# A Dynamic Mobility Traffic Model Based on Two Modes of Transport in Smart Cities

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## Abstract

**:**

## 1. Introduction

- A new dynamic mobility traffic (DMT) model was formulated based on the game-theoretic scheme.
- A new algorithm is proposed to manage riders’ needs in terms of mobility service. For each rider, optimal transportation planning is provided, whether by public bus, car or both, to reach their goal in a reduced time and at the lowest possible cost.
- Simulations were run to evaluate the developed scheme.
- A comparison with a multi-loading system introduced proposed in [7] proved the efficiency of the DMT.

## 2. Related Work

## 3. Model Overview and Methodology

#### 3.1. Public Bus Methodology

#### 3.2. Car Ride-Sharing Methodology

## 4. Problem Formulation: A Dynamic Mobility Traffic Model

## 5. Simulation and Results

#### 5.1. Simulation Setup

#### 5.2. Dynamic Mobility Traffic (DMT)—Experimental Evaluations

#### 5.2.1. A Comparative Analysis

#### 5.2.2. Results and Discussion

#### 5.3. Comparison between DMT and a Multi-Load Model

#### 5.3.1. A Multi-Load System Overview

#### 5.3.2. Main Differences between DMT and a Multi-Load Model

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Muñoz-Villamizar, A.; Montoya-Torres, J.R.; Faulin, J. Impact of the use of electric vehicles in collaborative urban transport networks: A case study. Transp. Res. Part D Transp. Environ.
**2017**, 50, 40–54. [Google Scholar] [CrossRef] - Ceccato, R.; Diana, M. Substitution and complementarity patterns between traditional transport means and car sharing: A person and trip level analysis. Transportation
**2018**, 1–18. [Google Scholar] [CrossRef] - Barth, M.; Todd, M. Simulation model performance analysis of a multiple station shared vehicle system. Transp. Res. Part C Emerg. Technol.
**1999**, 7, 237–259. [Google Scholar] [CrossRef] - Galland, S.; Knapen, L.; Yasar, A.U.H.; Gaud, N.; Janssens, D.; Lamotte, O.; Koukam, A.; Wets, G. Multi-agent simulation of individual mobility behavior in carpooling. Transp. Res. Part C Emerg. Technol.
**2014**, 45, 83–98. [Google Scholar] [CrossRef] - Huang, H.; Bucher, D.; Kissling, J.; Weibel, R.; Raubal, M. Multimodal Route Planning with Public Transport and Carpooling. IEEE Trans. Intell. Transp. Syst.
**2018**, 20, 3513–3525. [Google Scholar] [CrossRef] - Hariz, M.B.; Said, D.; Mouftah, H.T. Mobility traffic model based on combination of multiple transportation forms in the smart city. In Proceedings of the 2019 15th International Wireless Communications and Mobile Computing Conference (IWCMC), Tangier, Morocco, 24–28 June 2019; pp. 14–19. [Google Scholar]
- Miranda, D.M.; de Camargo, R.S.; Conceição, S.V.; Porto, M.F.; Nunes, N.T.R. A multi-loading school bus routing problem. Expert Syst. Appl.
**2018**, 101, 228–242. [Google Scholar] [CrossRef] - Baggag, A.; Abbar, S.; Zanouda, T.; Srivastava, J. Resilience analytics: Coverage and robustness in multi-modal transportation networks. EPJ Data Sci.
**2018**, 7, 14. [Google Scholar] [CrossRef][Green Version] - Furuhata, M.; Dessouky, M.; Ordóñez, F.; Brunet, M.E.; Wang, X.; Koenig, S. Ridesharing: The state-of-the-art and future directions. Transp. Res. Part B Methodol.
**2013**, 57, 28–46. [Google Scholar] [CrossRef] - Agatz, N.A.H.; Erera, A.L.; Savelsbergh, M.W.P.; Wang, X. Dynamic ride-sharing: A simulation study in metro Atlanta. Transp. Res. Part B Methodol.
**2011**, 45, 1450–1464. [Google Scholar] [CrossRef] - Bast, H.; Delling, D.; Goldberg, A.; Müller-Hannemann, M.; Pajor, T.; Sanders, P.; Wagner, D.; Werneck, R.F. Route planning in transportation networks. In Lecture Notes in Computer Science; Springer: Berlin/Heidelberg, Germany, 2016; Volume 9220, pp. 19–80. [Google Scholar]
- Akiba, T.; Iwatat, Y.; Kawarabayashi, K.I.; Kawata, Y. Fast shortest-path distance queries on road networks by pruned highway labeling. In Proceedings of the Workshop on Algorithm Engineering and Experiments, Portland, OR, USA, 5 January 2014; pp. 147–154. [Google Scholar]
