1 MESOSCOPIC SIMULATION EVALUATION OF DYNAMIC CONGESTION 2 PRICING STRATEGIES FOR CROSSINGS 3 4 Kaan Ozbay, Ph.D 5 Professor & Director, 6 Rutgers Intelligent Transportation Systems Laboratory 7 Rutgers, The State University of 8 Department of Civil and Environmental Engineering 9 623 Bowser Road, Piscataway, NJ 08854 10 Tel: +1 732 445 2792, Fax: +1 732 445 0577, Email: [email protected] 11 12 13 Ender Faruk Morgul (corresponding author) 14 Graduate Research Assistant, 15 Rutgers Intelligent Transportation Systems Laboratory 16 Rutgers, The State University of New Jersey 17 Department of Civil and Environmental Engineering 18 623 Bowser Road, Piscataway, NJ 08854 Email: [email protected] 19 20 21 Satish Ukkusuri, Ph.D 22 Associate Professor, 23 School of Civil Engineering, Purdue University, 24 550 Stadium Mall Drive, West Lafayette, IN 47907-2051, USA 25 Tel: +1 765 494 2296, Fax: +1 765 494 0395, Email: [email protected] 26 27 28 Shrisan Iyer 29 Research Associate, 30 Rutgers Intelligent Transportation Systems Laboratory 31 Rutgers, The State University of New Jersey 32 CoRE 736, 96 Frelinghuysen Road, Piscataway, NJ 08854 33 Tel: +1 732 445 6243 x274, Fax: +1 732 445 0577, Email: [email protected] 34 35 36 Wilfredo F. Yushimito 37 Graduate Research Assistant, 38 Department of Civil and Environmental Engineering, Rensselaer Polytechnic Institute, 39 110 Eighth Street, 5107 Jonsson Engineering Center, Troy, NY 12180-3590, USA 40 Tel: +1 518 276 8306, Fax: +1 518 276 4833, Email: [email protected] 41 42 43 Abstract: 205 words 44 Word count: 5,352 Text + 3 Figures + 5 Tables = 7,352 words 45 Submission Date: August 1st, 2010

TRB 2011 Annual Meeting Paper revised from original submittal. Ozbay, Morgul, Ukkusuri, Iyer, and Yushimito 1

46 ABSTRACT 47 48 Congestion pricing charges motorists during peak hours to encourage them to either switch their 49 travel times or to use alternative routes. In recent years, with the help of technological 50 developments such as electronic toll collection systems, pricing can be conducted dynamically; 51 tolls can be changed in real-time according to measured traffic conditions. Dynamic pricing is 52 currently deployed as High Occupancy Toll (HOT) lanes; however the time-dependent pricing 53 idea can be extended to a setting where drivers make route choices that are relatively more 54 complex. 55 In the case of New York City, many of the limited number of crossings to the island of 56 are tolled, and function as parallel alternatives. One of the key aspects of this study is 57 the estimation of realistic values of time (VOT) for different classes of users, namely, commuters 58 and commercial vehicles. New York region-specific VOT for commercial vehicles is estimated 59 using a logit model of stated preference data. In this paper a simulation-based evaluation of 60 dynamic congestion pricing on these crossings is conducted using a mesoscopic traffic 61 simulation model with a simple step-wise tolling algorithm. The simulation results are analyzed 62 to measure the change in volumes and toll revenues between potential dynamic pricing and static 63 tolling currently in place.

