# Impact of Accurate Detection of Freeway Traffic Conditions on the Dynamic Pricing: A Case Study of I-95 Express Lanes

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## Abstract

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## 1. Introduction

- A robust methodology is established to investigate the sensitivity of failed sensors and their erroneous data.
- The dynamic pricing algorithm used on Interstate-95 ELs in Florida is described and replicated (with proper calibration and validation) in MS Excel software by using Visual Basic for Applications (VBA).
- The individual impacts of the erroneous detection readings and completely failed sensors on the existing dynamic toll calculation algorithm and the resulting toll revenues of Interstate-95 ELs are quantified.
- The combined impact of multiple failed sensors and erroneous sensor data on the existing dynamic pricing algorithm and toll revenues of Interstate-95 ELs are quantified.

## 2. Literature Review

#### 2.1. Dynamic Congestion Pricing Algorithms

#### 2.2. Traffic Data Sensors

#### 2.3. Summary

## 3. Methodology

#### 3.1. Study Site and Data Collection

#### 3.1.1. Data Collection and Analysis

#### 3.1.2. Study Area

#### 3.1.3. Selection of Representative Days

- The tolling operations were not closed during any portion of the investigated period;
- The tolls do not reach the maximum value allowed by the algorithm (to avoid oversaturation conditions that can impact the results of the conducted experiments);
- The tolls exhibit smooth and noticeable toll changing patterns (that will ensure testing the sensitivity of sensors at various traffic ‘demand’ densities);
- The toll operations use the maximum number of sensors for toll calculations;
- The representative days experienced a close-to-an-average traffic volume in 2017.

#### 3.2. Pseudocode for Dynamic Toll Module

#### 3.3. Scenarios for Modeling Detection Errors

**Scenario 1**: Systematic detection errors—all sensors consistently generate erroneous readings with 5, 10, 15, or 20% error across the board. This scenario includes two subsets:**Subset 1**consisted of a set of uniform detection errors for all of the sensors on the tested segment, of ± 5, ±10, ±15, and ±20% of the detection values observed in the field. For example, a +5% error in volume (with a corresponding error in speed and the resulting error in density) had been applied to all of the sensors on the studied segments by multiplying their observed field volumes with a factor of 1.05.**Subset 2**consisted of a set of experiments where a certain percentage of sensors was considered to have failed completely (e.g., no reported traffic data), thus leaving the algorithm to rely only on the rest of the sensors (that have remained operational). Therefore, Subset 2 represents hypothetical field conditions when sensors either work or do not work—there is no error applied. However, various percentages of the available sensors were simulated to fail within the two analyzed EL segments.Table 2 lists all of the 25 experiments conducted under the Scenario 1 set, each with an associated percent of error or a percent of failed sensors. We note here that if 100% of sensors on a particular segment fail, it is assumed that the pre-designed tolls (from the day-of-week/time-of-day tables) are used.

**Scenario 2**: Stochastic detection errors—the Monte Carlo simulation method was utilized to randomly introduce errors and failures of the sensors at the two ELs segments. All sensors within the studied segments had equal probabilities of falling into the group of failing sensors or their erroneous data. A custom stochastic model was developed to model the errors and failures throughout the analyzed ELs segments. The logic behind this approach was that some of the sensors could ultimately fail while others will either work with erroneous outputs or work properly. The objective was to investigate how such stochastically distributed detection errors and failures would impact the ELs toll calculations. Table 3 shows how stochastic experiments were selected and executed. The first column of Table 3 shows experiment ID, the second column shows the percentage of sensors set to fail in the corresponding experiment, the third column lists the sensors that were operational (with or without an error), the fourth column shows the level of error applied to (some of) the operational sensors, and the fifth column lists the operational sensors that were modeled with an error. The rest of the sensors in each experiment were assumed to be 100% functional and accurate.

#### 3.4. Replication and Validation of the Toll Calculation Algorithm

#### 3.5. Modeling of Traffic Density in Evaluated Detection Scenarios

- Take the aggregated 15-min “true” volume and speed observations from the dataset, V1 and S1;
- Multiply V1 by percent of error—representing an erroneous reading (+/− Z%) to obtain V2;
- Insert V2 into the appropriate V-S relationship to obtain $\overline{S2}$ (the speed that corresponds to the adjusted volume, V2). A 40–50 mph speed range represents the queue discharge flow condition; thus, 45 mph is used as a threshold value to distinguish between undersaturated and oversaturated conditions.
- Calculate speed error percentage by using the following equation:$$F\%=\frac{\overline{S2}-S1}{S1}$$
- Apply speed error F% on the true speed S1 to obtain S2;$$S2=S1+S1\xb7\left(\frac{\pm F\%}{100}\right)$$
- Use V2 and S2 to calculate 15-min traffic density (D):$$D=\frac{V2}{S2}$$

