Dilruba Ozmen-Ertekin, Ph.D., P.E., Assistant Professor of Engineering
Former Secretary of Transportation Norman Mineta stated in 2001 that “congestion and delay not only waste our time as individuals, they also burden our businesses and our entire economy.” Recent statistics support this statement. Traffic congestion is a national problem. In 2009 urban areas in the United States experienced 4.8 billion vehicle-hours of delay, resulting in 3.9 billion gallons in additional fuel, and a congestion cost of $115 billion to highway users, households and firms throughout the nation .
In the New York/New Jersey metropolitan area (Figure 1), served by a vast multimodal transportation system, nearly 700,000 vehicles cross the Hudson River daily from New Jersey to New York . Given such intensity, moving people and goods efficiently to, from and within the region is no simple task. The complexity of this task is compounded by the rapidly growing city and port traffic and population, further escalating the levels of congestion, as well as air pollution and traffic accidents. Recent congestion statistics demonstrate the severity of the situation: In 2009 the New York-Newark area experienced 0.45 billion vehicle-hours of delay, resulting in 0.35 billion gallons in wasted fuel and a congestion cost of $10.9 billion .
Causes of Delays
Highway congestion occurs when traffic demand approaches or exceeds the available capacity of the highway system (creating bottleneck conditions). Traffic demands vary significantly depending on the season of the year, the day of the week, and even the time of day. Also, the capacity, often mistaken as constant, can change because of weather, work zones, or traffic incidents. Figure 2 shows sources of delays in the United States. Accordingly, bottleneck delays are the single largest cause of delays .
Estimating Delays: The Case of Toll Plazas
For delay estimation, toll plazas are considered here, as they are the perfect examples for traffic bottlenecks due to the fact that many toll payment approach lanes merge into a much fewer number of lanes beyond the toll plaza.
Even though toll plazas can have adverse capacity and safety impacts on traffic, especially on urban highways, they serve an important purpose, namely revenue generation for highway agencies. Various traffic management and electronic toll collection (ETC) strategies, such as regular and high-speed E-ZPass, and time-of-day pricing (TDP), are implemented as part of toll plaza operations to change traffic supply and demand characteristics to improve network-wide level of service. In recent years, due to the increasing need to better assess the impact of toll plazas combined with these various traffic management strategies, customized or off-the shelf microsimulation and macrosimulation models of toll plaza operations have been developed.
However, it is extremely difficult and expensive to calibrate and implement microsimulation models when projects have severe budget and time constraints. Therefore, it is necessary to develop alternative macroscopic approaches that are easy to use and inexpensive compared to the more complex microsimulation tools. Several studies, although not dealing with toll plaza operations specifically, used both macroscopic and microscopic tools to predict the traffic flow characteristics (e.g., , ). This kind of a comparative approach helps determine the validity of the macroscopic approaches.
Macroscopic models can also be easily embedded in four-step demand forecasting models to estimate toll plaza delays and the impact of demand management strategies and technologies planned as part of toll collection operations. This will, of course, help the planners to easily perform sensitivity analysis of various alternatives without resorting to the microsimulation models that might not be feasible for large-scale statewide studies.
Some Previous Studies About Toll Plaza Delay Estimation
In , an analytical delay model, which estimates total delay by accounting for extra travel time due to deceleration, toll paying, acceleration and time spent waiting in queue, was formulated.
To calibrate the model, a stochastic, microsimulation model was developed. The resulting incremental delay formulation was very similar to the formula given in . The results showed that the delay model can yield estimates within 10 percent of simulated values. The author recommended
that the delay model be used for preliminary screening of alternative designs and operations, and that
further investigation be conducted to determine if the model can adequately estimate delay based upon field data.
In , the deployment of ETC was studied by developing a model to maximize social welfare associated with a toll plaza. A payment choice model was developed to estimate the share of traffic using ETC as a function of delay, price, and a fixed cost of acquiring the in-vehicle transponder. Assuming that welfare depends on the market share of ETC, and includes delay, gasoline consumption, toll collection costs, and social costs such as air pollution, the authors examined the best combination of ETC lanes and toll discount to maximize welfare. The generalized delay model suggested by  for the new Highway Capacity Manual  was employed after slight modifications.
