# Framework for Onboard Bus Comfort Level Predictions Using the Markov Chain Concept

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Predictive Framework for ATIS Subsystem

#### 2.2. Prediction Methods in Public Transportation

## 3. Onboard Bus Comfort Level and Markov Chain Concept

#### 3.1. Bus Comfort Level

^{2}). The driving discomfort ${\mu}_{j}$ is calculated from the following formula (based on [39]):

^{2}/person).

- Comfort level A (corresponding to a factor of discomfort ${\mu}_{j}<0.8$)—means that: approximately 10–70% of the vehicle seats are occupied; each passenger has a guaranteed seating position without being forced to travel in the immediate vicinity of another passenger; passengers travel without difficulty in carrying luggage, trolleys, bicycles, etc.
- Comfort level B (corresponding to a factor of discomfort ${\mu}_{j}\u03f5[0.8,1.0$) means that: all or almost all seating positions are occupied (70–100%); possibility to easily carry a baggage, trolleys, bicycles, etc.
- Comfort level C (corresponding to a factor of discomfort ${\mu}_{j}\u03f5[1.0,1.4$) means that: the small number of standing places is occupied, but it is possible to have free movement within the vehicle: easy access to the punch (up to 2 persons/m
^{2}). - Comfort level D (corresponding to a factor of discomfort ${\mu}_{j}\u03f5[1.4,2.1$) indicates that the onboard occupancy level results in a difficulty of free movement in the vehicle and in access problems to the punch (up to 4 persons/m
^{2}). - Comfort level E (corresponding to the discomfort factor ${\mu}_{j}\u03f5[2.1,3.4$) indicates an already high onboard congestion causing very difficult access to the punch (up to 6–7 persons/m
^{2}). - Comfort level F (corresponding to a factor of discomfort ${\mu}_{j}\ge 3.4$ is characterised by: very high in-vehicle congestion, during which it is not possible to cancel the ticket; the ride involves a large physical effort, with standing passengers pressing into the seating area; there are large difficulties in closing the door and incidental damages to the closing device; it is necessary to give way to passengers getting off their seats (over 7 persons/m
^{2}).

#### 3.2. Short-Term In-Vehicle Occupation Predictions Based on Markov Chains Model

**Definition**

**1.**

**Definition**

**2.**

**Definition**

**3.**

**Definition**

**4.**

## 4. Case Study

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Adjustment of the forecasted vehicle occupancy states to the observed values for a given bus stop.

Issues Raised in the Papers | Articles |
---|---|

Optimal queuing of rolling stock at depots for line departure | Blasum M. Bussieck M.R., Hochstattler W., Moll C.H., Scheel H., Winter T. [7] |

Optimising the number of vehicles serving the urban public transport system | Haase K., Deaulniers G., Denosiers J. [8] Kidwai F.A., Marwah B.R., Deb K., Karim M.R. [9] |

Optimisation of the allocation of rolling stock to lines - environmental criteria | Jimenez F., Roman A., (2016), Li J.Q., Head K.L. [10] Li L., Lo H.K., Cen X. [11] Beltran B., Carrese S., Cipriani E., Petrelli M. [12] |

Allocation of rolling stock to lines, as part of public transport planning, day by day planning | Lusby R.M., Larsen J., Bull S. [13] |

Characteristics of management systems for the allocation of rolling stock to lines | Gancarz T. (1998), Papierkowski K. [14] Cejrowski M., Krych A., Pawłowski M. [15] Moreira J.M., de Sousa J.F. [16] |

Optimisation of the allocation of rolling stock to lines to minimise fuel consumption | Oziomek J., Rogowski A. [17,18] |

Author(s) | Methodology | Type | Modes |
---|---|---|---|

Y. Mo, Y. Su [21] | Neural networks | Transit passenger Flow | Bus |

Y. Li [22] | Grey Markov Chain model | Flow | Railway |

S. Z. Zhao, T. H. Ni, Y. Wang, X. T. Gao [23] | Wavelet analysis, Neural networks | Flow | Transit system |

L. Liu, R. C. Chen [24] | Deep learning method | Flow | Bus rapid transit |

Y. Li, X. Wang, S. Sun, X. Ma, G. Lu [25] | Multiscale radial basis function networks | Flow | Subway |

J. Zhang, D. Shen, L. Tu, F. Zhang, C. Xu, Y. Wang, C. Tian, X. Li, B. Huang, Z. Li [26] | Extended Kalman filter model | Flow | Bus transit system |

Q. Chen, W. Li, J. Zhao [27] | Least Squares Support Vector Machine | Flow | Bus |

R. Xue, D. J. Sun, S. Chen [28] | Time series and interactive multiple model (IMM) | Demand | Bus |

C. Zhou, P. Dai, R. Li [29] | Time-varying Poisson model, Weighted time-varying Poisson model, ARIMA | Demand | Bus |

Z. Ma, J. Xing, M. Mesbah, L. Ferreira [30] | Interactive Multiple, Model-based Pattern Hybrid (IMMPH) | Demand | Bus |

T. H. Tsai, C. K. Lee, C. H. Wei [31] | Neural network | Demand | Railway |

Z. Wang, C. Yang, C. Zang [32] | Hybrid model (BP neural network & time series model) | Flow prediction | Bus stop |

J. Roos, S. Bonnevay, G. Gavin [33] | Dynamic Bayesian network | Flow forecasting | Metro |

Z. Wei, Z. Jinfu [34] | Grey-Markov Method | Passenger traffic | Passenger turnover |

Z. S. Xiao, B. H. Mao, T. Zhang [35] | Hybrid model—BP neural network and Markov Chain | Daily passenger volume | Rail transit station |

