Innovations in Travel Demand Modeling, Volume 2: Papers (2008)

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resolving the equilibrium settings, and so forth. The flows seemed to be converging toward the observed counts, and the traffic control settings seemed to be con- verging to a stable set of parameters. This outcome is exactly what would be desired in practice, yet nothing in the theory indicates that this will happen. There is no model specification for the problem of simultaneously computing traffic control settings and DTA solutions. It is a bi- level optimization problem that has no particu- larly useful formulation— at least none that would pre- dict a convergent solution. Yet the experience indicates that the solution was moving toward convergence. While these results look promising, they do not tell the whole story. These results were for a fairly low level of demand (6:00 to 7:00 a.m.); results were not shown for subsequent hours (i.e., 7:00 to 8:00 a.m. or 8:00 to 9:00 a.m.). (They have been calculated but are not suffi- ciently converged or calibrated at this point.) In fact, flows are generally a little more than half of what their counts are in these later periods. The challenge is to iden- tify the reasons for these poor DTA results and develop a strategy once the causes are understood. The potential causes are many: ill- defined demand or temporal distri - bution of demand, network coding problems, model cal- ibration parameters, or even incorrectly defined counts. One must try to identify causes of the underestimation of flows by building reports and analysis procedures that will help inform other DTA models and not just try to find some settings to which the DTA is particularly sen- sitive and modify those to calibrate this one model. CONCLUSIONS This paper describes the experience of using DTA to cal- culate regionwide time- dependent flows for the purpose of specifying time- dependent origin–destination flows through a focused area for which detailed traffic 107DYNAMIC TRAFFIC ASSIGNMENT MODEL BREAKDOWN TABLE 1 Dynamic User–Equilibrium Summary Statistics After First Signal Retime vol7Range Volume Range Link Counts 6–7 a.m. Count 6–7 a.m. Flow Rel. Error % RMSE 0 <500 91 28,544 43,276 51.6% 126.5 1 500–999 46 32,877 32,797 0.2% 79.4 2 1,000–1,999 34 47,934 39,065 18.5% 62.7 3 2,000–4,999 21 72,760 75,987 4.4% 43.6 4 5,000+ 16 107,936 86,434 19.9% 45.6 Total 208 290,051 277,559 4.3% 77.6 TABLE 2 Dynamic User–Equilibrium Summary Statistics After Fourth Signal Retime vol7Range Volume Range Link Counts 6–7 a.m. Count 6–7 a.m. Flow Rel. Error % RMSE 0 <500 91 28,544 42,952 50.5% 119.0 1 500–999 46 32,877 33,295 1.3% 72.0 2 1,000–1,999 34 47,934 40,493 15.5% 62.4 3 2,000–4,999 21 72,760 83,557 14.8% 39.2 4 5,000+ 16 107,936 103,381 4.2% 32.7 Total 208 290,051 303,678 4.7% 63.0 0 1000 2000 vi st a 6– 7 obs count 6–7 3000 4000 5000 6000 7000 8000 9000 9000 8000 7000 6000 5000 4000 3000 2000 1000 0 10,000 Linear (linkFlow) linkFlow y = 0.8293x + 178 R2 = 0.8266 FIGURE 2 Dynamic user–equilibrium solution after first signal retime. vi st a 6– 7 9000 10000 8000 7000 6000 5000 4000 3000 2000 1000 0 0 1000 2000 obs count 6–7 3000 4000 5000 6000 7000 8000 9000 10,000 y = 0.974x + 101.83 R2 = 0.8783 Linear (linkFlow) linkFlow FIGURE 3 Dynamic user–equilibrium solution after fourth signal retime.