#### 3.6. Performance Measures to Evaluate the Impact of Detection Errors

- Mean absolute percentage error (MAPE), shown in Equation (7), was used to assess density variation in different scenarios. Equation (7) has three terms: TTD is true traffic density, which is the field-measured density, CTD is calculated traffic density after applying a percent of error to volume and speed readings, n is the number of 15-min intervals used in the calculation, and i is any 15-min interval.$$MAPE=\left(\frac{100\%}{n}\right){\displaystyle \sum}_{i=1}^{n}\Vert \frac{TT{D}_{i}\u2013CT{D}_{i}}{TT{D}_{i}}\Vert $$
- Absolute toll error (ABS) is important for observing the cumulative total absolute change in tolls for all 56 15-min intervals during the study period (6 a.m.–8 p.m.). Equation (8) shows how ABS is computed where true toll rate (TTR) represents the posted toll in the field, whereas calculated toll rate (CTR) is taken from the experiments, and i is any 15-min interval.$$\mathrm{ABS}15-\mathrm{min}\mathrm{toll}\mathrm{error}={\displaystyle \sum}_{i=1}^{n}\Vert TT{R}_{i}-CT{R}_{i}\Vert $$
- Total gross toll: a sum of the products of volumes of the charged vehicles and their tolls for each of the 15-min intervals. The total gross toll represents the total toll fees calculated for each scenario during the analysis period (6 a.m.–8 p.m.). It is crucial to mention here that all the total gross toll values are theoretical and not actual. By using “i” for any 15-min interval during the analysis period, the following equation defines the total gross toll:$$\mathrm{Total}\mathrm{gross}\mathrm{toll}={\displaystyle \sum}_{i=1}^{n}\left[T{V}_{i}\xb7CT{R}_{i}\right]$$
- Equation (10) computes the difference in total revenue between the true total gross toll charged in the field and the total gross toll calculated in the experiments with erroneous detection. This measure helps to see the impact of detection errors or failures on the total gross toll.$$\mathrm{Difference}\mathrm{in}\mathrm{total}\mathrm{revenue}={\displaystyle \sum}_{i=1}^{n}\left[TC{R}_{i}-TA{R}_{i}\right]$$

## 4. Results and Discussion

#### 4.1. Analysis of the Southbound Segment

#### 4.1.1. Scenario 1: Systematic Detection Errors

(A) Systematic Detection Experiments—Subset 1 | ||||||||
---|---|---|---|---|---|---|---|---|

Exp. ID | MAPE (Density) | Absolute 15-min Toll Error (USD) | Total Gross Toll (USD) | Profit/Loss (USD) | ||||

17 February | 23 March | 17 February | 23 March | 17 February | 23 March | 17 February | 23 March | |

1.1 | 0 | 0 | 0 | 0 | 18,394 | 25,548 | 0 | 0 |

1.2 | 5.85 | 4.79 | 1.25 | 2.25 | 18,752 | 26,667 | 358 | 1118 |

1.3 | 4.17 | 6.5 | 5.75 | 3.5 | 17,763 | 24,838 | 631 | 710 |

1.4 | 6.97 | 6.54 | 1.5 | 2.25 | 19,075 | 26,667 | 681 | 1118 |

1.5 | 9.05 | 10.2 | 1.25 | 5 | 17,763 | 24,135 | 631 | 1413 |

1.6 | 10.34 | 9.39 | 2.5 | 2.25 | 19,588 | 26,667 | 1194 | 1118 |

1.7 | 13.24 | 14.56 | 1.25 | 4.75 | 17,763 | 24,040 | 631 | 1507 |

1.8 | 19.44 | 12.04 | 7.5 | 3.5 | 22,061 | 27,297 | 3667 | 1748 |

1.9 | 18.89 | 18.89 | 4.75 | 4.75 | 16,972 | 23,297 | 1422 | 2035 |

(B) Systematic Detection Experiments—Subset 2 | ||||||||

1.19 | 2.22 | 3.92 | 4.75 | 4.75 | 18,394 | 24,235 | 0 | 1312 |

1.20 | 2.22 | 3.92 | 0 | 5.00 | 18,394 | 24,120 | 0 | 1428 |

1.21 | 3.07 | 6.05 | 12.25 | 6.25 | 23,722 | 24,019 | 5328 | 1529 |

1.22 | 23.62 | 23.62 | 13.00 | 13.00 | 19,659 | 20,170 | 1266 | 5378 |

**Figure 6.**Graphical interpretation of total gross toll for systematic and stochastic failure and error scenarios on Southbound direction.

