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I N N O VAT I V E M E T H O D S F O R P R I C I N G S T U D I E S 147 TABLE 3 Home-Based Shop Time-of-Day Choice Model Home to Shop Shop to Home Observations 3,590 5,616 Final log L 11,852.9 17,311.8 Rho-sq. (0) 0.047 0.111 Rho-sq. (constant) 0.011 0.004 Alternatives Variable Definition Coefficient tStat Coefficient tStat AM1AM10 AM Delay max(0, AM GC NI GC) 0.06 constant 0.3201 2.4 MD1MD10 MD Delay max(0, MD GC NI GC) 0.06 constant 0.06 constant PM1PM10 PM Delay max(0, PM GC NI GC) 0.08281 2.1 0.06 constant EV EV Delay max(0, EV GC NI GC) 0 0 AM1AM5 AM Shift Early AM Delay x (7.5t) 0.4556 5.5 AM1AM5 AM Shift Early2 AM Delay x (7.5t)2 0.1914 3.7 AM6AM10 AM Shift Later AM Delay x (t7.5) 0.07396 4.0 AM6AM10 AM Shift Later2 AM Delay x (t7.5)2 MD1MD5 MD Shift Early MD Delay x (12.5t) 0.1124 5.0 MD1MD5 MD Shift Later MD Delay x (t12.5) 0.03864 0.8 PM1PM5 PM Shift Early PM Delay x (17.0t) 0.05506 2.0 0.1413 4.5 PM1PM5 PM Shift Early2 PM Delay x (17.0t)2 0.0597 3.2 PM6PM10 PM Shift Later PM Delay x (t17.0) 0.02994 1.3 0.01379 1.7 PM6PM10 PM Shift Later2 PM Delay x (t17.0)2 AM1AM10 AM Shared ride dummy(car occ.>1) 1.896 4.4 MD1MD10 MD Shared ride dummy(car occ.>1) 0.5574 5.6 PM1PM10 PM Shared ride dummy(car occ.>1) 0.9826 9.3 EV EV Shared ride dummy(car occ.>1) 0.4935 5.7 AM1AM5 AM SR Shift Early AM Shared Ride x (7.5t) 1.255 4.9 AM6AM10 AM SR Shift Late AM Shared Ride x (t7.5) 0.7076 2.6 MD1MD5 MD HS Shift Early MD HH Size x (12.5t) 0.09479 4.2 MD1MD5 MD SR Shift Early MD Shared Ride x (12.5t) 0.2199 4.0 MD6MD10 MD HS Shift Late MD HH Size x (t12.5) 0.2284 5.9 PM1PM5 PM HS Shift Early PM HH Size x (17.0t) 0.09581 2.6 0.09922 4.3 PM1PM5 PM SR Shift Early PM Shared Ride x (17.0t) 0.237 2.8 PM6PM10 PM SR Shift Late PM Shared Ride x (t17.0) 0.1159 2.8 Travel cost differences by time of day are added These models have been integrated within the four-step separately into the models, but as part of the generalized trip-based modeling system and are being used to optimize cost impedance used in trip distribution. This comes throughput in select corridors by applying as many as 15 from the assignment procedure as a separate price or toll sets of toll rates that vary by direction and facility. 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- TOLL OPTIMIZATION STRATEGIES ing only between 6:00 and 9:00 a.m.). The models are applied in iteration with traffic To set rational toll policies that meet operational and rev- assignment, as the time-of-day models use the auto travel enue goals, the data from the travel model require a post- times from assignment, but in turn provide a different processing methodology, in part to perform simple peaking factor (peak-hour demand) to use in the 1-h accounting functions not available in normal travel mod- assignment. So, the assignment process constrains the els (such as revenue calculations), as well as to perform amount of peak spreading predicted by the time-of-day more complex toll optimization procedures, taking oper- models. ation constraints into account. This methodology adopts the language of optimization as its core approach. Policy In the application of the time-of-day model, we assign goals that do not have a specific numerical target, such as the peak 60-min time period for the a.m. peak and mid- throughput or revenue maximization, are expressed as an day time periods as input to the feedback process of travel objective function. Goals that have a specific target-- times for trip distribution and mode choice. After the final such as maintaining a specific level of service in a HOT iteration, the trips in each 30-min period are aggregated lane--are expressed as constraints on the objective. back to the five time periods (a.m. peak, midday, p.m. Toll optimization occurs in two phases, as illustrated in peak, evening, and night) for evaluation of performance Figure 1. First, the travel model is run for a set of toll rates on the system. that remain constant throughout the day. Then, these flat