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A S S I G N M E N T A D VA N C E S 39 that causes the path times to be equal. After the reason- traffic on signalized urban arterials in the Los Angeles able path set is determined, an allocation mechanism can metropolitan area. Intersection turning movement be used to try to achieve a more exact equilibrium solu- counts and GPS-equipped vehicles were used to obtain a tion over the fixed set of reasonable paths. total of 216 hourly observations of speed and traffic flow The Atlanta study included iteratively building a on 54 directional street segments at eight different sites reasonable rate set and solving the dynamic user- in the Los Angeles metropolitan area. In addition, 45 equilibrium for that route set. After each dynamic user- observations were conducted on the I-10 Freeway. equilibrium solution, routes that had previously received The data collection method measured intersection vehicles but no longer did were pruned from the rate set discharge rates rather than demand. If demand is less and new reasonable rates were determined. The initial than the discharge capacity for an intersection approach, simulation results included a small number of links with then the discharge rate and demand are identical. If travel times exceeding 1 hour. A timespace diagram of demand exceeds capacity, the demand diverges from the vehicles arriving at specific links was plotted. After cells observed discharge rate. The data points with observed in the Atlanta network became saturated while vehicles volumes not equaling the demand were identified and continued to arrive, the cell saturation effect moved excluded from the data set. upstream. The overcongested link caused other links Several candidate speedflow equations were upstream to become oversaturated. examined in the study. Five candidate equations--linear, Preliminary results from the VISTA model for the logarithmic, exponential, power, and polynomial--are 6:00 a.m. to 7:00 a.m. period were examined. Summary standard mathematical functions commonly used in data statistics for the number of links, total observed count, analysis. Two candidate equation forms--the Bureau of and total estimated flow for volume ranges, along with Public Roads (BPR) equation and the Akcelik equation-- relative error and percent root-mean-square error, were are specific to travel time and delay analysis. To allow reviewed. Scatter plots of the DTA results were also capacity constrained equilibrium assignments to be per- examined. Preliminary results from four iterations indi- formed by travel demand models, speedflow equations cated a relatively good fit with observed data. must meet several behavioral requirements. The equa- The work in Atlanta is ongoing. Efforts are focus- tions must be monotonically decreasing and continuous ing on resolving discrepancies between demand and net- functions of the volumecapacity ratio in order for all work counts and examining routes between origins and equilibrium assignment processes to arrive at a single destinations that could use these links but do not. Other unique solution. To prevent the travel model from con- activities are reviewing travel time data and the reason- fronting a request to divide by zero, the equations should ableness of the network times. Time-dependent ori- never intersect the x-axis, which would mean the pre- gindestination estimation and the use of subareas to dicted speed would be zero. reduce the size of DTA are also being explored. The exponential, BPR, and Akcelik equations were fitted through a least-squared error fitting process to the observed speedflow data. All three functional forms URBAN ARTERIAL SPEEDFLOW EQUATIONS FOR appear to account for some of the observed variation in TRAVEL DEMAND MODELS speed. Because the field data could not be used to eval- uate speedflow curve candidates for demands greater Richard Dowling and Alexander Skabardonis than capacity, a theoretical evaluation was conducted comparing their predicted delays for volumes greater Richard Dowling discussed a recent study conducted for than capacity against the delays predicted by queuing the Southern California Association of Governments theory. Based on queuing theory, when demand is (SCAG) to improve the accuracy of peak-period speeds greater than capacity, vehicles must wait their turn in predicted by the SCAG travel demand model. He line for the vehicles in front to pass through the intersec- described the purpose of the study, the data collection tion. The theoretical average delay can be graphed and activities conducted for the study, and the analysis of the compared with the predictions produced by the candi- data. Volume 2 contains a paper on the topic.2 The fol- date speedflow curves. lowing points were covered in his presentation. The fitted BPR and fitted Akcelik equations were calibrated for a volumecapacity ratio of greater than The objective of the study was to develop improved 1.0. The fitted BPR curve underestimated the delay due field-calibrated speedflow equations for use in the to queuing when demand exceeded the real-world capac- SCAG travel demand model to predict the mean speed of ity of an intersection at the end of a link. The fitted Akcelik curve is consistent with the queue delay line 2 See Dowling, R., and A. Skabardonis. Urban Arterial SpeedFlow because it is derived from classical queuing theory. The Equations for Travel Demand Models. Volume 2, pp. 109113. analysis also examined the impact of a 10% error in