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64 INTRODUCTION 65 66 Congestion pricing can successfully manage traffic congestion by charging users for travel, 67 particularly during peak hours, and can be implemented in static or dynamic form. Static pricing 68 refers to a tolling system where toll rates remain fixed or are changed depending on the time of 69 day, but the system toll rate schedule is not affected by the real-time traffic conditions. In 70 dynamic congestion pricing, real-time traffic conditions are also considered. Several traffic 71 parameters can be considered to determine the toll rate, including travel speed, occupancy, and 72 traffic delays. These parameters are measured in real-time and toll rates are updated within short 73 time intervals. Users are informed about the current toll rate with the help of variable message 74 signs and they are allowed to choose between a tolled, faster, option, or a slower, free (or lower 75 priced), option. 76 Dynamic pricing applications in the United States are limited to high occupancy toll lanes 77 (HOT) where drivers may choose a less-congested tolled lane to save travel time. This paper 78 aims to extend the idea of dynamic pricing to a network where drivers can choose from multiple 79 alternative facilities to reach their destination. The New York metropolitan network is 80 chosen for analysis, focusing on the and tunnels crossing to Manhattan, which are some 81 of the busiest tolled and non-tolled crossings in the country. A mesoscopic simulation network is 82 created using Transmodeler and calibrated using real-world counts and other available traffic 83 data. In the network users make route choices to cross to Manhattan depending on the 84 dynamically varying tolls of the crossings. The goal is to observe the effects of dynamically 85 priced tolls on traffic conditions using a similar tolling scheme being applied in current HOT- 86 lane deployments. 87 This paper also considers varying behavior for different classes of vehicles through the use of 88 realistic value of time (VOT) estimations. VOT is a significant input to pricing modeling as it 89 determines the users’ route choice in response to both congestion and tolling. Passenger car and 90 commercial vehicle values of time in the simulation network are different, with passenger car 91 VOT taken from previous studies while commercial vehicle VOT is estimated in this paper using 92 stated-preference data obtained from a 2004 region-specific study. The simulation output focuses 93 on differences in traffic congestion parameters and total daily toll revenues for the dynamically 94 priced network versus a simulation of the existing statically-tolled network. The output measures 95 are analyzed in detail to determine the feasibility of dynamic pricing in this application.

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96 LITERATURE REVIEW 97 98 Theoretical Dynamic Pricing Studies 99 The first studies of congestion pricing focused on static tolling, investigating the optimization of 100 toll rates, toll plaza locations, or links to be tolled in a large network. The idea of tolling on roads 101 has been an important topic of study for many decades. Pigou (1920) argued the idea of charging 102 motorists for the first time in “Economics of Welfare” (1). Following Pigou’s argument, Walters 103 (1961) gave the first comprehensive explanation of congestion pricing in his study about 104 measuring private and social costs of highway congestion (2). Within the following years, 105 Vickrey (1963) published a paper about road pricing in urban and suburban transport, Beckman 106 (1965) studied the optimal tolls for highways, bridges, and tunnels, and Vickrey (1969) 107 conducted another study about congestion theory. These studies constituted the fundamentals of 108 modern congestion pricing theory (3, 4, 5). 109 Although dynamic congestion pricing studies are more recent, there are several theoretical 110 studies available in the literature. Several authors conducted network optimization-based 111 theoretical studies for dynamic pricing considering both fixed and variable demands, and even 112 including different mode choices. Wie and Tobin (1998) provided two theoretical models for 113 dynamic congestion pricing of general networks. The first model considered day-to-day learning 114 of users with stable demands every day, and the second the case where users make independent 115 decisions each day under fluctuating travel demand conditions (6). Joksimovic et al. (2005) 116 presented a dynamic road pricing model with heterogeneous users for optimizing network 117 performance (7). Wie (2007) considered dynamic congestion pricing and the optimal time- 118 varying tolls with the Stackelberg game model (8). 119 Simulation-based models for dynamic pricing were also developed by some researchers. 120 Mahmassani et al. (2005) conducted a study on variable toll pricing with heterogeneous users 121 with different value of time preferences (9). Teodorovic and Edara (2007) proposed a real-time 122 road pricing model on a simple two-link parallel network (10). Their system made use of 123 dynamic programming and neural networks. Yin and Lou (2007) proposed and simulated two 124 models for dynamic tolling. The first one is a feedback-control based method similar to the 125 ALINEA concept in ramp-metering. The control logic for determining the toll rates is stated in 126 Equation (1): 127

