# Capacity Evaluation Method of Ship Terminal Area Based on Network Maximum Flow

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## Abstract

**:**

_{g}≥ 7, the bottleneck in the ship terminal area’s operation capacity is the deck runway. When 3 ≤ n

_{g}< 7, imbalanced take-off and landing tasks lead to a waste of runway resources, and when n

_{g}< 3, the number of gates becomes the bottleneck which limits the capacity. With the number of gates being reduced from seven to three, the capacity is reduced from twenty sorties per hour to six sorties per hour. The model and core idea proposed in this paper can not only quickly evaluate the capacity of the terminal area of ships but also provide a solid foundation for the development of future fleet groups and the full use of maritime airspace.

## 1. Introduction

#### 1.1. Capacity Evaluation Methods Based on Mathematical Modeling

#### 1.2. Capacity-Evaluation Methods Based on Historical Data

#### 1.3. Capacity Evaluation Methods Based on Control Load

#### 1.4. The Capacity Evaluation Method Based on Computer Simulation

## 2. Network Flow Model of Ship Terminal Area

#### 2.1. Problem Description

#### 2.2. Airspace Structure Design of the Terminal Area

- For route design, the overall flight time should be as short as possible, and the airspace occupied should be as small as possible.
- In view of the flight characteristics of shipboard aircraft at different stages, the risk of a collision with ships and obstacles is considered to ensure that the shipboard aircraft has sufficient safety during landing.
- Shipboard aircraft routes should not cross multiple aircraft carrier control sectors in a short distance so as to avoid a large load on the aircraft carrier air traffic control center.
- The climb or descent phase of shipboard aircraft routes shall be avoided as far as possible near the boundary of the control sector, thereby avoiding the transfer of control during the climb or descent phase.

#### 2.3. Shipboard Aircraft Arrival and Departure Network Flow

## 3. Capacity Evaluation Method Based on Network Flow Model

#### 3.1. Assumption Conditions

- The same deck runway is used during the arrival and departure of the shipboard aircraft;
- The length and position of each segment in the arrival and departure route of the shipboard aircraft are known;
- The shipboard aircraft shall fly at a constant speed in each segment;
- A certain safety separation should be maintained between the shipboard aircraft;
- The shipboard aircraft executes a fixed length of holding route.

#### 3.2. Model Establishment

#### 3.2.1. Objective Function

#### 3.2.2. Constraint Conditions

## 4. Algorithm Solution

Algorithm 1: Ship terminal capacity calculation method based on simulated annealing |

Input: Ship terminal network flow capacity matrix $C$, including each segment capacity ${C}_{ij}$, deck runway capacity ${C}_{r}$ and capacity of gates ${C}_{g}$; flow constraint matrix ${A}_{m\times n}$. |

Output: Ship terminal capacity based on SA $Capacity$. |

Initialization: Set initial annealing temperature, termination annealing temperature ${T}_{final}=1$, cooling parameter $\alpha =0.98$, inner loop length $meanMarkov=100$, step size in search $scale=0.5$, randomly generate decision vector ${Q}_{0}$ in the capacity matrix range, including each segment flow ${q}_{ij}$ and relaxation variable ${q}_{k}$. |

${Q}_{now}\leftarrow {Q}_{0}$, according to the Formulas (1)–(3), the current network total flow ${F}_{now}$ is calculated, and the penalty function ${D}_{now}=\mathrm{max}\left(0,{\left({A}_{m\times n}{Q}_{now}\right)}^{2}\right)$ and the current objective function ${f}_{now}={F}_{now}+{D}_{now}$ that the current flow configuration does not meet the constraints are calculated. |

${T}_{now}\leftarrow {T}_{initial}$ |

while${T}_{now}\ge {T}_{final}$ |

for $k=0,1,2,\cdots ,meanMarkov$ |

The random disturbance in decision vector ${Q}_{now}$ is generated to obtain ${Q}_{new}$ and calculate the objective function ${f}_{new}$. |

if ${f}_{new}>{f}_{now}$ |

${Q}_{now}\leftarrow {Q}_{new}$, ${f}_{now}\leftarrow {f}_{new}$ |

else |

$P={e}^{\frac{{f}_{new}-{f}_{now}}{k{T}_{now}}}$, Randomly generated real number of intervals [0, 1] $random$ |

if $P>random$ |

${Q}_{now}\leftarrow {Q}_{new}$, ${f}_{now}\leftarrow {f}_{new}$ |

end |

end |

end |

${T}_{now}\leftarrow \alpha \cdot {T}_{now}$ |

end |

After annealing, find the best flow configuration ${Q}_{best}\leftarrow {Q}_{now}$, corresponding ship terminal area capacity $Capacity\leftarrow {F}_{now}$ |