An application to California’s Carquinez Bridge revealed that too many ETC lanes cause excessive delay to non-equipped users, whereas too high a discount costs the highway agency revenue.
Macroscopic Approach to Estimating Toll Plaza Delays
The total delay experienced at the toll plazas by each vehicle can be expressed as:
di = incremental delay (s/veh)
dd = deceleration delay (s/veh)
dp = service time (s/veh)
da = acceleration delay (s/veh)
dq = initial queue delay (s/veh)
Deceleration delay is the extra travel time incurred while drivers decelerate before reaching a tollbooth. Equation 2 can be used to calculate the deceleration delay .
dd = average deceleration delay in toll lane (s/veh)
P = proportion of noncommercial vehicles
V = free-flow speed (m/s)
Vb= speed at toll booth (m/s)
d1 = deceleration rate of noncommercial vehicles (m/s2)
d2 = deceleration rate of commercial vehicles (buses and trucks in this case) (m/s2)
Acceleration delay depends on the free-flow speed and the acceleration characteristics of vehicles, and is
given as follows :
da = average acceleration delay in toll lane (s/veh)
a1 = acceleration rate of noncommercial vehicles (m/s2)
a2 = acceleration rate of commercial vehicles (m/s2)
Other variables as defined before.
According to , the incremental delay at signal-controlled intersections on principal arterials is:
d = incremental delay (s/veh)
T = duration of analysis period (hr)
X = lane group volume/capacity ratio or degree of saturation
k = incremental delay factor that is dependent on traffic controller settings
I = upstream filtering/metering adjustment factor
c = lane group capacity (vph)
In the case of toll plazas, however, because “k” is a parameter to adjust for traffic actuated signals and “I” is a parameter to adjust for filtering and metering by upstream signals, they can be taken as “0.5” (upper limit given in ) and “1,” respectively. As a result, the incremental delay equation used here reduces to the form given in Equation 5, which expresses the incremental delay experienced by each vehicle in the toll lane due to random variations in toll processing times and vehicle arrivals. Equation 5 assumes that there are no queuing vehicles at the beginning of the analysis period.
di = average incremental delay in toll lane (s/veh)
T = analysis period (hr)
X = volume/capacity ratio
C = capacity (vehicles per lane per hour, or vplph)
N = number of toll lanes
The major advantage of microscopic traffic simulation models is the level of detail in the modeling procedure.
In order to take any delay due to the presence of initial queues at the toll plaza at the beginning of the analysis period into account, delay component d3 from  is used here as dq.
dq = average initial queue delay in toll lane (s/veh)
t = duration of oversaturation within T (hr)
u = delay parameter
Qb = Total number of vehicles present
at the toll lanes at the beginning of T (veh)
c = toll lane group capacity (vph)
The service time required to pay the toll results in an additional delay to each vehicle, and is dependent on the method of payment (ETC or manual).
Here, the length of the analysis is kept at one hour, and the incremental delay was calculated for each hour and then summed to determine the total incremental delay for the peak period. Breaking up the entire four-hour peak period into one-hour blocks increases the accuracy of the macroscopic model.
The macroscopic approach described here can be implemented very easily by incorporating the delay formulations into a spreadsheet. Sensitivity analysis can also be performed very easily and in a few minutes just by varying the values of the desired variables, whereas each run takes about 1 hour in PARAMICS microsimulation.
Microscopic Modeling of Toll Plazas with PARAMICS
The major advantage of microscopic traffic simulation models is the level of detail in the modeling procedure. Modeling the dynamics of traffic flow is essential in the evaluation of the impacts of various operational strategies. Microsimulation provides necessary tools for this approach. Quadstone PARAMICS is a widely used microsimulation software package with a wide range of functionalities such as the default simulation logic in car following, lane changing, route choice, etc., that can be modified using Application Programming Interface (API).
Most of the existing microsimulation packages do not have an accurate toll plaza model. Hence, many researchers have developed customized toll plaza simulation models (e.g., , , ).
