# Data-Driven Performance Evaluation Framework for Multi-Modal Public Transport Systems

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## Abstract

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## 1. Introduction

## 2. Related Work

- We develop a performance evaluation framework for multi-modal public transport systems.
- We define and calculate a new performance metric, the operating speed, to characterize multi-modal public transport systems.
- We obtain enhanced OD matrices that extend the traditional knowledge regarding the percentage of trips between OD pairs, providing meaningful metrics of distance, time, and velocity for these journeys.
- We apply this performance evaluation framework to a complete public transport system, including every transport mode.
- We propose an adaption of the trip chaining method to multi-modal journeys to infer OD matrices in entry-only AFC systems.

## 3. The Adapted Trip Chaining Method

#### 3.1. Preamble

- Walking time: Transits made by foot through indoor corridors and streets traveled to (i) reach the boarding platform (which does not apply to the case of buses); (ii) change from one line to another on the same transport mode; or (iii) change from one mode to another.
- Waiting time: Since the moment the traveler reaches the boarding point (stop, platform, etc.) until she gets on the vehicle (bus, train, etc.).
- In-vehicle traveling time: The time the rider travels on the vehicles, including the times at each intermediate stop.

#### 3.2. Methodology

$\overrightarrow{{a}_{1}}$ | ⟶ | $\overrightarrow{{a}_{2}}$ | ⟶ | ⋯ | ⟶ | $\overrightarrow{{a}_{T}}$ | ⤏ | $\phantom{\rule{0.166667em}{0ex}}?$ |

$\overrightarrow{{b}_{1}}$ | ⟶ | $\overrightarrow{{b}_{2}}$ | ⟶ | ⋯ | ⟶ | $\overrightarrow{{b}_{T}}$ | ⤏ | $\phantom{\rule{0.166667em}{0ex}}?$ |

$\overrightarrow{{a}_{1}}$ | ⟶ | $\overrightarrow{{{a}}_{{2}}}$ | ⟶ | ⋯ | ⟶ | $\overrightarrow{{{a}}_{{T}}}$ | ⤏ | $\phantom{\rule{0.166667em}{0ex}}?$ |

≈ | ≈ | ≈ | ||||||

$?\phantom{\rule{0.166667em}{0ex}}$ | ⤎ | $\overrightarrow{{{b}}_{{T}}}$ | ⟶ | ⋯ | ⟶ | $\overrightarrow{{{b}}_{{2}}}$ | ⟵ | $\overrightarrow{{b}_{1}}$ |

- On one hand, we assign the location of the origin of each journey to the location of the destination of the other.$$\begin{array}{c}\hfill \overrightarrow{{a}_{1}}\to \overrightarrow{{a}_{2}}\to \cdots \to \overrightarrow{{a}_{T}}{\to}\overrightarrow{{{b}}_{{1}}}\hfill \\ \overrightarrow{{b}_{1}}\to \overrightarrow{{b}_{2}}\to \cdots \to \overrightarrow{{b}_{T}}{\to}\overrightarrow{{{a}}_{{1}}}\end{array}$$
- On the other hand, we assign the travel time of the first trip of each journey to the travel time of the last trip of the other.$$\begin{array}{cc}\hfill tt\left(\overrightarrow{{a}_{T}}\u27f6\overrightarrow{{b}_{1}}\right)& =tt\left(\overrightarrow{{b}_{1}}\u27f6\overrightarrow{{b}_{2}}\right)\hfill \\ \hfill tt\left(\overrightarrow{{b}_{T}}\u27f6\overrightarrow{{a}_{1}}\right)& =tt\left(\overrightarrow{{a}_{1}}\u27f6\overrightarrow{{a}_{2}}\right)\hfill \end{array}$$

## 4. Performance Evaluation Framework for Multi-Modal Public Transport Systems

#### 4.1. Dataset

#### 4.2. Statistical Characterization

#### 4.3. Signature of a Public Transport System

#### 4.4. Journeys Departure Time

#### 4.5. Operating Speed

#### 4.6. Enhanced OD Matrices

## 5. Discussion, Conclusions, and Further Research

#### 5.1. Comparative Study

**HMS18**and

**PEF**include the corresponding percentages of each category resulting from the Household Mobility Survey and the performance evaluation framework, respectively. We can observe how both approaches reach very similar results in each category (deviations below $7.5\%$), which indicates the capability of the proposed framework to represent the detailed mobility in the Comunidad de Madrid.

#### 5.2. Parameter Selection

#### 5.3. Conclusions and Further Research

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Statistical characterization for journeys (23 November 2018): (

**a**) distance. (

**b**) duration. (

**c**) speed.

**Figure 3.**Space-time representation of journeys (23 November 2018): (

**a**) points of individual journeys; (

**b**) contour lines.

**Figure 4.**Number of journeys depending on the time of departure (23 November 2018): (

**a**) outbound journeys; (

**b**) return journeys.

HMS18 | PEF | |
---|---|---|

Intercity Bus–Subway | $24.38\%$ | $29.82\%$ |

Commuter Train–Subway | $23.88\%$ | $31.17\%$ |

Urban Bus–Subway | $21.89\%$ | $20.97\%$ |

Urban Bus–Urban Bus | $15.92\%$ | $8.72\%$ |

Commuter Train–Urban Bus | $5.47\%$ | $4.69\%$ |

Urban Bus–Intercity Bus | $5.47\%$ | $3.05\%$ |

Intercity Bus–Intercity Bus | $2.99\%$ | $1.59\%$ |

Parameter Value | $45\phantom{\rule{0.166667em}{0ex}}\mathbf{min}.$ | $60\phantom{\rule{0.166667em}{0ex}}\mathbf{min}.$ | $90\phantom{\rule{0.166667em}{0ex}}\mathbf{min}.$ |
---|---|---|---|

%Journeys | $\downarrow 11.37\%$ | $100\%$ | $\downarrow 1.79\%$ |

Parameter Value | $175\phantom{\rule{0.166667em}{0ex}}\mathbf{m}$ | $200\phantom{\rule{0.166667em}{0ex}}\mathbf{m}$ | $225\phantom{\rule{0.166667em}{0ex}}\mathbf{m}$ |
---|---|---|---|

% Journeys | $\downarrow 1.75\%$ | $100\%$ | $\uparrow 1.31\%$ |

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**MDPI and ACS Style**

Rodríguez González, A.B.; Vinagre Díaz, J.J.; Wilby, M.R.; Fernández Pozo, R.
Data-Driven Performance Evaluation Framework for Multi-Modal Public Transport Systems. *Sensors* **2022**, *22*, 17.
https://doi.org/10.3390/s22010017

**AMA Style**

Rodríguez González AB, Vinagre Díaz JJ, Wilby MR, Fernández Pozo R.
Data-Driven Performance Evaluation Framework for Multi-Modal Public Transport Systems. *Sensors*. 2022; 22(1):17.
https://doi.org/10.3390/s22010017

**Chicago/Turabian Style**

Rodríguez González, Ana Belén, Juan José Vinagre Díaz, Mark R. Wilby, and Rubén Fernández Pozo.
2022. "Data-Driven Performance Evaluation Framework for Multi-Modal Public Transport Systems" *Sensors* 22, no. 1: 17.
https://doi.org/10.3390/s22010017