- Allulli, L.; Italiano, G.F.; Santaroni, F. Exploiting GPS data in public transport journey planners. In International Symposium on Experimental Algorithms; Springer: Berlin/Heidelberg, Germany, 2014; pp. 295–306. [Google Scholar] [CrossRef]
- Dibbelt, J.; Pajor, T.; Wagner, D. User-Constrained Multimodal Route Planning. J. Exp. Algorithmics
**2015**, 19, 1.1–1.19. [Google Scholar] [CrossRef][Green Version] - Pajor, T. Multi-Modal Route Planning. Universität Karlsruhe. 2009. Available online: https://i11www.iti.kit.edu/extra/publications/p-mmrp-09.pdf (accessed on 21 February 2021).
- Bucher, D.; Jonietz, D.; Raubal, M. A heuristic for multi-modal route planning. In Progress in Location-Based Services; Springer: Cham, Switzerland, 2016; pp. 211–229._11. [Google Scholar] [CrossRef]
- Massobrio, R.; Fagúndez, G.; Nesmachnow, S. Multiobjective evolutionary algorithms for the taxi sharing problem. Int. J. Metaheuristics
**2016**, 5, 67–90. [Google Scholar] [CrossRef] - Zhu, M.; Liu, X.-Y.; Tang, F.; Qiu, M.; Shen, R.; Shu, W.; Wu, M.-Y. Public vehicles for future urban transportation. IEEE Trans. Intell. Transp. Syst.
**2016**, 17, 3344–3353. [Google Scholar] [CrossRef] - Jung, J.; Jayakrishnan, R.; Park, J.Y. Dynamic shared-taxi dis- patch algorithm with hybrid-simulated annealing. Comput.-Aided Civil Infrastruct. Eng.
**2016**, 31, 275–291. [Google Scholar] [CrossRef] - Aïvodji, U.M.; Gambs, S.; Huguet, M.J.; Killijian, M.O. Meeting points in ridesharing: A privacy-preserving approach. Transp. Res. Part C Emerg. Technol.
**2016**, 72, 239–253. [Google Scholar] [CrossRef][Green Version] - Czioska, P.; Trifunović, A.; Dennisen, S.; Sester, M. Location- and time-dependent meeting point recommendations for shared interurban rides. J. Locat. Based Serv.
**2017**, 11, 181–203. [Google Scholar] [CrossRef][Green Version] - Zhu, M.; Liu, X.Y.; Wang, X. An Online Ride-Sharing Path-Planning Strategy for Public Vehicle Systems. IEEE Trans. Intell. Transp. Syst.
**2019**, 20, 616–627. [Google Scholar] [CrossRef] - Aissat, K.; Varone, S. Carpooling as complement to multi-modal transportation. In International Conference on Enterprise Information Systems; Springer: Berlin/Heidelberg, Germany, 2015; pp. 236–255. [Google Scholar]
- Varone, S.; Aissat, K. Multi-modal transportation with public transport and ride-sharing: Multi-modal transportation using a path-based method. In Proceedings of the 17th International Conference on Enterprise Information Systems, Barcelona, Spain, 27–30 April 2015. [Google Scholar]
- Pi, X.; Ma, W.; Qian, Z. A general formulation for multi-modal dynamic traffic assignment considering multi-class vehicles. Transp. Res. Part Emerg. Technol.
**2019**, 104, 369–389. [Google Scholar] [CrossRef] - Dimokas, N.; Kalogirou, K.; Spanidis, P.; Kehagias, D. A mobile application for multimodal trip planning. In Proceedings of the 2018 9th International Conference on Information, Intelligence, Systems and Applications (IISA), Zakynthos, Greece, 23–25 July 2018; pp. 1–8. [Google Scholar]
- Cangialosi, E.; Di Febbraro, A.; Sacco, N. Designing a multimodal generalised ride sharing system. IET Intell. Transp. Syst.
**2016**, 10, 227–236. [Google Scholar] [CrossRef]