Although PARAMICS has some of the basic features that can be used to build a toll plaza model, additional work using API had been performed to represent toll plaza operations accurately by  using NJ Turnpike data. The main feature of this approach is the lane changing logic involved at the toll plaza. The lane choice decision in PARAMICS is performed two links before a junction. A toll plaza consists of many links with a varying number of lanes. To model this in PARAMICS, it is necessary to have a number of small links with a different number of lanes. Additionally, toll plaza configurations on the NJ Turnpike are such that, after crossing the toll plaza, vehicles traveling north or south have to choose an appropriate ramp to enter the freeway. The lane choice logic in PARAMICS, when encountered by a decision of different paths as described above, will fail in the case of a toll plaza with many short links. Figure 3 illustrates the process of improved lane choice logic.
A very important aspect of modeling traffic using microsimulation is the calibration and validation of the models using real-world data. There are many model parameters that have to be adjusted to replicate performance closer to the real-world. In , the geometry was obtained from satellite images and incorporated as overlays in the model. Service time distributions were collected from videographic data collected at two toll plazas (15W and 16E) on the NJ Turnpike . For the simulation of facilities such as the Hudson River crossings, the average service times from the exit toll plazas of 15W and 16E have been used. This is because the cash users do not carry any ticket, but they only pay the requisite toll when they cross the toll plaza.
In the development of the customized toll plaza model,  used the disaggregate vehicle-by-vehicle electronic transaction data at each toll plaza. From this raw data, Origin-Destination demand in terms of number of E-ZPass and cash users was extracted for the peak and off-peak periods for a typical weekday. This dataset replicates the arrival distribution at the toll plazas in the most accurate fashion. In , the toll plaza model was validated for the travel time between ODs, volumes on the freeway mainline volume, and proportion of lane usage at the toll plaza.
Comparing Macroscopic and Microscopic Approaches
The validity of macroscopic delay calculations was tested using data from three of the Hudson River crossings, namely, the Holland and Lincoln Tunnels and the Goethals Bridge, and the results were compared to the delays estimated by PARAMICS. Some of the input data used in this comparison are as follows:
• Service time, dp: 9.6 seconds for cash, 3 seconds for E-ZPass, simply taken as the inverse of the capacity. This approach is recommended for the cases where field observations are not available.
• Capacity, C: 1150 vplph for E-ZPass and 375 vplph for cash toll lanes (using the average observed capacity values obtained from NJTA through an email correspondence in 2002).
• Free flow speed, V :
Goethals: 22.35 m/s (50 mph) before the plaza, 20.12 m/s (45 mph) after the plaza
Holland: 15.65 m/s (35 mph)
Lincoln: 20.12 m/s (45 mph) before the plaza, 15.65 m/s (35 mph) after the plaza
• Speed at toll booth, Vb: 0 for cash, 6.71 m/s (15 mph) for E-ZPass (posted).
• Based on the acceleration and deceleration rates reported in
the literature that varies between 0.56-2.69 m/s2 for acceleration rates and between 0.56-3.09 m/s2 for deceleration rates (, , , ), the deceleration rate for noncommercial vehicles, d1, the deceleration rate for commercial vehicles, d2, the acceleration rate for noncommercial vehicles, a1, and the acceleration rate for commercial vehicles, a2, are taken as 2.4 m/s2,
1.48 m/s2, 1.5 m/s2, and 0.97 m/s2, respectively.
• Analysis period, T: 1 hr.
• Number of toll lanes, N :
The lane configurations are shown
in Figure 4.
Goethals: 3 lanes mixed, 5 lanes for E-ZPass
Holland: 4 lanes mixed, 5 lanes for E-ZPass
Lincoln: 7 lanes mixed, 6 lanes for E-ZPass
• Total demand (volume, vph): Obtained from  and :
Goethals: AM Peak: 3041 for mixed, 3713 for E-ZPass;
PM Peak: 5432 for mixed, 6786 for E-ZPass
Holland: AM Peak: 5087 for mixed, 5864 for E-ZPass;
PM Peak: 5896 for mixed, 4725 for E-ZPass
Lincoln: AM Peak: 7544 for mixed, 11003 for E-ZPass;
PM Peak: 5379 for mixed,
5038 for E-ZPass
• Initial queue, Qb (assumed values):
AM Peak: 5 veh/cash lane,
4 veh/E-ZPass lane;
PM Peak: 2 veh/cash lane,
1 veh/E-ZPass lane
The results (Table 1) from the macro and micro-level approaches for the Holland and Lincoln Tunnels, and the Goethals Bridge compare very closely, especially for the AM peak period. This justifies the use of macroscopic delay equations in lieu of more complex microsimulation approaches that are both labor intensive and costly to develop.