#### 4.1.2. Scenario 2: Stochastic Detection Errors

Exp. ID | MAPE (Density) | Abs 15-min Toll Error (USD) | Total Gross Toll (USD) | Profit/Loss (USD) | ||||
---|---|---|---|---|---|---|---|---|

17 February | 23 March | 17 February | 23 March | 17 February | 23 March | 17 February | 23 March | |

2.1 | 18.99 | 3.48 | 15.75 | 2.25 | 17,763 | 26,667 | 631 | 1118 |

2.2 | 16.47 | 5.06 | 15.25 | 3.5 | 18,983 | 24,838 | 589 | 710 |

2.3 | 16.68 | 2.98 | 15.25 | 2.25 | 18,983 | 26,667 | 589 | 1118 |

2.4 | 18.42 | 5.52 | 15.75 | 3.5 | 17,763 | 24,838 | 631 | 710 |

2.5 | 16 | 4.52 | 15 | 2.25 | 19,075 | 26,667 | 681 | 1118 |

2.6 | 19.46 | 9.27 | 15.75 | 3.75 | 17,763 | 24,722 | 631 | 825 |

2.7 | 15.9 | 5.9 | 15 | 2.25 | 19.075 | 26,667 | 681 | 1118 |

2.8 | 20.89 | 8.78 | 15.75 | 3.75 | 17,763 | 24,722 | 631 | 825 |

2.9 | 16.56 | 5.59 | 15.25 | 3.5 | 18,983 | 24,838 | 589 | 710 |

2.10 | 18.05 | 71.28 | 16.75 | 4.5 | 18,276 | 24,092 | 118 | 1426 |

2.11 | 17.08 | 32.15 | 16.25 | 4.75 | 18,507 | 24,040 | 113 | 1507 |

2.12 | 20.57 | 7.01 | 16 | 4.25 | 17,648 | 25,439 | 746 | 109 |

2.13 | 24.76 | 14.65 | 18.25 | 4.75 | 16,472 | 23,780 | 1922 | 1768 |

2.14 | 17.79 | 8.98 | 15.25 | 2.25 | 18,983 | 26,667 | 589 | 1118 |

2.15 | 17.6 | 6.32 | 15.5 | 5.5 | 18,907 | 24,401 | 513 | 696 |

2.16 | 21.63 | 13.3 | 15.75 | 5.5 | 17,763 | 10,852 | 631 | 1655 |

2.17 | 17.82 | 21.07 | 15.5 | 4.75 | 18,907 | 23,893 | 513 | 1324 |

2.18 | 26.85 | 16.48 | 20.75 | 6 | 15,205 | 23,192 | 3189 | 2355 |

2.19 | 17.68 | 71.88 | 14.5 | 23.75 | 19,383 | 13,999 | 989 | 11,549 |

2.20 | 21.74 | 7.19 | 16.25 | 4.5 | 17,520 | 26,323 | 874 | 775 |

2.21 | 20.32 | 11.52 | 13.25 | 5.5 | 24,866 | 28,056 | 6473 | 2507 |

2.22 | 21.63 | 56.08 | 15.75 | 14 | 17,763 | 18,682 | 631 | 6866 |

#### 4.2. Analysis of the Northbound Segment

#### 4.2.1. Scenario 1: Systematic Detection Errors

(A) Systematic Detection Experiments—Subset 1 | ||||||||
---|---|---|---|---|---|---|---|---|

Exp. ID | MAPE (Density) | Absolute 15-min Toll Error (USD) | Total Gross Toll (USD) | Profit/Loss (USD) | ||||

