# Private Car O-D Flow Estimation Based on Automated Vehicle Monitoring Data: Theoretical Issues and Empirical Evidence

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review on FCD Usage

#### 2.1. Path Choice and Route Attribute Evaluation

#### 2.2. O-D Demand Flow Estimation

## 3. Methodology

- Car trip detection: according to some predefined rules, this stage aims to detect the activity stops performed by each sampled vehicle; therefore, the individual trips (with origin and destination) undertaken by each surveyed vehicle can be obtained;
- Sample O-D matrices; according to study area zoning, the origin and destination of each sample vehicle trip is identified; then, through an aggregation procedure, the sampled O-D vehicle trips are then merged in order to obtain the daily (or timely) O-D matrix;
- Expansion to the universe of investigation; in this step, the sample daily (or timely) O-D matrices need to be expanded to the universe of observation in order to obtain the daily/timely-dependent vehicle O-D matrices of the study area. This step can be considered the core of the procedure, given that the statistical significance of the sample needs to be determined.

#### 3.1. Car Trip Detection

#### 3.2. Sample O-D Matrices

_{i}is a transport zone i presented as the array of coordinates ${\langle \phi ,\lambda \rangle}_{j}$ relative to a generic point j spatially within the zone border.

_{a}only if

_{j}can be grouped into larger administrative units, such as municipalities and provinces:

_{j,od}is the generic trip j revealed with origin zone o (Z

_{o}) and destination zone d (Z

_{d}).

#### 3.3. Expansion to the Universe of Investigation

_{k}vehicles: n

_{k}elements are drawn from each stratum.

_{k}is the weight of stratum k with respect to the universe N.

- ${\widehat{s}}_{k}^{2}$ is the sample estimate of the variance of the variable ${n}_{od}^{ik}$:$${\widehat{s}}_{k}^{2}=1/\left({n}_{k}-1\right)\cdot {{\displaystyle \sum _{i}\left({T}_{od}^{ik}-{\overline{T}}_{od}^{k}\right)}}^{2}.$$
- α
_{k}is the sampling rate in the k-th stratum.

## 4. Application to a Real Test Case

#### 4.1. The Study Area and Available Data

^{2}and 4,905,037 inhabitants. The main socio-economic characteristics of the region are summarised in Table 1 (sources: ISTAT [71], ACI [72]).

#### 4.2. Car Trip Detection

#### 4.3. Sample O-D Matrices

- The predominance of intra-province trips;
- The O-D matrices reproduce quite well the spatial distribution revealed by ISTAT with very limited daily variation.

#### 4.4. Expansion to the Universe of Investigation

_{k}may be obtained.

#### 4.5. O-D Matrix Validation

**f*** (road flow vector whose elements, ${f}_{l}^{*}$, are calculated assigning to the network the O-D flows calculated through Equations (3) and (4)) and the true road link vector

**f**, whose element is f

_{l}. The mean square error between the two demand vectors, MSE(

**f***,

**f**), is one of the most commonly used divergence measures:

_{l}is the number of road links.

**f***. Table 7 summarises the mean square error (MSE) and the ratio between the square root of the mean square error and the average demand (RMSE) calculated, while Figure 8 reports a comparison between the revealed and estimated vehicle link flows. The estimates are slightly scattered. However, the model yields good results, especially because the results are less fluctuating. Then, further analyses were developed in order to verify the dispersion of estimates.

_{1}(x, $\hat{d}$) and z

_{2}(v(x), $\hat{f}$) are the “distance” measures: z

_{1}measures the “distance” of the unknown demand x from the a priori estimate $\hat{d}$ (from AVM data) and z

_{2}measures the “distance” of the flows v(x) obtained by assigning x to the network from the traffic counts $\hat{f}$. Thus, the problem is to search the vector d* that is closest to the a priori estimate $\hat{d}$, and, once it is assigned to the network, produces the flows v(d*) closest to the counts $\hat{f}$. The results of this step are summarised in Table 7 and Figure 9, proving the limited increase in performance (less than 3%) that can be obtained. The accuracy of estimates through AVM/FCD in reproducing the current origin–destination matrix is shown. This is also evidenced by the small difference (about 1%) between the expanded matrix and estimation with traffic counts. The results discussed in this section were obtained with a reasonable computational cost, i.e., about 20 s using a routine implemented within a commercial macrosimulation tool (running in a Windows environment) through a PC desktop with Intel(R) Core(TM) i7-9700F CPU @ 3.00 GHz and 32 GB of RAM. The routine time includes the computational times for estimating the initial network costs and for running the updating procedure of Equation (9). Such a performance opens new opportunities for its integration within real-time procedures. In fact, the real-time traffic counts coming from the network could feed such a proposed procedure for producing real-time (e.g., updated every 15 min) and dynamic O-D matrices.