**Figure 4.**The data exchanged between the regional manager, the public buses, the ride-sharing cars and the riders.

**Figure 12.**Average user satisfaction for the DTM and the multi-load model when the number of users is 40,000.

**Figure 13.**Average user satisfaction for the DMT and the multi-load model when the number of users is 100,000.

**Figure 14.**Average stress level for the DMT and the multi-load model when the number of users is 24,000.

Notation | Definition |
---|---|

$cb$ | The maximum public bus capacity |

$TT({l}_{b,n},s{b}_{i})$ | The total trip period from the recent location of the public bus to the current station of the rider |

${l}_{b,n}$ | Current location of the public bus |

$s{b}_{i}$ | The current rider station |

$SB$ | Set of stations in the public bus schedule |

B | Set of public buses |

$TB$ | Set of departure and arrival times for the public buses |

$RB$ | Set of routers for the public buses |

$SCB$ | Set of public buses schedule |

b | The public bus identity |

$ssb$ | The origin public bus station identity |

$sdb$ | The destination public bus station identity |

$\alpha $ | The time constraint for a public bus trip |

$tsb$ | The time in the origin public bus station |

$tdb$ | The time in the destination public bus station |

$rb$ | The public bus route |

$WT{B}_{j}$ | the total waiting time in a public bus station |

$TP{B}_{i}$ | The total fare of the public bus trip |

$TT{B}_{i}$ | The total period time of the public bus trip |

$TT{B}_{j}$ | the total time from the source station to the destination station |

Notation | Definition |
---|---|

$RC$ | Set of car ride-sharing requests |

$SC$ | Set of car ride-sharing stations |

C | Set of cars |

c | The ride-sharing car’s identity |

$cc$ | The capacity of specific car |

$ssc$ | The start car station identity |

$dsc$ | The destination car station identity |

$\eta $ | The acceptable time detour |

$TT({l}_{c,n},s{c}_{i})$ | A time from the current location of the car to the current station |

${l}_{c,n}$ | Current location of the car |

$s{c}_{i}$ | The current rider station |

$tc$ | The requested car ride-sharing time |

$WT{C}_{j}$ | The total waiting time in a car ride-sharing station |

$TP{C}_{i}$ | The total fare of the car ride-sharing trip |

$TT{C}_{i}$ | The total period time of the ride-sharing trip |

$TT{C}_{j}$ | The total time from the source station to the destination station |

Notation | Definition |
---|---|

$s{s}_{i}$ | The origin rider station |

$d{s}_{i}$ | The destination rider station |

$T{T}_{i}$ | The total trip time |

$T{P}_{i}$ | The total trip price |

$n\_r$ | The number of the riders |

$i\in R$ | Each rider i belongs to R |

R | Set of riders |

$\sigma $ | The acceptable detour distance in the trip |

$D(s{s}_{i},d{s}_{i})$ | The shortest distance between the origin and the destination |