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128 r( t 1)  r ( t )  K ( o ( t )  o *) (1) 129 where, r(t) and r (t+1) are the toll rates at time intervals t and t+1, respectively, o(t) is the 130 measured occupancy, K is the regulator parameter and o* is the desired occupancy for the tolled 131 lane. 132 The second method is a reactive-self learning approach in which motorists’ willingness to 133 pay can be learned gradually, and this data can be used to determine the toll rates (11). Lu et al. 134 (2008) conducted a study on dynamic user equilibrium traffic assignment and provided a 135 solution algorithm for dynamic road pricing. Their model considers traffic dynamics and 136 heterogeneous user types with their responses to toll charges (12). Friesz et al. (2007) considered 137 the dynamic optimal toll problem with user equilibrium constraints and presented two algorithms 138 with numerical examples (13). Karoonsoontawong et al. (2008) provided a simulation-based 139 dynamic marginal cost pricing algorithm. They compared the dynamic and static scenarios in 140 simulation and obtained minor system benefits in dynamic case (14). Feedback-based algorithms 141 for dynamic pricing were also developed for practical applications. Zhang et al. (2008) 142 developed a feedback-based dynamic tolling algorithm for HOT (High Occupancy Toll) lane 143 applications. In their model they used travel speed and toll changing patterns as parameters to 144 calculate optimal flow ratio for the HOT lanes using feedback-based piecewise linear function. 145 Then using the discrete route choice model they calculate the required toll rate by backward 146 calculation (15). 147 148 Road Pricing Applications 149 Major road pricing applications in the United States and their tolling methods are listed in 150 Table 1. Currently, dynamic pricing applications are limited to HOT lanes. 151 Table 1: Major Value Pricing Applications in the United States

Facility Initiation Date Pricing Method

Facilities with Static Pricing Orange County SR-91, CA December 1995 Pre-determined toll schedule (16) Houston I-10, TX January 1998 HOT lanes (17) Lee County, FL August 1998 Time-of-day pricing on bridges (18) New Jersey Turnpike, NJ Fall 2000 Time-of-day pricing (19)

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Houston US 290, TX November 2000 HOT lanes (20) Port Authority of NY&NJ March 2001 Time-of-day pricing (21) Interstate Crossings San Joaquin Hills Toll Road, February 2002 Time-of-day pricing (22) Orange County, CA Illinois Tollway, IL Winter 2005 Time-of-day pricing (23) Facilities with Dynamic Pricing San Diego I-15, CA April 1998 Dynamic pricing in HOT lanes (24) Minnesota I-394, MN Spring 2005 Dynamic pricing in HOT lanes (25) WA167, WA May 2008 Dynamic pricing in HOT lanes (26) I-95, FL Summer 2008 Dynamic pricing in HOT lanes (27)

152 153 Value of Time 154 Value of time (VOT) which is defined as the change in user’s willingness to pay for a unit 155 change in travel time is one of the most important factors affecting driver behavior in response to 156 congestion tolls. Blayac et al. (2001) proposed the idea of relaxing the constancy of marginal 157 utilities and derived analytical functions to relate VOT, time, price, income level, and 158 departure/arrival time restrictions (28). Following the same idea, Ozbay et al. (2008) improved 159 the functions by adding departure time choices and used a nested logit model to estimate value of 160 travel time of New Jersey Turnpike (NJTPK) users under the presence of a time-of-day pricing. 161 Their findings showed that the value of time of NJTPK users was between $15-$20 (29). 162 Although there are many studies on commuter VOT there is a limited research on 163 commercial vehicle VOT. One of the first studies on commercial vehicle VOT was published by 164 Haning and McFarland (1963). Their analysis showed that commercial vehicle VOT should be 165 greater than that of passenger cars, even if no cargo is being carried (30). Kawamura (1999) 166 defined a commercial vehicle VOT using two different methods: switching point analysis and a 167 random coefficient logit model. In his study, he analyzed the stated preference by conducting a 168 survey on 77 trucking companies. His findings showed that commercial vehicle VOT has a mean 169 of $23.4/hr and a standard deviation of $32/hr (31). Smalkoski and Levinson (2003) conducted a 170 value of time determination for commercial vehicle operators in Minnesota. They fit a tobit