#### 4.6. The Road Ahead and Open Research Challenges

#### 4.6.1. Sample Size

- ${\overline{VT}}_{o}$ is the mean of VT for province o;
- ${\mu}_{o}$ is the estimated mean of the travelling vehicles VT
_{o}; - ${\gamma}_{\alpha /2}$ is the quantile of the distribution (under Prob = 0.95 equals 1.96);
- ${\sigma}_{VTo}$ is the sample standard deviation for VT
_{o}; - S
_{o}is the number (days) of observations for VT_{o}.

- ${n}_{od(s)}^{cars}$ is the number of cars that should be monitored for O-D pair od according to sampling statistics data in day s;
- ${\overline{\omega}}_{\left(s\right)}$ is the average number of trips made by vehicles between or within provinces during the observation day s;
- ${\sigma}_{{\omega}_{\left(s\right)}}^{2}$ is the variance of number of trips made by vehicles between or within provinces during the observation day s;
- $C{V}_{{\omega}_{o(s)}}^{2}$ is the coefficient of variation of number of trips made by vehicles between or within provinces during the observation day s;
- $\overline{{\tau}_{s}}$ is the average number of trips made by one vehicle during day s;
- ${\omega}_{od(s)}$ is the detected (revealed) flow between zone o and zone d between or within the provinces in survey (observation) day s;
- ${M}_{o(s)}$ is the detected number of origin zones in day s for province o;
- ${W}_{o(s)}$ is the detected number of destination zones in day s for province o.

#### 4.6.2. Sampling Days

- ${n}_{od}^{days}$ is the number of survey days required for the flows between zones (provinces) o and d;
- ${\varphi}_{od}$ is the average value of flows on O-D pair od within S days;
- ${\sigma}_{od(\phi )}^{2}$ is the variance of flows on O-D pair od within S days;
- ${\overline{\omega}}_{{}_{od}(s)}$ is the average O-D flow between zone (province) pair od for the survey day s.

#### 4.6.3. Example of Application to the Veneto Region

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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Province | Area, [km^{2}] | Inhabitants | Males | Females | Number of Cars | Average No. of Vehicles per Inhabitant | Sampled Vehicles * |
---|---|---|---|---|---|---|---|

Belluno | 3678 | 204,900 | 49% | 51% | 135,261 | 0.660 | 918 (0.7%) |

Padua | 2141 | 936,740 | 49% | 51% | 603,290 | 0.644 | 7503 (1.2%) |

Rovigo | 1789 | 236,400 | 49% | 51% | 159,231 | 0.674 | 420 (0.3%) |

Treviso | 2477 | 887,420 | 49% | 51% | 588,052 | 0.663 | 5875 (1.0%) |

Venice | 2463 | 853,552 | 48% | 52% | 471,324 | 0.552 | 3274 (0.7%) |

Verona | 3121 | 922,821 | 49% | 51% | 614,838 | 0.666 | 3870 (0.6%) |

Vicenza | 2722 | 863,204 | 49% | 51% | 577,339 | 0.669 | 7298 (1.3%) |

Total | 18,391 | 4,905,037 | 49% | 51% | 3,149,335 | 0.642 | 29,158 (0.9%) |

Sampling/Surveyed Days | No. of Observations in the Database | ||
---|---|---|---|

Sampled Vehicles Travelling | Trip Description | Trip Details | |

15.10.2018 | 16,760 | 66,639 | 797,408 |

22.10.2018 | 16,674 | 67,057 | 794,775 |

07.11.2018 | 16,958 | 69,447 | 799,604 |

15.11.2018 | 17,139 | 71,304 | 883,329 |

23.11.2018 | 17,427 | 74,548 | 924,729 |

Average | 16,992 | 69,799 | 839,969 |

Province of Vehicle Registration | Survey Day | Average No. of Cars Sampled | Standard Deviation, Cars | ||||
---|---|---|---|---|---|---|---|