17 February | 23 March | 17 February | 23 March | 17 February | 23 March | 17 February | 23 March | |

1.10 | 0 | 0 | 0 | 0 | 13,425 | 10,264 | 0 | 0 |

1.11 | 4.24 | 10.8 | 0 | 0 | 13,425 | 10,264 | 0 | 0 |

1.12 | 4.79 | 10.22 | 0 | 0 | 13,425 | 10,264 | 0 | 0 |

1.13 | 13.94 | 4.67 | 0.5 | 0 | 13,590 | 10,264 | 165 | 0 |

1.14 | 9.18 | 14.79 | 0 | 0 | 13,425 | 10,264 | 0 | 0 |

1.15 | 11.33 | 9.05 | 0.75 | 0.25 | 13,708 | 10,401 | 283 | 137 |

1.16 | 16.13 | 18.65 | 1.25 | 0 | 13,023 | 10,264 | 403 | 0 |

1.17 | 14.45 | 12.31 | 1.25 | 0.5 | 13,961 | 10,514 | 536 | 250 |

1.18 | 20.31 | 23.13 | 2.25 | 0 | 12,816 | 10,264 | 609 | 0 |

(B) Systematic Detection Experiments—Subset 2 | ||||||||

1.23 | 0.48 | 1.48 | 0 | 0 | 13,425 | 10,264 | 0 | 0 |

1.24 | 1.48 | 1.67 | 0 | 0 | 13,425 | 10,264 | 0 | 0 |

1.25 | 14.14 | 14.14 | 0 | 0 | 10,844 | 10,264 | 2581 | 0 |

Level of Service | Traffic Density [Veh/Mile/ln] | Toll Amount (USD) | ||
---|---|---|---|---|

Minimum | Maximum | Minimum | Maximum | |

A | 0 | 11 | USD 0.50 | USD 0.50 |

B | 12 | 18 | USD 0.50 | USD 0.50 |

C | 19 | 26 | USD 0.50 | USD 0.75 |

D | 27 | 35 | USD 0.75 | USD 2.00 |

E | 36 | 45 | USD 2.00 | USD 3.00 |

F | 46 | 60 | USD 3.00 | USD 3.00 |

**Figure 8.**Graphical interpretation of total gross toll for systematic and stochastic failure and error scenarios on Northbound direction.

#### 4.2.2. Scenario 2: Stochastic Detection Errors

Exp. ID | MAPE (Density) | Abs 15-min Toll Error (USD) | Total Gross Toll (USD) | Profit/Loss (USD) | ||||
---|---|---|---|---|---|---|---|---|