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171 model to the data they obtained from the adapted stated preference survey. Fifty companies were 172 interviewed and they found a VOT of $49.42/hr (32). 173 Most value of time estimation studies are based on stated preference user surveys. In these 174 surveys, there are questions to get an idea about the traveler choice behavior under different 175 circumstances. Vilain and Wolfram (2001) conducted a survey of truckers in the New York 176 region and their study indicated that the response of truckers to congestion charges would be 177 relatively modest (33). Holguin-Veras et al. (2005) state that 61.6% of commercial vehicles 178 travel at the time they do because of customer requirements (34). This is an important finding 179 showing that most of the truckers do not have schedule flexibility. In addition to stated 180 preference, analysis of revealed preference data also gives an idea about possible trucker 181 behavior. Ozbay et al. (2006) conducted an analysis of the impacts of time-of-day pricing 182 application initiated in 2001 by the Port Authority of New York and New Jersey (PANYNJ), 183 which operates the three crossings between Manhattan and New Jersey, as well as two other 184 crossings in the region. The authors concluded that there is a decrease in truck traffic on peak 185 shoulders but they also noted that there may be other factors affecting this decline, such as the 186 economic recession that began in the New York region in 2001 (35). 187 188 Value of Time Estimation for NY-NJ Commercial Vehicles 189 In this section, an estimation of commercial vehicle value of time (VOT) using a binary logit 190 model based on data obtained from the PANYNJ survey is presented, which is then used in 191 dynamic pricing simulations. The statistical data analysis software STATA is used for the logit 192 model construction and evaluation. A methodology was developed similar to Kawamura’s (1999) 193 work on commercial vehicle value of time estimation using a logit model (31). A utility function 194 for an individual or a firm n choosing an alternative i was assumed as in Equation (2): 195 UCT     (2) 196 in in in in

197 where Cin is the monetary cost of travel and Tin is the monetary cost of travel time for using

198 alternative i for an individual or firm n. The coefficients  and  are parameters and the random

199 variable in is the unobserved portion of the utility which is assumed identically and

200 independently distributed (IID) with extreme value distribution. The unobserved portion of the

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201 utility includes unobserved attributes, taste variations, measurement errors and imperfect 202 information (31).

203 The standard logit formula is then used to calculate the probability Pin of choosing

204 alternative i among j alternatives, as in Equation (3): 205

exp(Vin ) 206 Pin  j (3) exp(Vin ) i1

207 where Vin is the observable part of the utility (i.e. CTin in ). Coefficients  and  can be 208 obtained by the maximum likelihood estimation method and the marginal utilities can be found 209 by Equation (4) and Equation (5): 210

V 211 in   (4) C in V 212 in   (5) T in 213 These ratios give the marginal effects of each parameter on the utility function and the value of 214 time is simply calculated by the ratio of the two coefficients as in Equation (6): 215  216 Value of Time = (7)  217 The ratio in Equation (6) is how much an individual or a firm is willing to pay to reduce travel 218 time by one unit. In a more simple way, this equation can be written as in Equation (7): 219 p 220 Value of Time = (8) t 221 where p is the unit change in price and t is the unit change in travel time. Unit change in

222 price can be either a change in toll rate or any other savings or extra costs that are proposed when 223 the user changes his/her behavior. 224 Independent variables used to define the cost related parameter  and time related parameter

225  are type of business and trip distance respectively. Levinson, et al. (2004) provided a detailed

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226 study for per kilometer costs for different industries in Minnesota, depending on their trucker 227 survey. The values they provided are for 2004 which is the same year of the PANYNJ survey. 228 The regional consumer price indexes obtained from Bureau of Labor Statistics (BLS) are used 229 for adjustment to the New York region, and per-mile operation costs are calculated for all data 230 points. 231 In the PANYNJ survey, each respondent was asked for the origin and destination states of 232 their regular trips. The time parameter is calculated for every data point by determining the 233 average distance they travel. Analysis is conducted for different combinations of carrier types 234 and origins (e.g. county or state) where the respondents’ trips originated. However there is a 235 limited sample size for some regions. 236 The results showed that commercial vehicles that generate their trips from New York have a 237 higher VOT compared to the commercial vehicles that generate trips from New Jersey. In 238 addition when the shipment sizes are considered, less-than-truckload (LTL) type carriers have a 239 higher VOT compared to the truckload (TL) type of carriers. Table 3 shows the estimation 240 results obtained. When the data is not categorized a VOT of $33.62 is obtained for commercial 241 vehicles. In a previous trucker interview that was conducted by PANYNJ for truckers, one 242 respondent stated that if there was an exclusive truck lane he would prefer paying $5 or $6 toll 243 for an extra ten minute time savings. This can be interpreted as a value of time between $30-$36 244 per hour, which agrees with the estimation (36). 245 Table 2: Commercial Vehicle VOT Estimation and Estimations from Literature Cost Time VOT 2 Sample Group Sample Size coefficient, Chi coefficient,  ($)  Origin: New York 32 137.4 4.16 5.14 $32.99 Origin: New Jersey 152 79.48 4.01 4.21 $19.82 Origin: Middlesex 65 48.03 0.84 3.49 $56.72 County, Union County Size: LTL 93 17.4 0.44 3.64 $38.9 Size: TL 52 29.8 2.2 3.74 $13.5 All samples 198 35.1 1.04 4.45 $33.62

