# Comparative Study of Aircraft Boarding Strategies Using Cellular Discrete Event Simulation

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## Abstract

**:**

## 1. Introduction

## 2. Background

#### Cellular Discrete Event Approach

_{int}, δ

_{ext}, τ, λ, D>,

_{int}is the internal transition function; δ

_{ext}is the external transition function; τ is the local computation function; λ is the output function; and D is the state’s duration function. The modular interface (I) represents the input/output ports of the cell and their connection to the neighbor cell. Communications among cells are performed through these ports. The values inserted through input ports are used to compute the future state of the cell by evaluating the local computation function τ. Once τ is computed, if the result is different from the current cell’s state, this new state value must be sent out to all neighboring cells informing the state change. Otherwise, the cell remains in its current state and therefore no output will be propagated to other cells. This will happen when the time given by the delay function expires. Finally, the internal, external transition functions and output functions (λ) define this behavior. Cell-DEVS improves execution performance of cellular models by using a discrete-event approach. It also enhances the cell’s timing definition by making it more expressive.

## 3. Modeling Assumptions

- Walking Speed: the speed range at which passenger walks from the moment he/she enters the aircraft till reaching the target seat (unit: meter per second).
- Clearing Time: the time range passengers spend on storing their luggage in the overhead compartment or underneath the seat in the front (unit: seconds).
- Getting out of Seat: the time range a passenger takes to get up from their seat, allowing other passengers to sit within that row (unit: seconds).
- Passenger Flow Rate: the range number of passengers that enter the aircraft at a certain amount of time (unit: passenger per second).

- Walking Delay: the average time it takes a passenger to pass a row (unit: milliseconds).
- Luggage Delay: the average time spent by individual passengers to store their luggage in the overhead compartment (unit: milliseconds).
- Middle Seat Delay: the delay time a window passenger should wait at the row until middle/aisle passengers who are already seated within that row get up (unit milliseconds).
- Aisle Seat Delay: the delay time a window or middle passenger should wait at the row until aisle passenger who is already seated within that row gets up (unit milliseconds).

## 4. System Design

- type: cell
- width: 10
- height: 43
- neighbors: aircraft(−1,−1) aircraft(−1,0) aircraft(−1,1) aircraft(0,−4)
- neighbors: aircraft(0,−3) aircraft(0,−2) aircraft(0,−1) aircraft(0,0)
- neighbors: aircraft(0,1) aircraft(0,2) aircraft(0,3)
- neighbors: aircraft(1,−1) aircraft(1,0) aircraft(1,1)

## 5. Implementation Details

#### 5.1. Seat Generation in Back-to-Front Strategy

#### 5.2. Seat Generation in Random Strategy

#### 5.3. Seat Generation in Window Middle Aisle (WMA) Strategy

#### 5.4. Seat Generation in Zone Rotate Strategy

#### 5.5. Seat Generation in Reverse Pyramid (RP) Strategy

#### 5.6. Seat Generation in Optimal Strategy

#### 5.7. Seat Generation in Optimal Practical Strategy

#### 5.8. Seat Generation in Efficient Strategy

#### 5.9. Aircraft Rules Specification and Implementation

- pre-seat rules: a set of nine rules with responsibilities to send requests to the Passenger Generator model to release passengers and guide passengers at the aircraft door to walk to the beginning of the seats aisle. The area that pre-seat rules apply to is from cell (0, 0) to cell (6, 0) where cell (y, x) defines the y and x coordinates of the cell on the grid. The affected area by pre-seat rules is highlighted in a surrounding solid box in Figure 17.
- seating rules: a set of 33 rules handling passengers’ forward movement within the aisle and occupation of seats. These rules only apply to the cells that represent the seats (both first-class and economy) and the aisle, as well as passengers on these cells. This area is highlighted in Figure 17 with a surrounding dashed box.

## 6. Simulation Results

## 7. Conclusions

## Author Contributions

## Conflicts of Interest

## References

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**Figure 18.**Sample macros defining various delay values based on Table 2 ranges.

**Table 1.**Basic parameters ranges [22].

Parameter | Range | Unit |
---|---|---|

Walking Speed | 0.27–0.44 | [m/s] |

Clearing Time | 6–30 | [s] |

Getting out of seat | 3–4.2 | [s] |

Passenger flow rate | 0.2–1 | [pax/s] |

**Table 2.**Various delay values [22].

Parameter | Time | Unit |
---|---|---|

Walking delay | 2270 | ms |

Luggage Delay | 18,000 | ms |

Two passengers get out of seats | 4200 | ms |

Middle passenger gets out of seat | 3600 | ms |

Aisle passenger gets out of seat | 3000 | ms |

State Name | State Value | Color | Description |
---|---|---|---|

Wall | 0 | Black | Wall or obstacle |

Aisle | 1, 51–76 | Gray | Aisle |

Door Open | 2 | Green | Boarding door is open |

Cabin | 3 | Blue | Cabin or bathroom or cafe |

Empty Passenger Seat | 100–3000 | white | Passenger seat |

Walking Passenger | 10,000–300,000 | Red | Walking Passenger |

Seats with passenger | 4 | Yellow | Seat is occupied with passenger |

Door Closed | 9 | Green | All the passengers have been boarded |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Jafer, S.; Mi, W.
Comparative Study of Aircraft Boarding Strategies Using Cellular Discrete Event Simulation. *Aerospace* **2017**, *4*, 57.
https://doi.org/10.3390/aerospace4040057

**AMA Style**

Jafer S, Mi W.
Comparative Study of Aircraft Boarding Strategies Using Cellular Discrete Event Simulation. *Aerospace*. 2017; 4(4):57.
https://doi.org/10.3390/aerospace4040057

**Chicago/Turabian Style**

Jafer, Shafagh, and Wei Mi.
2017. "Comparative Study of Aircraft Boarding Strategies Using Cellular Discrete Event Simulation" *Aerospace* 4, no. 4: 57.
https://doi.org/10.3390/aerospace4040057