17 February | 23 March | 17 February | 23 March | 17 February | 23 March | 17 February | 23 March | |

2.23 | 1.1 | 20.23 | 2.75 | 0.5 | 14,216 | 10,524 | 791 | 260 |

2.24 | 1.25 | 23.35 | 1 | 0 | 13,216 | 10,264 | 209 | 0 |

2.25 | 0.32 | 24.04 | 1.25 | 1.75 | 13,784 | 11,118 | 359 | 854 |

2.26 | 95.37 | 95.25 | 0.25 | 0 | 13,534 | 10,264 | 72 | 0 |

2.27 | 0.63 | 9.99 | 0.25 | 0 | 13,497 | 10,264 | 72 | 0 |

2.28 | 0.16 | 9.52 | 0.25 | 0 | 13,354 | 10,264 | 72 | 0 |

2.29 | 0.39 | 13.25 | 0.5 | 0.25 | 13,590 | 10,377 | 164 | 113 |

2.30 | 0.16 | 11.15 | 0 | 0 | 13,425 | 10,264 | 0 | 0 |

2.31 | 0.19 | 18.03 | 0.25 | 0 | 13.497 | 10,264 | 72 | 0 |

2.32 | 0.32 | 18.03 | 0.25 | 0 | 13,353 | 10,264 | 72 | 0 |

2.33 | 0.24 | 11.15 | 0 | 0 | 13,425 | 10,264 | 0 | 0 |

2.34 | 0.49 | 10.74 | 0 | 0 | 13,425 | 10,264 | 0 | 0 |

2.35 | 0.65 | 12.32 | 0 | 0 | 13,425 | 10,264 | 0 | 0 |

2.36 | 0.37 | 12.32 | 0 | 0 | 13,425 | 10,264 | 0 | 0 |

2.37 | 0.39 | 14.63 | 0.5 | 0.25 | 13,590 | 10,389 | 164 | 124 |

2.38 | 0.29 | 13.75 | 0 | 0 | 13,425 | 10,264 | 0 | 0 |

2.39 | 0.53 | 10.74 | 0 | 0 | 13,425 | 10,264 | 0 | 0 |

2.40 | 0.23 | 10.74 | 0 | 0 | 13,425 | 10,264 | 0 | 0 |

2.41 | 0.39 | 21.94 | 0.5 | 0.5 | 13,590 | 10,524 | 164 | 260 |

2.42 | 0.38 | 20.29 | 0 | 0 | 13,425 | 10,264 | 0 | 0 |

## 5. Conclusions

- Uniformly applied detection errors (±5, 10, 15, and 20%) for all of the sensors on the Southbound segment show consistent results—underestimated traffic volumes result in a loss of the gross tolls. In contrast, the overestimated volumes result in a surplus of the tolls.
- Uniformly applied detection errors (±5, 10, 15, and 20%) for all of the sensors on the Northbound segment show that change in total gross toll occurs when the volume is overestimated by more than 15% for a day with an average traffic volume. In contrast, the detection error as low as 10% caused changes in toll amounts for a day with high traffic volumes.
- Considering the demonstrated cases in which detection errors of 5–10% did not trigger any changes in the tolls in the Northbound direction, the authorities could require that the accuracy of their detection systems cannot be lower than 90%.
- Experiments with multiple failed/erroneous sensors lead to results that are not easy to interpret systematically. In these experiments, the results vary between losses and gains based on the percentages of failed sensors and the magnitude of introduced errors on each sensor. The unpredictability of the resulting tolls appears to be more significant on the Southbound segment because it is more dynamic, traffic-wise, than the Northbound segment.
- In summary, the findings show that the detection errors greater than 10% should present a concern for the toll authorities in terms of possible underestimates or overestimates of reported traffic volumes, which reduce the algorithm’s effectiveness in determining the appropriate toll rates.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Disclaimer

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Variable | Description |
---|---|

TD | Traffic link density (veh/mile/ln) |

F_{TL} | Traffic link flow (vehicles per hour) |

S_{TL} | Traffic link speed (miles per hour) |

NL | Number of lanes |

V_{TLC} | Traffic link volume count (vehicles per data collection interval) |

DCI | Data collection interval (900 s = 15 min) |

S_{i} | Average of one vehicle’s speeds (miles per hour) |

TD_{c} | Calculated traffic density (veh/mile/ln) |

TD_{p} | Previously calculated traffic density (veh/mile/ln) |

ΔTD | Change in traffic density (veh/mile/ln) |

ΔTR | Toll rate adjustment (USD) |

TR_{s or p} | Seed or previously calculated toll rate (USD) |

LOS_{e} | Existing level of service (A, B, C, D, E, or F) |

TR_{i} | Initial toll rate (USD) |

TR_{f} | Final toll rate (USD) |

Experiments ID’s of Subset 1 (Uniform Errors Applied for All Sensors) | |||||||||
---|---|---|---|---|---|---|---|---|---|

Uniform Error | 0% | +5% | −5% | +10% | −10% | +15% | −15% | +20% | −20% |

Experiment ID—Southbound | 1.1 | 1.2 | 1.3 | 1.4 | 1.5 | 1.6 | 1.7 | 1.8 | 1.9 |

Experiment ID—Northbound | 1.10 | 1.11 | 1.12 | 1.13 | 1.14 | 1.15 | 1.16 | 1.17 | 1.18 |

Experiments ID’s and Used Sensor for Each Experiment in Subset 2 | |||||||||

Experiment ID | Southbound | Exp.ID | Northbound | ||||||

Y% of Sensors Failed | Used Sensor(s) | Y% of Sensors Failed | Used Sensor(s) | ||||||

1.19 | 25% | 14.3,14.9,15.1 | 1.23 | 33.33% | 14.5,14.9 | ||||

1.20 | 50% | 14.6,15.1 | 1.24 | 66.67% | 14.6 | ||||

1.21 | 75% | 14.9 | |||||||

1.22 | 100% | Time of Day table | 1.25 | 100% | Time of Day table |

Random Detection Error Scenarios for Southbound Segment | ||||
---|---|---|---|---|

Experiment ID | Y% of Sensors Failed | Used Sensor(s) | X% Modeled Error | Sensor(s) Subjected to X% Error, Respectively |

