# Field Trial Measurements to Validate a Stochastic Aircraft Boarding Model

## Abstract

**:**

## 1. Introduction

#### 1.1. Status quo

#### 1.2. Objectives and Document Structure

## 2. Stochastic Boarding Model

## 3. Measurements and Calibration

#### 3.1. Field Measurements and Airline Trials

#### 3.2. Boarding Times

_{B}is weighted by the amount of passengers n

_{p}, so the boarding rate is r

_{nB}= t

_{B}/n

_{p}.

_{nB}can be characterized by the following quantiles: Q.10, Q.25, Q.50, Q.75 and Q.90 with values of 4.5 s/pax, 5.0 s/pax, 5.6 s/pax, 6.5 s/pax and 8.0 s/pax, respectively (positive skew). This descriptive summary demonstrates that 80% of r

_{nB}is in the range of 4.5 s/pax and 8.0 s/pax (between Q.10 and Q.90). According to the median (Q.50 = 5.6 s/pax), this is a spread of the boarding time from −19% to +44%. For a detailed analysis, the linear boarding progress is compared against the boarding measurements; a Q–Q plot is used (see Figure 4). In a Q–Q plot, the probability functions of two distributions are compared against each other. In the case of similarity, the data points converge to a diagonal line. Comparing the expected (linear function with t

_{B}= 5.5 s/pax × n

_{p}) and the measured distribution of the boarding rate (boarding time weighted by number of passengers), a constant linear correlation does not seem to be a valid assumption.

#### 3.3. Arrival Rates and Deboarding Rates

_{inter-arrival time}.

_{inter-arrival time}= 3.7 s, which results in a chi-squared test value of 0.64 (acceptance level of 14.07, using significance level of 5% and 7 degrees of freedom).

#### 3.4. Hand Luggage Storage

_{min}to store the hand luggage is zero, no offset is required to derive the distribution parameter (x

_{min}= 0).

#### 3.5. Seat Interactions

#### 3.6. Simulation-Validation of Prior Results

## 4. Field Trials, Validation of Simulation Results

#### 4.1. Airline Trials 1

#### 4.2. Airline Trials 2

## 5. Conclusions and Outlook

## Conflicts of Interest

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**Figure 2.**Example for back-to-front and outside-in boarding strategy (darker seats are boarded first, block sequence is I-II-III) modelled in the simulation environment.

**Figure 3.**Boarding times of 282 measured flights with different number of passengers assuming a linear correlation between passengers and boarding time with both defined offset (bold line) and no offset (thin line).

**Figure 4.**Q–Q plot of cumulative distribution functions (CDF) of boarding rate percentiles with measured boarding rates against a linear boarding progress with r

_{nB}= 5.5 s/pax.

**Figure 7.**Passenger arrival rates decrease during aircraft boarding (arrival at aircraft door or at corresponding queue). Coverage of flights (green dashes) is indicated on secondary y-axis.

**Figure 9.**Expected amount arriving passengers in 5 s interval considering field measurement data and Poisson distribution (λ = 0.74).

**Figure 10.**Deboarding outflow rates of passengers during the deboarding progress (measured at aircraft door). Coverage of flights (green dashes) is indicated on secondary y-axis.

**Figure 16.**Comparison of simulation results and measured boarding times using the block strategy (validation Scenario S1) and the standard outside-in boarding strategy.

**Table 1.**Boarding time using different classifications of linear behavior (slow, medium, fast, and average).

Boarding Classification | Boarding Time (min) | |||||
---|---|---|---|---|---|---|

Boarding Rate r_{nB} (pax/s) | Offset (min) | Passengers | ||||

80 | 110 | 140 | 170 | |||

slow | 1.0 | 12.3 | 13.6 | 14.0 | 14.5 | 15.0 |

medium | 1.2 | 8.2 | 9.9 | 10.5 | 11.1 | 11.7 |

fast | 2.2 | 3.5 | 6.4 | 7.5 | 8.6 | 9.7 |

average—no offset | 5.5 | 0 | 7.3 | 10.1 | 12.8 | 15.6 |

average—best fit | 4.5 | 2.3 | 8.3 | 10.5 | 12.7 | 15.0 |

Boarding Scenario | Boarding Strategies | |||
---|---|---|---|---|

1 door/2 doors | random | outside-in | back-to-front | block |

Boarding time (%) | ||||

1 door, non-calibrated | 100 (reference) | 80.9 | 110.5 | 96.2 |

1 door, calibrated | 100 (reference) | 79.5 | 109.2 | 95.3 |

2 doors, non-calibrated | 74.2 | 63.8 | 75.3 | 76.2 |

2 doors, calibrated | 74.1 | 62.5 | 75.0 | 76.2 |

Standard deviation (%) | ||||

1 door, non-calibrated | 7.1 | 5.5 | 7.9 | 6.6 |

1 door, calibrated | 7.3 | 5.7 | 8.1 | 6.9 |

2 doors, non-calibrated | 4.6 | 2.9 | 4.8 | 5.3 |

2 doors, calibrated | 5.9 | 5.5 | 5.9 | 5.8 |

Boarding Strategies | Boarding Time (%) | ||||||
---|---|---|---|---|---|---|---|

Field Measurements | Simulation Results | Difference | Quantiles | ||||

Q.10 | Q.25 | Q.75 | Q.90 | ||||

Seat load factor 90% | |||||||

random | 101.4 | 100 (reference) | −1.4 | −8.6 | −4.6 | 4.9 | 9.5 |

Scenario S1 | 93.7 | 104.5 | 10.8 | −9.3 | −5.1 | 5.2 | 10.2 |

Scenario S2 | 87.0 | 83.8 | −3.2 | −7.4 | −4.0 | 4.4 | 8.4 |

Scenario S2* | 80.5 | ||||||

Seat load factor 76% ± 5% | |||||||

random | 102.6 | 100.0 | −2.6 | −10.6 | −5.7 | 6.2 | 11.8 |

Scenario S1 | 94.8 | 98.7 | 3.9 | −11.5 | −6.3 | 6.6 | 12.7 |

Scenario S2 | 88.0 | 83.4 | −4.6 | −8.9 | −4.8 | 5.2 | 10.2 |

Scenario S2* | 80.8 |

Seat Load Factor | Transfer Mode | Destination | |||||
---|---|---|---|---|---|---|---|

Bus | Gate | Walk | Tourist | EU | Germany | No Tag | |

60–80% | 1 | 14 | 13 | 7 | 7 | 12 | 2 |

80–90% | 0 | 4 | 16 | 6 | 5 | 6 | 4 |

90–100% | 0 | 7 | 10 | 6 | 5 | 5 | 1 |

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**MDPI and ACS Style**

Schultz, M.
Field Trial Measurements to Validate a Stochastic Aircraft Boarding Model. *Aerospace* **2018**, *5*, 27.
https://doi.org/10.3390/aerospace5010027

**AMA Style**

Schultz M.
Field Trial Measurements to Validate a Stochastic Aircraft Boarding Model. *Aerospace*. 2018; 5(1):27.
https://doi.org/10.3390/aerospace5010027

**Chicago/Turabian Style**

Schultz, Michael.
2018. "Field Trial Measurements to Validate a Stochastic Aircraft Boarding Model" *Aerospace* 5, no. 1: 27.
https://doi.org/10.3390/aerospace5010027