## 5. Example Analysis

#### 5.1. Parameter Settings

#### 5.1.1. Ship Parameters

#### 5.1.2. Shipboard Aircraft Parameters

#### 5.1.3. Segment Parameters

#### 5.2. Result Analysis

#### 5.2.1. Arc Capacity Analysis

#### 5.2.2. Analysis of Arrival and Departure Capacity

#### 5.2.3. Sensitivity Analysis

- (1)
- Number of gates

- (2)
- Ship Moving Speed

## 6. Conclusions

_{g}≥ 7, the bottleneck of the ship terminal area operation capacity is the deck runway. When 3 ≤ n

_{g}< 7, imbalanced take-off and landing tasks lead to waste of runway resources. Furthermore, when n

_{g}< 3, the number of gates becomes the bottleneck, which limits the capacity. With the number of gates reduces from seven to three, the capacity reduces from twenty sorties per hour to six sorties per hour. Moreover, the ship’s own operation speed has little impact on the actual operation.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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Name | Meaning |
---|---|

$s$ | Starting point |

${h}_{i}$ | $\mathrm{Holding}\text{}\mathrm{point}\text{}i$ |

${a}_{i}$ | $\mathrm{Arrival}\text{}\mathrm{point}\text{}i$ |

${o}_{i}$ | $\mathrm{Initial}\text{}\mathrm{approach}\text{}\mathrm{fix}\text{}i$ |

$c$ | Intermediate approach point |

$f$ | Final approach point |

$m$ | Missed approach point |

$d$ | Ship landing area |

$r$ | Ship runway |

$g$ | Gates |

$t$ | Departure point |

Parameter | Number | Unit |
---|---|---|

Length of deck runway | 260 | m |

Number of gates | 13 | / |

Average maintenance time | 20 | min |

Maximum speed | 30 | kn |

Average landing time | 5 | min |

Average take-off time | 3 | min |

Parameter | Number | Unit |
---|---|---|

Take-off airspeed | 130 | kn |

Final approach average airspeed | 140 | kn |

Intermediate approach average airspeed | 140 | kn |

Average initial approaching airspeed | 250 | kn |

Average arrival airspeed | 250 | kn |

Longitudinal safety separation | 5 | n mile |

Parameter | Number | Unit |
---|---|---|

Length of descending segment | 150 | n mile |

Average altitude of descending segment | 10,000 | ft |

Length of holding segment | 8 | n mile |

Average altitude of holding segment | 6000 | ft |

Length of arrival segment | 30 | n mile |

Average altitude of arrival segment | 6000 | ft |

Length of initial approach segment | 7.5 | n mile |

Average altitude of starting segment | 3100 | ft |

Length of intermediate approach segment | 9.5 | n mile |

Average altitude of intermediate segment | 1200 | ft |

Length of last approach | 3 | n mile |

Average altitude of final segment | 600 | ft |

Length of departure segment | ∞ | n mile |

Segment | Arc Capacity (Number) |
---|---|

Descending segment | 89 |

Arrival segment | 53 |

Initial approach segment | 48 |

Intermediate approach segment | 31 |

Final approach section | 27 |

Missed approach segment | 45 |

The deck runway (landing) | 12 |

Gates | 39 |

Deck runway (takeoff) | 20 |

Departure segment | ∞ |

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## Share and Cite

**MDPI and ACS Style**

Zhong, G.; Fei, Y.; Yi, J.; Feng, D.; Feng, O.
Capacity Evaluation Method of Ship Terminal Area Based on Network Maximum Flow. *Sustainability* **2022**, *14*, 10470.
https://doi.org/10.3390/su141710470

**AMA Style**

Zhong G, Fei Y, Yi J, Feng D, Feng O.
Capacity Evaluation Method of Ship Terminal Area Based on Network Maximum Flow. *Sustainability*. 2022; 14(17):10470.
https://doi.org/10.3390/su141710470

**Chicago/Turabian Style**

Zhong, Gang, Yuhan Fei, Jia Yi, Dikun Feng, and Ouge Feng.
2022. "Capacity Evaluation Method of Ship Terminal Area Based on Network Maximum Flow" *Sustainability* 14, no. 17: 10470.
https://doi.org/10.3390/su141710470