2.1 | 0% | 14.3,14.6,14.9,15.1 | +5, +15% | 14.3,14.6 |

2.2 | 0% | 14.3,14.6,14.9,15.1 | −5, −15% | 14.3,14.6 |

2.3 | 0% | 14.3,14.6,14.9,15.1 | +10, +5% | 14.6,14.9 |

2.4 | 0% | 14.3,14.6,14.9,15.1 | −10, −5% | 14.6,14.9 |

2.5 | 0% | 14.3,14.6,14.9,15.1 | +10, +15, +5% | 14.3,14.9,15.1 |

2.6 | 0% | 14.3,14.6,14.9,15.1 | −10, −15, −5% | 14.3,14.9,15.1 |

2.7 | 0% | 14.3,14.6,14.9,15.1 | +10, +10, +20% | 14.3,14.6,15.1 |

2.8 | 0% | 14.3,14.6,14.9,15.1 | −10, −10, −20% | 14.3,14.6,15.1 |

2.9 | 0% | 14.3,14.6,14.9,15.1 | +15% | 14.9 |

2.10 | 0% | 14.3,14.6,14.9,15.1 | −15% | 14.9 |

2.11 | 25% | 14.3,14.9,15.1 | +10, +15% | 14.9,15.1 |

2.12 | 25% | 14.3,14.9,15.1 | −10, −15% | 14.9,15.1 |

2.13 | 25% | 14.3,14.9,15.1 | +10, +15, +20% | 14.3,14.9,15.1 |

2.14 | 25% | 14.3,14.9,15.1 | −10, −15, −20% | 14.3,14.9,15.1 |

2.15 | 50% | 14.6,15.1 | +15% | 15.1 |

2.16 | 50% | 14.6,15.1 | −15% | 15.1 |

2.17 | 50% | 14.3,15.1 | +10, +20% | 14.3,15.1 |

2.18 | 50% | 14.3,15.1 | −10, −20% | 14.3,15.1 |

2.19 | 75% | 14.9 | +10% | 14.9 |

2.20 | 75% | 14.9 | −10% | 14.9 |

2.21 | 75% | 14.3 | +15% | 14.3 |

2.22 | 75% | 14.3 | −15% | 14.3 |

Random detection error scenarios for Northbound segment | ||||

2.23 | 0% | 14.5,14.6,14.9 | +10, +15, +20% | 14.5,14.6,14.9 |

2.24 | 0% | 14.5,14.6,14.9 | −10, −15, −20% | 14.5,14.6,14.9 |

2.25 | 0% | 14.5,14.6,14.9 | +10, +20% | 14.5,14.6 |

2.26 | 0% | 14.5,14.6,14.9 | −10, −20% | 14.5,14.6 |

2.27 | 0% | 14.5,14.6,14.9 | +10, +10% | 14.5,14.9 |

2.28 | 0% | 14.5,14.6,14.9 | −10, −10% | 14.5,14.9 |

2.29 | 0% | 14.5,14.6,14.9 | +5, +20% | 14.6,14.9 |

2.30 | 0% | 14.5,14.6,14.9 | −5, −20% | 14.6,14.9 |

2.31 | 33.33% | 14.5,14.6 | +15% | 14.9 |

2.32 | 33.33% | 14.5,14.6 | −15% | 14.9 |

2.33 | 33.33% | 14.5,14.6 | +10% | 14.9,15.1 |

2.34 | 33.33% | 14.5,14.6 | −10% | 14.9,15.1 |

2.35 | 33.33% | 14.5,14.6 | +10, +15% | 14.3,14.9,15.1 |

2.36 | 33.33% | 14.5,14.6 | −10, −15% | 14.3,14.9,15.1 |

2.37 | 33.33% | 14.5,14.6 | +15, +20% | 15.1 |

2.38 | 33.33% | 14.5,14.6 | −15, −20% | 15.1 |

2.39 | 66.67% | 14.6 | +10% | 14.6 |

2.40 | 66.67% | 14.6 | −10% | 14.6 |

2.41 | 66.67% | 14.9 | +20% | 14.9 |

2.42 | 66.67% | 14.9 | −20% | 14.9 |

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**MDPI and ACS Style**

Alshayeb, S.; Stevanovic, A.; Mitrovic, N.; Dimitrijevic, B.
Impact of Accurate Detection of Freeway Traffic Conditions on the Dynamic Pricing: A Case Study of I-95 Express Lanes. *Sensors* **2021**, *21*, 5997.
https://doi.org/10.3390/s21185997

**AMA Style**

Alshayeb S, Stevanovic A, Mitrovic N, Dimitrijevic B.
Impact of Accurate Detection of Freeway Traffic Conditions on the Dynamic Pricing: A Case Study of I-95 Express Lanes. *Sensors*. 2021; 21(18):5997.
https://doi.org/10.3390/s21185997

**Chicago/Turabian Style**

Alshayeb, Suhaib, Aleksandar Stevanovic, Nikola Mitrovic, and Branislav Dimitrijevic.
2021. "Impact of Accurate Detection of Freeway Traffic Conditions on the Dynamic Pricing: A Case Study of I-95 Express Lanes" *Sensors* 21, no. 18: 5997.
https://doi.org/10.3390/s21185997