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⢠Travel cost differences by time of day are added separately into the models, but as part of the generalized cost impedance used in trip distribution. This comes from the assignment procedure as a separate price or toll skim by time of day. Unlike travel time, however, the user is able to specify this cost to remain constant over a specific period (e.g., a congestion pricing policy operat- ing only between 6:00 and 9:00 a.m.). ⢠The models are applied in iteration with traffic assignment, as the time-of-day models use the auto travel times from assignment, but in turn provide a different peaking factor (peak-hour demand) to use in the 1-h assignment. So, the assignment process con strains the amount of peak spreading predicted by the time-of-day models. In the application of the time-of-day model, we assign the peak 60-min time period for the a.m. peak and mid- day time periods as input to the feedback process of travel times for trip distribution and mode choice. After the final iteration, the trips in each 30-min period are aggregated back to the five time periods (a.m. peak, midday, p.m. peak, evening, and night) for evaluation of performance on the system. These models have been integrated within the four-step trip-based modeling system and are being used to optimize throughput in select corridors by applying as many as 15 sets of toll rates that vary by direction and facility. TOLL OPTIMIZATION STRATEGIES To set rational toll policies that meet operational and rev- enue goals, the data from the travel model require a post- processing methodology, in part to perform simple accounting functions not available in normal travel mod- els (such as revenue calculations), as well as to perform more complex toll optimization procedures, taking oper- ation constraints into account. This methodology adopts the language of optimization as its core approach. Policy goals that do not have a specific numerical target, such as throughput or revenue maximization, are expressed as an objective function. Goals that have a specific targetâ such as maintaining a specific level of service in a HOT laneâare expressed as constraints on the objective. Toll optimization occurs in two phases, as illustrated in Figure 1. First, the travel model is run for a set of toll rates that remain constant throughout the day. Then, these flat 147INNOVATIVE METHODS FOR PRICING STUDIES TABLE 3 Home-Based Shop Time-of-Day Choice Model Home to Shop Shop to Home Observations 3,590 5,616 Final log L â11,852.9 â17,311.8 Rho-sq. (0) 0.047 0.111 Rho-sq. (constant) 0.011 0.004 Alternatives Variable Definition Coefficient tâStat Coefficient tâStat AM1âAM10 AM Delay max(0, AM GC â NI GC) â0.06 constant â0.3201 â2.4 MD1âMD10 MD Delay max(0, MD GC â NI GC) â0.06 constant â0.06 constant PM1âPM10 PM Delay max(0, PM GC â NI GC) â0.08281 â2.1 â0.06 constant EV EV Delay max(0, EV GC â NI GC) 0 0 AM1âAM5 AM Shift Early AM Delay x (7.5ât) 0.4556 5.5 AM1âAM5 AM Shift Early2 AM Delay x (7.5ât)2 â0.1914 â3.7 AM6âAM10 AM Shift Later AM Delay x (tâ7.5) 0.07396 4.0 AM6âAM10 AM Shift Later2 AM Delay x (tâ7.5)2 MD1âMD5 MD Shift Early MD Delay x (12.5ât) 0.1124 5.0 MD1âMD5 MD Shift Later MD Delay x (tâ12.5) 0.03864 0.8 PM1âPM5 PM Shift Early PM Delay x (17.0ât) 0.05506 2.0 0.1413 4.5 PM1âPM5 PM Shift Early2 PM Delay x (17.0ât)2 â0.0597 â3.2 PM6âPM10 PM Shift Later PM Delay x (tâ17.0) 0.02994 1.3 0.01379 1.7 PM6âPM10 PM Shift Later2 PM Delay x (tâ17.0)2 AM1âAM10 AM Shared ride dummy(car occ.>1) â1.896 â4.4 MD1âMD10 MD Shared ride dummy(car occ.>1) 0.5574 5.6 PM1âPM10 PM Shared ride dummy(car occ.>1) 0.9826 9.3 EV EV Shared ride dummy(car occ.>1) 0.4935 5.7 AM1âAM5 AM SR Shift Early AM Shared Ride x (7.5ât) â1.255 â4.9 AM6âAM10 AM SR Shift Late AM Shared Ride x (tâ7.5) 0.7076 2.6 MD1âMD5 MD HS Shift Early MD HH Size x (12.5ât) â0.09479 â4.2 MD1âMD5 MD SR Shift Early MD Shared Ride x (12.5ât) â0.2199 â4.0 MD6âMD10 MD HS Shift Late MD HH Size x (tâ12.5) â0.2284 â5.9 PM1âPM5 PM HS Shift Early PM HH Size x (17.0ât) â0.09581 â2.6 â0.09922 â4.3 PM1âPM5 PM SR Shift Early PM Shared Ride x (17.0ât) â0.237 â2.8 PM6âPM10 PM SR Shift Late PM Shared Ride x (tâ17.0) 0.1159 2.8