15.10.2018 | 22.10.2018 | 07.11.2018 | 15.11.2018 | 23.11.2018 | |||

Belluno | 449 | 441 | 449 | 461 | 441 | 448.2 | 7.33 |

Padua | 4421 | 4412 | 4475 | 4545 | 4412 | 4453.0 | 51.64 |

Rovigo | 236 | 236 | 238 | 235 | 236 | 236.2 | 0.98 |

Treviso | 3760 | 3747 | 3804 | 3832 | 3747 | 3778.0 | 34.17 |

Venice | 1519 | 1514 | 1513 | 1566 | 1514 | 1525.2 | 20.51 |

Verona | 2249 | 2233 | 2271 | 2288 | 2233 | 2254.8 | 21.67 |

Vicenza | 4126 | 4091 | 4208 | 4212 | 4091 | 4145.6 | 54.13 |

Unknown location | 955 | 945 | 961 | 985 | 945 | 958.2 | 14.73 |

Extra Veneto region | 1377 | 1337 | 1296 | 1389 | 1337 | 1347.2 | 33.06 |

Total | 19,092 | 18,956 | 19,215 | 19,513 | 18,956 | - | - |

**Table 4.**Average yearly share of O-D flows by car from census data (source: ISTAT [71]).

SW_{od} | Verona | Vicenza | Belluno | Treviso | Venice | Padua | Rovigo | Total |

Verona | 97.05% | 2.18% | 0.00% | 0.05% | 0.08% | 0.42% | 0.22% | 100.00% |

Vicenza | 1.28% | 94.37% | 0.08% | 1.08% | 0.14% | 3.02% | 0.03% | 100.00% |

Belluno | 0.01% | 0.24% | 96.83% | 2.62% | 0.16% | 0.14% | 0.00% | 100.00% |

Treviso | 0.04% | 2.01% | 0.57% | 89.76% | 5.43% | 2.18% | 0.01% | 100.00% |

Venice | 0.13% | 0.48% | 0.04% | 8.35% | 79.90% | 10.41% | 0.69% | 100.00% |

Padua | 0.90% | 4.77% | 0.03% | 2.35% | 4.65% | 85.88% | 1.42% | 100.00% |

Rovigo | 2.22% | 0.27% | 0.02% | 0.11% | 2.42% | 6.50% | 88.46% | 100.00% |

SP_{d} | 19.04% | 20.20% | 4.43% | 19.54% | 13.06% | 19.36% | 4.37% | 100.00% |

Province of Origin | Parameter | Province of Destination | ||||||
---|---|---|---|---|---|---|---|---|

Verona | Vicenza | Belluno | Treviso | Venice | Padua | Rovigo | ||

Verona | No. of O-D pairs | 0.02 | 0.11 | 0.00 | 0.26 | 0.34 | 0.09 | 0.21 |

Average O-D trip value | 0.02 | 0.03 | 0.00 | 0.00 | 0.00 | 0.03 | 0.02 | |

Vicenza | No. of O-D pairs | 0.13 | 0.02 | 0.45 | 0.07 | 0.23 | 0.03 | 0.30 |

Average O-D trip value | 0.02 | 0.03 | 0.06 | 0.04 | 0.02 | 0.04 | 0.00 | |

Belluno | No. of O-D pairs | 0.71 | 0.10 | 0.05 | 0.06 | 0.24 | 0.18 | n.a. |

Average O-D trip value | 0.00 | 0.00 | 0.03 | 0.03 | 0.00 | 0.00 | n.a. | |

Treviso | No. of O-D pairs | 0.39 | 0.07 | 0.02 | 0.02 | 0.06 | 0.03 | 0.57 |

Average O-D trip value | 0.00 | 0.04 | 0.04 | 0.02 | 0.01 | 0.05 | 0.00 | |

Venice | No. of O-D pairs | 0.31 | 0.24 | 0.32 | 0.05 | 0.02 | 0.04 | 0.16 |

Average O-D trip value | 0.00 | 0.02 | 0.00 | 0.02 | 0.03 | 0.02 | 0.07 | |

Padua | No. of O-D pairs | 0.12 | 0.04 | 0.28 | 0.05 | 0.05 | 0.02 | 0.08 |

Average O-D trip value | 0.03 | 0.04 | 0.04 | 0.03 | 0.02 | 0.01 | 0.03 | |

Rovigo | No. of O-D pairs | 0.13 | 0.27 | n.a. | 1.41 | 0.16 | 0.10 | 0.02 |

Average O-D trip value | 0.10 | 0.00 | n.a. | 0.00 | 0.14 | 0.02 | 0.05 |

Sampling/Surveyed Days | Number of Trips Made by One Vehicle | Number of Estimated Vehicles | |||
---|---|---|---|---|---|

