# Path Mapping Approach for Network Function Virtualization Resource Allocation with Network Function Decomposition Support

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## Abstract

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## 1. Introduction

**The contribution:**The goal of this study is to develop a new placement algorithm that can meet a rapid response time to avoid high embedding cost, which might occur due to mapping multiple paths of service requests to long physical paths. Thus, we propose a path mapping approach, which uses path identification to reduce the number of candidate physical nodes and links. The proposed path identification can be realized in the NFV repository while it can also consider the use of different virtualization techniques to enhance the resiliency. To realize the path mapping approach, we formulate the NFV-RA problem as an Integer Linear Programming (ILP), then, we solve it with ILP-based and heuristic schemes. These two solutions—namely ILP-P and DcPSM—are the main contribution of this work; where ILP-P is an Integer Linear Programming for Path mapping based on an exact scheme, while DcPSM is a Decomposition Path Selection Mapping based on a heuristic scheme.

## 2. Related Works

## 3. The Proposed Exact Scheme

#### 3.1. Modeling of Physical Network

#### 3.2. Path Identification

#### 3.3. Service Requests

#### 3.4. Problem Formulation

#### 3.4.1. Variables of the Problem

#### 3.4.2. Objective Function

#### 3.4.3. Constraints of the Problem

**1. Decomposition Constraint:**Only one decomposition of the service request should be embedded as expressed in Equation (12) below:

**2. Virtual Network Function Constraint:**The constraint in Equation (13) is to prevent embedding virtual network functions more than once. It also guarantees that only the nodes from the selected decomposition will be embedded.

**3. Physical Node Constraint:**If there are two virtualization types $t,t1\in T$ in the network, then it is not allowed to map a virtual function ${f}^{t}$ of the type $t1$ on physical node ${N}_{u}^{t1}$ if $t\ne t1$. In addition, the sum of allocated resources ${R}_{f}^{k}$ of the type k for all virtual functions f that are mapped on ${N}_{u}$ must be less than, or equal to, the available resources ${R}_{{N}_{u}}^{k}$ in ${N}_{u}$.

**4. Path Length Constraint:**For mobile network, the connections between the virtual functions of service might traverse through transmission mediums, which might be with high cost. The path length embedding constraint in Equation (16) determines if it is allowed to embed end-to-end paths on physical paths longer than required. One of the reasons behind high embedding cost is the mapping of virtual links to more than one hub physical link. In the other hand, mapping virtual links to more than one hub physical link might improve the acceptance ratio. This trade-off between the embedding cost and the acceptance ratio can be controlled by the network operator through determining the value of $h|h\in \{0,1,2,\cdots \}$ in Equation (16), where h value should be equal to the maximum allowed additional hubs to the virtual path length.

**5. Unsplittable Path Flow Constraint:**When a virtual link is mapped to more than one physical link, the traffic on that link should not be split in more than one path. Then, if we assume that the outgoing link from a node to next node has a positive sign and the opposite incoming link has a negative sign. Then, the Unsplittable path flow constraint can be expressed as in Equation (17) below:

**6. Bandwidth Constraint:**The sum of bandwidth for all virtual links that are mapped to a physical link should not exceed the bandwidth capacity of that physical link as expressed in Equation (18) below:

**7. Path Delay Constraint:**The end-to-end delay for all physical links to which a virtual link is mapped to, should not exceed the allowed delay for that virtual link, as in Equation (19) below:

