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DYNAMIC TRAFFIC ASSIGNMENT MODEL BREAKDOWN 107 TABLE 1 Dynamic UserEquilibrium Summary Statistics After First Signal Retime vol7Range Volume Range Link Counts 67 a.m. Count 67 a.m. Flow Rel. Error % RMSE 0 <500 91 28,544 43,276 51.6% 126.5 1 500999 46 32,877 32,797 0.2% 79.4 2 1,0001,999 34 47,934 39,065 18.5% 62.7 3 2,0004,999 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 9000 10000 8000 9000 y = 0.974x + 101.83 y = 0.8293x + 178 R2 = 0.8266 R2 = 0.8783 7000 8000 6000 7000 6000 vista 67 vista 67 5000 5000 4000 4000 3000 3000 2000 2000 1000 1000 linkFlow linkFlow Linear (linkFlow) Linear (linkFlow) 0 0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10,000 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10,000 obs count 67 obs count 67 FIGURE 2 Dynamic userequilibrium solution after first FIGURE 3 Dynamic userequilibrium solution after fourth signal retime. signal retime. TABLE 2 Dynamic UserEquilibrium Summary Statistics After Fourth Signal Retime vol7Range Volume Range Link Counts 67 a.m. Count 67 a.m. Flow Rel. Error % RMSE 0 <500 91 28,544 42,952 50.5% 119.0 1 500999 46 32,877 33,295 1.3% 72.0 2 1,0001,999 34 47,934 40,493 15.5% 62.4 3 2,0004,999 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 resolving the equilibrium settings, and so forth. The counts are in these later periods. The challenge is to iden- flows seemed to be converging toward the observed tify the reasons for these poor DTA results and develop a counts, and the traffic control settings seemed to be con- strategy once the causes are understood. The potential verging to a stable set of parameters. This outcome is causes are many: ill-defined demand or temporal distri- exactly what would be desired in practice, yet nothing in bution of demand, network coding problems, model cal- the theory indicates that this will happen. There is no ibration parameters, or even incorrectly defined counts. model specification for the problem of simultaneously One must try to identify causes of the underestimation of computing traffic control settings and DTA solutions. It flows by building reports and analysis procedures that is a bi-level optimization problem that has no particu- will help inform other DTA models and not just try to larly useful formulation--at least none that would pre- find some settings to which the DTA is particularly sen- dict a convergent solution. Yet the experience indicates sitive and modify those to calibrate this one model. 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 CONCLUSIONS 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 This paper describes the experience of using DTA to cal- 9:00 a.m.). (They have been calculated but are not suffi- culate regionwide time-dependent flows for the purpose ciently converged or calibrated at this point.) In fact, of specifying time-dependent origindestination flows flows are generally a little more than half of what their through a focused area for which detailed traffic