Mean | Standard Deviation | Min | Max | ||

15.10.2018 | 3.98 | 1.51 | 1 | 19 | 16,760 |

22.10.2018 | 4.02 | 1.52 | 1 | 16 | 16,674 |

07.11.2018 | 4.10 | 1.46 | 1 | 17 | 16,958 |

15.11.2018 | 4.16 | 1.47 | 1 | 16 | 17,139 |

23.11.2018 | 4.28 | 1.49 | 1 | 16 | 17,427 |

Type of Estimation | MSE | RMSE | MAE |
---|---|---|---|

Through AVM/FCD data | 74 | 5507 | 3104 |

Updating using traffic counts | 74 | 5489 | 3040 |

Province of Vehicle Registration | VT [%] | Mean [%] | Standard Deviation [%] | Confidence Interval | |||||
---|---|---|---|---|---|---|---|---|---|

15.10 | 22.10 | 07.11 | 15.11 | 23.11 | Left Side [%] | Right Side [%] | |||

Belluno | 48.91 | 48.04 | 48.91 | 50.22 | 48.04 | 48.82 | 0.80 | 48.12 | 49.52 |

Padua | 58.92 | 58.80 | 59.64 | 60.58 | 58.80 | 59.35 | 0.69 | 58.75 | 59.95 |

Rovigo | 56.19 | 56.19 | 56.67 | 55.95 | 56.19 | 56.24 | 0.24 | 56.03 | 56.45 |

Treviso | 64.00 | 63.78 | 64.75 | 65.23 | 63.78 | 64.31 | 0.58 | 63.80 | 64.82 |

Venice | 46.4 | 46.24 | 46.21 | 47.83 | 46.24 | 46.58 | 0.63 | 46.03 | 47.13 |

Verona | 58.11 | 57.70 | 58.68 | 59.12 | 57.70 | 58.26 | 0.56 | 57.77 | 58.75 |

Vicenza | 56.54 | 56.06 | 57.66 | 57.71 | 56.06 | 56.81 | 0.74 | 56.16 | 57.46 |

Province of Origin | Province of Destination | Required No. of Survey Days | ||||||
---|---|---|---|---|---|---|---|---|

Verona | Vicenza | Belluno | Treviso | Venice | Padua | Rovigo | ||

Verona | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

Vicenza | 1 | 1 | 5 | 2 | 1 | 2 | 1 | 5 |

Belluno | 1 | 1 | 1 | 1 | 1 | 1 | n.a. | 1 |

Treviso | 1 | 3 | 3 | 1 | 1 | 4 | 1 | 4 |

Venice | 1 | 1 | 1 | 1 | 1 | 1 | 8 | 8 |

Padua | 1 | 3 | 3 | 1 | 1 | 1 | 1 | 3 |

Rovigo | 14 | 1 | n.a. | 1 | 31 | 1 | 5 | 31 |

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## Share and Cite

**MDPI and ACS Style**

Comi, A.; Rossolov, A.; Polimeni, A.; Nuzzolo, A.
Private Car O-D Flow Estimation Based on Automated Vehicle Monitoring Data: Theoretical Issues and Empirical Evidence. *Information* **2021**, *12*, 493.
https://doi.org/10.3390/info12120493

**AMA Style**

Comi A, Rossolov A, Polimeni A, Nuzzolo A.
Private Car O-D Flow Estimation Based on Automated Vehicle Monitoring Data: Theoretical Issues and Empirical Evidence. *Information*. 2021; 12(12):493.
https://doi.org/10.3390/info12120493

**Chicago/Turabian Style**

Comi, Antonio, Alexander Rossolov, Antonio Polimeni, and Agostino Nuzzolo.
2021. "Private Car O-D Flow Estimation Based on Automated Vehicle Monitoring Data: Theoretical Issues and Empirical Evidence" *Information* 12, no. 12: 493.
https://doi.org/10.3390/info12120493