## 4. The Proposed Heuristic Scheme

#### 4.1. Decomposition Selection Algorithm

Algorithm 1: Decomposition Selection Algorithm |

#### 4.2. Service Mapping Algorithm

Algorithm 2: Service Mapping Algorithm |

#### 4.3. Path Mapping Algorithm

Algorithm 3: Path Mapping Algorithm |

## 5. Performance Evaluation

#### 5.1. Simulation Environment

#### 5.2. Performance Metrics

**Execution time**($ET$): measures the time consumed by an algorithm to find the embedding solution.**Acceptance ratio**($\mathbf{AR}={\mathbf{R}}^{A}/{\mathbf{R}}^{T}$): measures the accepted service requests (${\mathbf{R}}^{A}$), which are successfully mapped to the total number of arrived requests (${\mathbf{R}}^{T}$).**Embedding cost**(${\mathbf{C}}_{avg}$): it is the average of total used resources for mapping service requests over 100 time unit. It is calculated based on the objective Equation (11).**Average embedding cost/average revenue**(${\mathbf{R}}_{c/r}={\mathbf{C}}_{avg}/{\mathbf{R}}_{avg}$): it is the ratio between the average embedding cost ${\mathbf{C}}_{avg}$ and the average revenue ${\mathbf{R}}_{avg}$ of a service requests over 100 time units. The revenue of a service request is calculated as the product of the total resources of virtual nodes and the average physical nodes cost, plus the product of the total bandwidth of virtual links and the average cost of physical links.

#### Distribution of Mapped Service Requests

#### 5.3. Results

#### 5.3.1. Execution Time

#### 5.3.2. Acceptance Ratio

#### 5.3.3. Embedding Cost

#### 5.3.4. Ratio of Average Cost to Average Revenue

#### 5.3.5. The Impact of Decomposition Selection Cost Parameters

## 6. Conclusions and Future work

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Decomposition main types: decomposition into sub-functions or control/user planes. (

**b**) Example of independent scaling of one sub-function in the decomposed user plane. (

**c**) Example of path types, which might be generated after decomposing a single NF.

**Figure 4.**The counters for service requests with: (

**a**) specific number of nodes and specific number of edges; (

**b**) specific number of virtual edges and specific number of paths.

**Figure 5.**Average execution time of 10 simulation runs vs. the number of physical nodes over 6 scenarios with 3 types of service requests and 2 types of physical networks.

**Figure 6.**Average execution time for service requests vs. (

**a**) the number of nodes and edges; (

**b**) the number of edges and paths.

**Figure 7.**Average acceptance ratio for: (

**a**) Simple-Small, (

**b**) Simple-Large, (

**c**) Multiple-Small, and (

**d**) Multiple-Large scenarios. The shaded background behind each curve represents the 95% confidence interval on the reported average values.

**Figure 8.**Average acceptance ratio for service requests vs. (

**a**) the number of nodes and edges; (

**b**) the number of paths and edges.

**Figure 9.**Average embedding cost for: (

**a**) Simple-Small, (

**b**) Simple-Large, (

**c**) Multiple-Small, and (

**d**) Multiple-Large scenarios. The shaded background behind each curve represents the 95% confidence interval on the reported average values.

**Figure 10.**Average embedding cost for service requests with: (

**a**) specific number of nodes and specific number of edges; (

**b**) specific number of paths and specific number of edges.

**Figure 11.**Average cost to average revenue for: (

**a**) Simple-Small, (

**b**) Simple-Large, (

**c**) Multiple-Small, and (

**d**) Multiple-Large scenarios. The shaded background behind each curve represents the 95% confidence interval on the reported average values.

**Figure 12.**Average embedding cost to average revenue for service requests vs. (

**a**) the number of nodes and edges; (

**b**) the number of paths and edges.

Ref# | Strategy | Scenario | Contribution |
---|---|---|---|

Virtual Network Embedding (VNE) | |||

[27] | Exact | Cloud | Introduced a Green Virtual Network Embedding (GVNE) framework to minimize energy consumption. |

[28] | Heuristic | Data center | Proposed Markov Chain-based Algorithm for VNE (MCA-VNE) to minimizerequest rejection and maximize revenues. |

[29] | Heuristic | Cloud | Proposed SR-VNE algorithm to maximize revenue and acceptance in long term. |

[30] | Heuristic | Service provider network | Proposed MaVEn-M and MaVEn-S algorithms using the multi-commodity flow and Markov decision processes to maximize revenue. |

[31] | heuristic | Cloud | proposed Adaptive-VNE algorithm to maximize revenue, acceptance, and end-user satisfaction. |

Virtual Network Function Placement (VNF-P) | |||

[33] | Heuristic, Metaheuristic | Operator network | Proposed three greedy and a tabu search-based algorithms for VNF embedding and process scheduling to maximize revenue. |

