# The Value of Simple Heuristics for Virtualized Network Function Placement

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## Abstract

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## 1. Introduction

- Random placement: The first heuristic places NFs randomly in the network and connects the source and destination of the request to the NFs based on their order in the SG via a shortest path. This heuristic can be used as a benchmark to show the worst result that can be expected, placing NFs randomly.
- Shortest path placement: The second heuristic considers the shortage of BW in wireless multi-hop networks due to the presence of interference. This heuristic first finds a shortest path between source and destination of a request by using the Dijkstra algorithm and places NFs along the shortest path based on their order in the service graph.
- All shortest path placement: The third heuristic considers the probability of having more than one shortest path and chooses the one with more nodal resources along the path. The main idea here is to increase the chance of placing the current request successfully. In this heuristic, we rank the shortest paths based on their available nodal resources and select the one ranked first. NFs will be placed along the chosen shortest path based on their order in the SG.
- Fast and Cost-Efficient (FACE) placement: The fourth and last heuristic is named FACE. FACE uses the same method as the all shortest path heuristic to choose a shortest path but places NFs differently. In placing the NFs, FACE gives priority to the one that has fewer options for placement.

## 2. Related Work

## 3. Placement Heuristics

#### 3.1. Random Placement

#### 3.2. Shortest Path Placement

#### 3.3. All Shortest Path Placement

- $dis{t}_{u}$: An array that represents the shortest distance (number of hops) from the source node.
- $node{s}_{u}$: A set which records nodes involved in each shortest path found from source node to node u.

Algorithm 1 Finding all shortest paths. |

#### 3.4. Fast and Simple Heuristic Algorithm (FACE)

#### 3.5. Accessible Scope Heuristic

#### 3.6. Optimization Model

#### 3.7. Summary

## 4. Modeling Environment and Results

#### 4.1. Performance Metrics

- Accepted requests: The total number of accepted requests during a simulated network lifetime of 20,000 s.
- Average Cost: Average of the BW and nodal resource units used for the deployed requests that are not expired. Please note that this includes the bandwidth of links actually used by flows, as well as the bandwidth consumed on adjacent links due to interference.
- Execution time: The total time that it takes to place all requests over the simulated network lifetime of 20,000 s.

#### 4.2. Results

- In a first scenario, we applied our heuristic models to wireless multi-hop networks of increasing size to evaluate their performance in terms of the time it takes to solve the placement problem and their success in placing the requests. To benchmark our results, we applied the Integer Linear Programming (ILP) model for wireless multi-hop networks introduced in [1] to the same topologies and the same set of requests as our heuristic models. We compared our results with the accessible scope heuristic proposed in [13] that we reviewed earlier.
- In a second scenario, we focus on the first four proposed heuristics and apply them to a larger size network of 100 nodes to compare their performance in terms of the number of accepted requests, average cost, and execution time. In this scenario, we maintain the number of nodes and increase the available links’ BW.
- In a third scenario, similar to the second scenario, we compare the performance of our proposed heuristics as resource availability changes. Here we increase the nodal resource of the nodes while keeping the number of nodes constant at 100. In this scenario, in addition to comparing the relative performance of the proposed heuristics, we can also identify the impact of increasing nodal resources on the number of accepted requests.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Acronym | Description |
---|---|

BW | Bandwidth |

CI | Confidence Interval |

CAPEX | Capital Expenditure |

DP | Dynamic Programming |

FACE | Fast and Cost-Efficient |

ILP | Integer Linear Programming |

LFGL | the Least-First-Greatest-Last |

LP | Linear Programming |

MA | Markov Approximation |

NF | Network Function |

NFEP | Network Function Embedding Problem |

NFV | Network Function Virtualization |

OPEX | Operational Expenditure |

SG | Service Graph |

SLFL | Simple Lazy Facility Location |

VNF | Virtualized Network Function |

Network Size | 20 | 30 | 40 | 100 |
---|---|---|---|---|

ILP model | 142.6 | 427.3 | 967.22 | - |

The accessible scope heuristic | 49.9 | 66.5 | 96.80 | - |

FACE | 1.45 | 3.4 | 6.5 | 43.82 |

All shortest path | 1.21 | 3.2 | 5.4 | 40.32 |

Shortest path | 0.53 | 1.1 | 1.5 | 2.3 |

Random | 1.3 | 5.2 | 6.1 | 137 |

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**MDPI and ACS Style**

Jahedi, Z.; Kunz, T.
The Value of Simple Heuristics for Virtualized Network Function Placement. *Future Internet* **2020**, *12*, 161.
https://doi.org/10.3390/fi12100161

**AMA Style**

Jahedi Z, Kunz T.
The Value of Simple Heuristics for Virtualized Network Function Placement. *Future Internet*. 2020; 12(10):161.
https://doi.org/10.3390/fi12100161

**Chicago/Turabian Style**

Jahedi, Zahra, and Thomas Kunz.
2020. "The Value of Simple Heuristics for Virtualized Network Function Placement" *Future Internet* 12, no. 10: 161.
https://doi.org/10.3390/fi12100161