Congestion Management Strategies
There is no “one size fits all” strategy to mitigate traffic congestion; a solution that works well in one geographic area might not be suitable for another area. Each region must identify the projects, programs and policies that achieve goals, solve problems and capitalize on opportunities. The most effective strategy is one where agency actions are complemented by efforts of businesses, manufacturers, commuters and travelers . Generally speaking, however, strategies to deal with congestion fall into three categories :
1. Capacity Expansions – This can include expanding the base capacity (by adding additional lanes or building new highways) as well as redesigning specific bottlenecks such as interchanges and intersections to increase their capacity. Additional roadways reduce the rate of congestion increase.
2. Demand Management Through Operational Changes – Getting more out of the existing system.
3. Greener Transportation Choices – Mass transit, non-automotive travel modes, and land use management.
Demand management using advanced technology (known as Intelligent Transportation Systems, ITS) is the major policy advocated by many agencies, although it might not be possible to completely avoid exanding capacity by building new roads. ITS solutions include:
• Electronic toll collection (ETC)
• Vehicle tracking using ETC for travel time estimation and incident detection
• Time-of-day pricing by providing
a financial incentive for drivers to switch to times, routes, or modes of transportation that are less congested. It encourages drivers to use the existing highways more efficiently. It can also be linked to strategies to improve mobility by making alternatives to the private automobile, such as subways, buses, or commuter rail service, more attractive during peak periods.
• Incident management by identifying incidents more quickly, improving response times, and managing incident scenes more effectively.
• Work zone management by reducing the amount of time work zones need to be used and moving traffic more effectively through work zones, particularly at peak times.
• Road weather management by prediction of bad weather conditions (such as rain, snow, ice, and fog) in specific areas and on specific roadways, allowing for more effective road surface treatment.
• Planned special events traffic management through pre-event planning and coordination and traffic control plans.
• Freeway, arterial, and corridor management using advanced computerized control of traffic signals, ramp meters, and lane usage (lanes that can be reversible, truck-restricted, or exclusively for high occupancy vehicles).
• Traveler information, i.e., providing travelers with real-time information on roadway conditions, delays, and advice on alternative routes .
Estimated Changes in Delay Due to TDP
The macroscopic methodology that was validated by comparison with the well-calibrated PARAMICS microsimulation model as discussed in the previous section can be used to estimate the changes in toll plaza delays due to changes in demand resulting from TDP implemented at the Hudson River crossings since March 25, 2001, for the users of E-ZPass.
The changes in delays were estimated for all the Hudson River crossings, not just for the three crossings used in the validation process presented in the previous section. Delays were calculated with the macroscopic approach using July 2000 (before TDP) and July 2001 (after TDP) data, for the weekday and weekend peak and off-peak periods. The peak hours for the facilities considered are 6-9 a.m. and 4-7 p.m. on weekdays. Weekend peak hours are from noon-8 p.m.. The off-peak hours are the rest of the day when the peak periods are subtracted. As can be seen in Table 2, TDP resulted in significant reductions (>10%) in delay (gray cells), especially for the weekday afternoon peak and weekend peak periods. It is important to note that delays presented here are only validated using the PARAMICS model, but not validated using real-world data, thus might not reflect observed delays in the real world.[The analysis results reported in this article are a small portion of the detailed and more comprehensive work previously published in “A Simple Approach to Estimating Changes in Toll Plaza Delays,” Transportation Research Record: Journal of the Transportation Research Board, No. 2047, pp. 66-74, co-authored by Dr. Ozmen-Ertekin and her colleagues.]