Travel Demand Model - OKI

OKI/MVRPC Travel Demand Model – Version 6.0between counted traffic on the links that comprise the optimal path between O-D zone pairs and theexpected traffic that would result from an assignment of the O-D matrix to the network. In this case, theoptimal (least cost or shortest travel time) path is that which would result from an all-or-nothingassignment to the network.Figure 2-7, below, shows the steps in the algorithm. As described in Nielsen’s (1993) research paper, it isa bi-level algorithm that begins with an assignment of the seed matrix to the network. 1 At the first level,the algorithm attempts to minimize the difference (squared error) between the counted traffic and thepredicted traffic assigned to the network through a trial-and-error method of adjusting networkassignment parameters. This is described by Nielsen as a “possible” step, one that seems to have beenleft out of the TransCAD 4.0 implementation.At the second level, matrix estimation, the ratio of counted-to-predicted traffic (resulting from the firstlevel) is calculated for each link with a count. This ratio is multiplied times the previous zone-to-zoneflows that use that link as a shortest path to calculate an expected traffic flow between each zone pairusing that link. Next, for each O-D pair, the sum of the expected traffic flows from each link on theshortest path between i and j is used to calculate a mean expected traffic flow for that O-D pair. Thismean expected i-j flows for each O-D pair become the new predicted trip matrix. This new matrix isassigned to the network and, again, the squared error between counted and predicted traffic flows forlinks with counts is calculated.At this point, the algorithm returns to the first level to adjust network assignment parameters, a stepwhich, again, is not implemented in TransCAD 4.0. If the error is within an acceptable tolerance range orreaches the maximum number of iterations, the algorithm terminates. Otherwise, the algorithm returnsto the second level and another matrix is estimated as before. This continues until either an acceptablemaximum error measure is computed, or until a maximum number of iterations reached. The procedureallows estimation of only one vehicle class at a time, requiring SU and MU truck trip tables to becalibrated separately.The user equilibrium method of assignment was used for this work, based on a daily assignment of theseed matrix to the auxiliary truck network, described above in Section 2.1.2. The assignment processuses pre-loaded daily passenger-vehicle flows as background traffic, including them in the volume-delaycalculations to simulate congested travel conditions, as shown in the following equation:Tc= TVpreload. pass.veh.+ Vtrucksβ[ 1+α () ]0 CThe pre-loaded auto volumes were created during the process of generating travel time skims in the tripdistribution step of the seed matrix development, described above in Section 2.2.2. As with thegeneration of travel time skims, the BPR volume-delay function was used with α and β parameters valuesdeveloped by OKI for specific link functional class and area types.During development it was found that running the procedure until an acceptable tolerance of 0.1 wasreached tended to produce a final matrix that differed substantially from the seed matrix. To produce asynthetic matrix that is closer to the original matrix, while still fitting the matrix flows to the counts,Nielsen (1993, p. 14) recommends using five to ten iterations. For consistency, all of the truck trip tableswere produced using eight iterations, which proved to provide a good fit to the counts while preservingthe general distribution of interchange values found in the seed matrix.1 Nielsen, O. A., 1993. “A New Method for Estimating Trip Matrices from Traffic Counts. Paper 1993-3,Technical University of Denmark.Truck Model - Base-Year Truck Model Development 21