for an intersection approach, then the discharge rate and demand are identical. If demand exceeds capacity, the demand diverges from the observed discharge rate. The data points with observed volumes not equaling the demand were identified and excluded from the data set. • Several candidate speed–flow equations were examined in the study. Five candidate equations— linear, logarithmic, exponential, power, and polynomial— are standard mathematical functions commonly used in data analysis. Two candidate equation forms— the Bureau of Public Roads (BPR) equation and the Akcelik equation— are specific to travel time and delay analysis. To allow capacity constrained equilibrium assignments to be per- formed by travel demand models, speed–flow equations must meet several behavioral requirements. The equa- tions must be monotonically decreasing and continuous functions of the volume–capacity ratio in order for all equilibrium assignment processes to arrive at a single unique solution. To prevent the travel model from con- fronting a request to divide by zero, the equations should never intersect the x- axis, which would mean the pre- dicted speed would be zero. • The exponential, BPR, and Akcelik equations were fitted through a least- squared error fitting process to the observed speed–flow data. All three functional forms appear to account for some of the observed variation in speed. Because the field data could not be used to eval- uate speed–flow curve candidates for demands greater than capacity, a theoretical evaluation was conducted comparing their predicted delays for volumes greater than capacity against the delays predicted by queuing theory. Based on queuing theory, when demand is greater than capacity, vehicles must wait their turn in line for the vehicles in front to pass through the intersec- tion. The theoretical average delay can be graphed and compared with the predictions produced by the candi- date speed–flow curves. • The fitted BPR and fitted Akcelik equations were calibrated for a volume–capacity ratio of greater than 1.0. The fitted BPR curve underestimated the delay due to queuing when demand exceeded the real- world capac- ity of an intersection at the end of a link. The fitted Akcelik curve is consistent with the queue delay line because it is derived from classical queuing theory. The analysis also examined the impact of a 10% error in 39ASSIGNMENT ADVANCES 2 See Dowling, R., and A. Skabardonis. Urban Arterial Speed–Flow Equations for Travel Demand Models. Volume 2, pp. 109–113.