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Results from Literature Author Year Region VOT ($)(2004 values) Southwestern Haning & 1963 Region of the $20.33-$26.46 McFarland US Kawamura 1999 California, US $31.37 Smalkoski & 2003 Minnesota, US $25.08-$51.43 Levinson

246 247 SIMULATION 248 249 Both dynamic and static congestion pricing scenarios are studied in a mesoscopic simulation 250 model of the Manhattan crossings, with a primary focus on charging tolls to enter Manhattan. 251 The traffic simulation software TransModeler is used for simulating the dynamic pricing 252 schemes at the mesoscopic level. Static pricing, which is currently applied at most of the 253 crossings modeled, has fixed toll rates throughout the day (in some cases off-hour discounts 254 exist). Traffic conditions do not affect the toll rates, as they would in a dynamic pricing case. A 255 static pricing scenario is simulated for comparison to the dynamic case. 256 257 Simulation Network 258 The network used for pricing simulations is shown in Figure 1, compared to the real NY-area 259 highway network. This network is a modified version of an extracted sub-network from the New 260 York Best Practice Model, a regional travel demand model. Since pricing is expected to affect 261 users’ route decisions, major connecting roads are included outside of Manhattan so that 262 simulated drivers may select a different to either save money due to different toll costs or 263 travel times as a result of congestion. One of the major requirements in real world dynamic 264 pricing implementations is the availability of an alternative route for travelers to select in case 265 they are not willing to pay the toll. Dynamic pricing of High Occupancy Toll (HOT) lanes, 266 where only one or two lanes of a free highway are tolled, allows users who prefer to avoid 267 congestion in regular lanes to use HOT lanes by paying a dynamically priced toll. Travel speeds 268 in HOT lanes are guaranteed to be higher than a previously set level of service by adjusting toll 269 rates in accordance to the congestion level. Dynamic pricing application for Manhattan crossings

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270 can be conducted when two or more crossings serve as the alternatives of each other. This 271 system allows users to select either cheapest or faster routes by comparing toll rates and selecting 272 the best possible alternative to enter Manhattan. 273 The major crossings to enter Manhattan currently consist of a mixture of free and tolled 274 alternatives with different toll rates. The crossings used in the simulation network are: 275 Manhattan-/ Crossings (east of Manhattan) 276  Triborough (Tolled) 277  (Free) 278  Queens Midtown Tunnel (Tolled) 279  (Free) 280  (Free) 281  (Free) 282  Brooklyn Battery Tunnel (Tolled) 283 Manhattan-New Jersey crossings (west of Manhattan) 284  George (Tolled) 285  (Tolled) 286  (Tolled) 287 288 The network includes two connecting roads for Manhattan-New Jersey crossings for users 289 who want to use an alternative route to cross to Manhattan. These two routes are New Jersey 290 Turnpike (NJTPK), a major highway, and Route 1-9, an arterial, which increases the complexity 291 of the network since NJTPK is tolled and Route 1-9 is free. The crossings from New Jersey to 292 Manhattan are all tolled at a uniform rate. On the east side of Manhattan, I-278 (Brooklyn- 293 Queens Expressway) is provided to link the alternative crossings. These crossings are a mixture 294 of tolled and free routes. 295 296 297 298 299 300

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George Washington B. Triborough B.. NJTPK

Lincoln T. Queensboro B.. G.W.B I-278 (BQE) Rt 1-9 Lincoln T.

Queens Midtown T. NJTPK Williamsburg B.

Manhattan B.