MEAN ABSOLUTE PERCENTAGE ERRORS [%] | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

ANALYZED TIME HORIZON [days] | ||||||||||||||

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | ||

Number of bus stop | 1 | 0,0 | 0,0 | 0,0 | 1,8 | 0,0 | 0,0 | 0,0 | 0,0 | 0,0 | 0,0 | 0,0 | 0,0 | 0,0 |

2 | 0,0 | 0,0 | 0,0 | 1,8 | 0,0 | 0,0 | 0,0 | 0,0 | 0,0 | 0,0 | 0,0 | 0,0 | 0,0 | |

3 | 0,0 | 0,5 | 0,5 | 2,3 | 1,0 | 0,0 | 0,0 | 0,0 | 0,0 | 0,5 | 0,5 | 0,0 | 0,0 | |

4 | 0,5 | 2,5 | 0,5 | 3,3 | 0,5 | 1,4 | 0,0 | 0,5 | 1,5 | 1,5 | 3,5 | 0,0 | 0,0 | |

5 | 2,0 | 2,2 | 1,0 | 3,8 | 1,0 | 4,2 | 2,1 | 2,5 | 2,5 | 3,0 | 2,2 | 0,5 | 0,7 | |

6 | 6,5 | 9,5 | 3,5 | 11,3 | 7,2 | 9,4 | 2,1 | 8,2 | 10,4 | 9,5 | 12,4 | 5,5 | 2,4 | |

7 | 8,5 | 11,7 | 4,7 | 12,3 | 8,2 | 5,2 | 20,8 | 7,5 | 10,0 | 9,5 | 12,3 | 7,7 | 5,2 | |

8 | 9,2 | 10,9 | 5,5 | 14,0 | 11,2 | 5,9 | 6,3 | 9,5 | 16,3 | 14,5 | 15,7 | 8,5 | 7,3 | |

9 | 10,2 | 11,4 | 7,2 | 12,2 | 12,4 | 9,7 | 7,6 | 11,2 | 19,5 | 18,2 | 15,8 | 10,7 | 7,3 | |

10 | 11,7 | 12,2 | 8,0 | 17,3 | 13,2 | 20,0 | 6,3 | 15,0 | 23,8 | 25,2 | 18,7 | 9,7 | 9,7 | |

11 | 19,0 | 21,6 | 12,2 | 23,7 | 24,9 | 23,1 | 14,2 | 21,7 | 24,2 | 21,7 | 23,3 | 12,9 | 8,0 | |

12 | 22,5 | 24,4 | 20,4 | 15,6 | 20,6 | 18,5 | 21,0 | 19,5 | 24,3 | 19,0 | 22,6 | 20,8 | 13,9 | |

13 | 22,8 | 23,3 | 25,4 | 20,6 | 17,8 | 13,3 | 22,4 | 19,9 | 23,3 | 20,9 | 20,1 | 20,1 | 24,5 | |

14 | 23,0 | 24,7 | 36,8 | 19,5 | 21,1 | 17,5 | 25,5 | 18,7 | 21,4 | 27,2 | 18,6 | 18,7 | 25,8 | |

15 | 24,5 | 24,0 | 32,0 | 21,0 | 22,9 | 17,3 | 19,4 | 16,6 | 21,1 | 25,1 | 22,4 | 20,2 | 26,3 | |

16 | 25,8 | 23,0 | 27,1 | 19,3 | 18,0 | 19,3 | 17,8 | 19,3 | 22,5 | 30,1 | 21,6 | 18,7 | 26,9 | |

17 | 24,4 | 23,3 | 26,8 | 20,1 | 19,4 | 17,9 | 18,1 | 18,0 | 22,2 | 28,9 | 19,1 | 19,0 | 26,9 | |

18 | 19,4 | 18,7 | 24,5 | 19,7 | 20,9 | 15,3 | 14,4 | 18,1 | 17,5 | 30,5 | 21,1 | 20,7 | 17,8 | |

19 | 7,5 | 10,1 | 10,2 | 8,1 | 8,8 | 12,7 | 4,5 | 6,5 | 11,7 | 27,3 | 10,3 | 10,4 | 12,2 |

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**MDPI and ACS Style**

Więcek, P.; Kubek, D.; Aleksandrowicz, J.H.; Stróżek, A.
Framework for Onboard Bus Comfort Level Predictions Using the Markov Chain Concept. *Symmetry* **2019**, *11*, 755.
https://doi.org/10.3390/sym11060755

**AMA Style**

Więcek P, Kubek D, Aleksandrowicz JH, Stróżek A.
Framework for Onboard Bus Comfort Level Predictions Using the Markov Chain Concept. *Symmetry*. 2019; 11(6):755.
https://doi.org/10.3390/sym11060755

**Chicago/Turabian Style**

Więcek, Paweł, Daniel Kubek, Jan Hipolit Aleksandrowicz, and Aleksandra Stróżek.
2019. "Framework for Onboard Bus Comfort Level Predictions Using the Markov Chain Concept" *Symmetry* 11, no. 6: 755.
https://doi.org/10.3390/sym11060755