$TD(s{s}_{i},d{s}_{i})$ | The total distance of the trip |

$T{P}_{Max}$ | The maximum price |

$T{T}_{Max}$ | The maximum time |

$max\_w$ | The maximum passenger waiting time |

P | The rider preference |

Parameters | Values |
---|---|

Vehicle Type | Car ride-sharing, Public bus |

Road Network | NETCONVERT |

Time Period to Simulate | 6 a.m–11:59 p.m |

Length of Time Step | 1 min |

Dimension of Simulation Area | 20 km × 20 km |

The Integration Method | Euler Update |

Parameters | Values |
---|---|

$n\_b$ | 10 public buses in the simulation |

$n\_c$ | 10 cars in the simulation |

$n\_r$ | 40,000 passengers |

$ns\_b$ | 30 public bus station |

$ns\_c$ | 20 car ride-sharing station |

$cb$ | 50 |

$cc$ | 4 |

Simulation Period | 6 a.m.–11:59 p.m. |

P | =1 If a public bus only |

=2 If a car only | |

=3 If a public bus and car |

Passenger Number | Public Bus and Car Ride-Sharing (%) | Public Bus Only(%) | Saving Rate (%) |
---|---|---|---|

[1–1500] | 95 | 60 | 36.8 |

[1501–7000] | 85 | 45 | 47.06 |

[7001–10,000] | 80 | 30 | 62.5 |

Passenger Number | Public Bus and Car Ride-Sharing(%) | Car Ride-Sharing Only (%) | Saving Rate (%) |
---|---|---|---|

[1–1500] | 95 | 30 | 68.42 |

[1501–7000] | 85 | 25 | 70.6 |

[7001–10,000] | 80 | 20 | 75 |

**Table 8.**Savings rate of average stress level in the case of using a public bus or car ride sharing.

Day Time | Public Bus and Car Ride-Sharing (%) | Car Ride-Sharing or Public Bus (%) | Saving Rate (%) |
---|---|---|---|

[6:00 a.m.–11:00 a.m.] | 49 | 65 | 24.6 |

[11:01 a.m.–3:00 p.m.] | 30 | 60 | 50 |

[3:01 p.m.–11:59 p.m.] | 10 | 10 | 0 |

**Table 9.**Average user satisfaction savings rate in the case of using the DMT or the multi-load model.

Passenger Number Interval | DMT (%) | Multi-Load Model (%) | Saving Rate (%) |
---|---|---|---|

[1–40,000] | 72 | 59 | 18.06 |

[40,001–60,000] | 70 | 45 | 35.71 |

[60,001–100,000] | 65 | 20 | 69.23 |

Day Time | DMT (%) | Multi-Load Model (%) | Saving Rate (%) |
---|---|---|---|

[6:00 a.m.–9:00 a.m.] | 50 | 55 | 9.09 |

[9:01 a.m.–3:00 p.m.] | 30 | 62 | 51.61 |

[3:01 p.m.–5:00 p.m.] | 45 | 63 | 28.57 |

[5:01 p.m.–12:00 p.m.] | 10 | 65 | 84.61 |

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**MDPI and ACS Style**

Bin Hariz, M.; Said, D.; Mouftah, H.T.
A Dynamic Mobility Traffic Model Based on Two Modes of Transport in Smart Cities. *Smart Cities* **2021**, *4*, 253-270.
https://doi.org/10.3390/smartcities4010016

**AMA Style**

Bin Hariz M, Said D, Mouftah HT.
A Dynamic Mobility Traffic Model Based on Two Modes of Transport in Smart Cities. *Smart Cities*. 2021; 4(1):253-270.
https://doi.org/10.3390/smartcities4010016

**Chicago/Turabian Style**

Bin Hariz, Mohammed, Dhaou Said, and Hussein T. Mouftah.
2021. "A Dynamic Mobility Traffic Model Based on Two Modes of Transport in Smart Cities" *Smart Cities* 4, no. 1: 253-270.
https://doi.org/10.3390/smartcities4010016