Brooklyn B. Holland T. Holland T. B.Battery T. 301 302 Figure 1: NY Highway Map (left) (37) and Crossings and Routes Used in the TransModeler 303 Simulation Network (right) 304 305 Network Calibration 306 Network calibration is performed ensure that traffic volumes are realistically distributed to 307 the crossings. After several calibration trials all the crossings have at most a 10% error in traffic 308 volume between the simulation volumes and real volume data, by modification of the link 309 characteristics (e.g. free flow speed, speed limit, lane width etc.) (38). For dynamic pricing 310 simulations the behavior of users in response to the dynamically priced tolls necessitates its own 311 calibration. Driver values of time are adjusted to successfully implement the dynamic toll rate 312 schedule, along with error factors defined in TransModeler which affect the perception of the 313 shortest path of the user, such as how many links in advance users consider before doing a 314 change in their route choice or gap acceptance models. These parameters were adjusted to ensure 315 as realistic a simulation possible, however their true values are unknown since this application 316 has not been field tested. 317 318 Toll Rates 319 In the static pricing scenario, toll rates given in Table 3 are held constant throughout the day, 320 which is the current tolling application in all of the tolled crossings. Toll rates in static pricing 321 are defined differently by vehicle class, but since not all vehicle classes are defined in the 322 simulation, average values for each class are used. Truck tolls are calculated by taking the traffic

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323 volume percentages of truck classes by axle. The data obtained from static pricing simulations is 324 used for comparison with dynamic pricing output data. The same demands are used in both 325 simulations to compare the different volume distributions to the crossings and different toll 326 revenues. 327 328 Table 3: Static Pricing Simulation Toll Rates MANHATTAN-NEW JERSEY CROSSINGS (George W. Bridge, Lincoln Tunnel, Holland Tunnel) Vehicle Class Toll Rate Passenger Car $8.00 Trucks $27.00 Small Commercials $13.00 MANHATTAN-BROOKLYN/QUEENS TOLLED CROSSINGS (Triborough Bridge, Queens-Midtown Tunnel, Brooklyn Battery Tunnel) Vehicle Class Toll Rate Passenger Car $5.50 Trucks $24.00 Small Commercials $11.00

329 330 In the dynamic pricing scenario a robust tolling model is needed to meet driver satisfaction, 331 by offering them acceptable toll rates to travel and to meet the minimum requirements for a 332 previously set level of service for traffic. TransModeler enables dynamic pricing with two 333 parameters, “minimum occupancy” and “maximum speed”. In this simulation study only average 334 occupancy level was considered in determining the real-time toll rates. 335 Figure 2 shows the toll rate change in New Jersey-Manhattan and Brooklyn/Queens- 336 Manhattan crossings compared with occupancy values. In the static pricing scenario an average 337 occupancy rate of 11.6% is observed for New Jersey-Manhattan crossings, therefore the static 338 pricing rates are set to 11% occupancy in the dynamic case. The Manhattan-Queens/Brooklyn 339 Crossings have an average occupancy of 12% throughout the day. Therefore static toll rates are 340 set to the minimum 12% occupancy interval in the dynamic pricing toll schedule. In the 341 simulation, toll rates are updated every five minutes.

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a) NJ-Manhattan Crossings 45 40 35 30 25 20 Toll ($) Toll 15 10 5 0 7 9 11b) Brooklyn/Queens13 15 -Manhattan17 Crossings19 21 23 25 45 Minimum Occupancy (%) 40 Passenger Cars Pickups Trucks 35 342 343 30 25 20 Toll ($) Toll 15 10 5 0 7 9 11 13 15 17 19 21 23 25 Minimum Occupancy (%) Passenger Cars Pickups Trucks Static Toll Rates

344 Figure 2: Toll Rate Change by Occupancy and Vehicle Class for a) NJ-Manhattan 345 Crossings, and b) Brooklyn/Queens-Manhattan Crossings 346 347 MESOSCOPIC SIMULATION RESULTS 348 349 Both static pricing and dynamic pricing simulations are run for four separate periods (AM: 350 6–10am, MD: 10am–3pm, PM: 3–7pm, NT: 7pm–6am). Table 4 shows the simulation data 351 obtained from the point sensors located in each crossing for each period, respectively, comparing 352 the static and dynamic pricing cases. Sensors measure the traffic count within the simulation 353 period and the average occupancies. Lower occupancy values indicate better flow conditions and 354 higher speeds. The percent difference values indicate how different the dynamic case is from the 355 static case.

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356 Table 4: Time-of-day Comparison by Traffic Volumes and Occupancies AM MD PM NT VOL OCC VOL OCC VOL OCC VOL OCC Facility % Diff. % Diff. % Diff. % Diff. % Diff. % Diff. % Diff. % Diff. Manhattan-New Jersey Crossings Holland Tunnel -4.5% -1.1% -11.0% -2.0% -0.5% -2.0% -8.2% -1.1% Lincoln Tunnel -1.0% 7.3% 8.6% -0.8% -2.9% -1.3% 8.4% 0.4% 0.4% 0.4% -0.2% 0.0% 2.7% 1.3% -0.1% 0.0% Manhattan-Brooklyn/Queens Crossings Triborough Bridge 0.0% -0.6% 0.0% -0.7% -0.8% -1.1% 0.0% 0.4% Queensboro Bridge 12.7% 0.8% 6.7% 0.1% 8.2% 0.4% 1.3% 0.5% Queens-Midtown Tunnel -26.1% 4.9% -23.9% -2.4% -22.6% -2.2% -12.3% -0.5% Williamsburg Bridge 17.3% 3.4% 14.3% -0.9% 16.8% 0.7% 5.3% 0.2% Manhattan Bridge 4.3% 0.7% 1.9% -0.2% 3.4% 0.1% 0.3% 0.0% Brooklyn Bridge 0.5% 0.0% -0.3% 2.9% 4.3% 2.1% 0.3% 1.0% 357 Brooklyn Battery Tunnel -3.6% 0.9% -2.3% -0.1% -9.5% -0.7% -0.4% 0.0% 358 359 For the Brooklyn/Queens crossings, the tolled crossings (Triborough Bridge, Queens- 360 Midtown Tunnel and Brooklyn Battery Tunnel) carry less traffic in dynamic pricing simulations 361 than the free bridges. This is due to users avoiding higher tolls and using alternative routes in the 362 peak periods, increasing the free crossings’ (Queensboro, Williamsburg, Manhattan and 363 Brooklyn Bridges) traffic volumes. As expected, all of the free crossings’ average occupancies 364 increased with the traffic shifted from tolled crossings. Similarly, traffic volumes increased for 365 the free crossings and decreased or did not change for the tolled crossings. Average occupancies 366 show that Brooklyn-Battery Tunnel and Queens-Midtown Tunnel had higher average toll rates 367 compared to the static pricing and this fact further encouraged users to select one of the free 368 alternative crossings. Significant changes are observed in traffic volumes for Queens-Midtown 369 Tunnel, Williamsburg Bridge and Brooklyn Battery Tunnel. 370 On the NJ side, AM period results show that average occupancies of Holland Tunnel 371 decrease as opposed to Lincoln Tunnel and George Washington Bridge, where average 372 occupancies increased. Similar to the tolled Queens-Midtown Tunnel and free Williamsburg 373 Bridge, a route shift can be also observed between Lincoln and Holland Tunnels. Traffic using 374 George Washington Bridge is almost the same therefore it can be concluded that approximately 375 8% traffic was switched from Holland Tunnel to Lincoln Tunnel due to higher toll rates in the 376 Holland Tunnel from high occupancy values.

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377 Figure 3 shows the response of users of NJ-Manhattan crossings due to dynamic tolling. 378 With an increasing number of vehicles in the system, higher toll rates are charged and the 379 number of vehicles changing their routes increases, as expected. The total daily toll revenues 380 calculated from the simulation network for both scenarios are given in Table 5. Results show that 381 with the assumed toll schedules all NJ-Manhattan crossings collect higher revenues in the 382 dynamic pricing scenario compared to the static pricing scenario. However on the 383 Queens/Brooklyn-Manhattan side, the Queens-Midtown Tunnel generates far lower revenues due 384 to the nearby free alternatives. Users must pay a toll in any route decision on the NJ-Manhattan 385 side, therefore in the peak hours it is inevitable that they pay higher tolls compared to the static 386 pricing case due to the network charging higher tolls to maintain the occupancy requirements in 387 the crossings. Thus revenues increase throughout the network when dynamic pricing is deployed 388 network-wide, even with a negative change in revenues from the Brooklyn/Queens-Manhattan 389 crossings. 390 391 Table 5: Total Daily Toll Revenues by Scenario Facility Toll Revenues Increase Static Pricing Dynamic Pricing Holland Tunnel $482,520 $563,830 17% Lincoln Tunnel $594,110 $686,587 16% George Washington Bridge $1,437,000 $1,841,780 28% Triborough Bridge $358,717 $361,225 1% Queens-Midtown Tunnel $317,030 $228,048 -28% Brooklyn Battery Tunnel $187,005 $222,435 19% TOTAL $3,376,382 $3,903,905 16% 392 393

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a) Average Hourly Toll Rates 14 12 10 8 6

Toll Rate ($) Rate Toll 4 2 Holland Tunnel Lincoln Tunnel G.Washington Bridge 0 b) Total Vehicle Counts 12000 394 395 10000 8000

6000

Vehicles 4000

2000

0 c) Vehicles Changing Paths 7000 6000 5000 4000 3000 Vehicles 2000 1000

0

1:00 PM 1:00 PM 2:00 PM 3:00 PM 4:00 PM 5:00 PM 6:00 PM 7:00 PM 8:00 PM 9:00

6:00 AM 6:00 AM 7:00 AM 8:00 AM 9:00 AM 1:00 AM 2:00 AM 3:00 AM 4:00 AM 5:00

12:00 PM 12:00 PM 10:00 PM 11:00

11:00 AM 11:00 AM 12:00 10:00 AM 10:00

396 Figure 3: Dynamic Pricing Simulation NJ-Manhattan Crossings Statistics for a) Average 397 Hourly Toll Rates, b) Total Vehicle Counts, c) Number of Vehicles Changing Paths 398 399 CONCLUSION 400 401 Two important issues in the deployment of successful dynamic congestion pricing are 1) the 402 capability of changing toll rates in response to the changes in the network, and 2) the accurate 403 estimation of value of time (VOT) for different classes of users. The former issue can be

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404 addressed by using time-dependent toll rates while the latter requires estimation of VOT values 405 using either revealed or stated preference data. One key issue is quantification of the advantages 406 of dynamic tolling strategies before they can be deployed in real-world, which can be achieved 407 through simulation. In this paper differences between dynamic and static pricing are analyzed 408 using a real network through a mesoscopic simulation-based analysis. Driver behavior in response 409 to real-time changing toll rates is incorporated into the simulation model by defining two different 410 values of time for commuter and commercial vehicles. 411 Simulation results with realistic VOT values for different classes of users showed that 412 dynamic pricing can achieve less congested conditions, especially at peak periods, when the 413 occupancies at some of the tolled crossings are high. In addition, 16% higher toll revenues are 414 collected in the hypothetical dynamic pricing scenario compared to the simulated static tolled 415 scenario. Thus, it can be concluded that dynamic tolling strategies not only improve traffic 416 conditions but increase revenues when applied to a large network similar to the one simulated. 417 Further improvements can be made using an advanced dynamic tolling algorithm (e.g. feedback 418 based) that gives more realistic toll rates in response to time-dependent changes in traffic 419 conditions, a topic of research for another paper. 420 421 ACKNOWLEDGEMENTS 422 423 The authors would like to acknowledge USDOT for funding this innovative research study, as 424 well as New York/New Jersey-area transportation agencies such as NYMTC, NYSDOT, 425 NYCDOT, NJDOT, NJTA, and PANYNJ for providing data and models used in this study. Their 426 support is appreciated. 427 428 REFERENCES 429 430 1. Pigou, A.C., (1920), The Economics of Welfare, MacMillan and Co. Ltd., London, accessed 431 on 11/11/2009 at http://www.econlog.econlib.org/library/NPDBooks/Pigou/pgEW.html 432 2. Walters, A.A., (1961), The Theory and Measurement of Private and Social Cost of Highway 433 Congestion, Econometrics 29 (4), 676-699.

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TRB 2011 Annual Meeting Paper revised from original submittal.