[34,35] | Exact, Metaheuristic | Operator network | Formulated VNFs chaining scheduling as problem as a series of scheduling decisions for services to minimize scheduling latency. |

[36] | Exact, Heuristic | Mobile network | Proposed a proof of concept that NFV management can be extended to the radio segment of mobile network. |

[37] | Exact, Heuristic | Operator network | Proposed an ILP formulation for VNF orchestration problem and a dynamic programming heuristic to minimize the operational cost and physical resource fragmentation. |

[38] | Heuristic | Operator cloud | Proposed a placement algorithms with two objectives and used bargaining Nash theory to find a fair trade-off between them to minimize end-to-end path and user’s mobility. |

Service Function Chaining Placement Problem (SFC-PP) | |||

[24] | Heuristic | Operator network | Proposed a primary backup redundant scheme mapping to maximize the service continuity. |

[11] | Exact, Heuristic | Service provider network | Proposed NF decomposition selection based on VNF clustering using virtualization technique type to minimize mapping cost. |

[12] | Exact, Heuristic | Operator network | Proposed a SFC placement with function scalability to realize the dynamic operations on NFV. |

[42] | Heuristic | Operator network | Proposed a consolidation algorithm based on migration policy to reduce the cost of QoS degradation during VNF migration. |

[43] | Heuristic | NFV network | Presented an automatic policy-based approach to solve service chain composition on NFV ot reduce operational cost. |

[44] | Exact, Heuristic | Operator network | Proposed a NF Consolidation on NFV to minimize resource occupation by reducing the number of VNF. |

[45] | Exact, Heuristic | Optical network | Proposed placement algorithm based on game theory to minimize mapping cost. |

[46] | Heuristic | Data center | Optimized VNF placement and service chaining using a Markov approximation with many-to-one matching theory in coordinated approach to minimize the cost. |

[47] | Exact, Heuristic | NFVI | Proposed a coordinated approach to jointly optimize NFV-RA in the three stages of the problem. |

[48] | Exact | Hybrid network | Proposed a customizable SFC composition to minimize the mapping and the management cost. |

[49] | Exact, Heuristic | Service provider network | Proposed a survivability for SFC with multi-path link mapping in order to maximize survivability and minimize resource redundancy |

[50] | Heuristic | Cloud | Proposed an eigen-decomposition based approach to maximize revenues. |

[51] | Heuristic | NFV network | Proposed a coordinated placement algorithm that solves service chain composition and embedding with reasonable execution time in large-scale physical networks. |

Notation | Description |
---|---|

ILP-A | ILP-based scheme of the benchmark. |

DSBM | Heuristic scheme of the benchmark. |

ILP-P | Proposed optimal implementation of path mapping, which is ILP-based scheme. |

DcPSM | Proposed heuristic implementation of path mapping approach. |

Topology | Nodes | Links | |
---|---|---|---|

BT Europe | 24 | 37 | |

Interout | 110 | 148 | |

BT${}^{+}$ | 24 | 65 | |

Int${}^{+}$ | 110 | 180 | |

Topology | Nodes | ${\mathit{E}}_{\mathbf{3}}$ | ${\mathit{E}}_{\mathbf{4}}$ |

Synthetic | 10 | 14 | 21 |

30 | 50 | 64 | |

60 | 98 | 133 | |

90 | 156 | 198 | |

120 | 227 | 265 | |

150 | 265 | 333 |

Run | Scenario | Request Type | Topology |
---|---|---|---|

Long | Simple-Small | Simple/Forking | BT Europe |

Multiple-Small | Multiple | BT Europe | |

Simple-Large | Simple/Forking | Interout | |

Multiple-Large | Multiple | Interout | |

${S}_{{P}_{5}}^{BT}$, ${S}_{{P}_{10}}^{BT}$, ${S}_{{P}_{20}}^{BT}$ | ${P}_{5}$, ${P}_{10}$, ${P}_{20}$ | BT Europe | |

${S}_{{P}_{5}}^{{BT}^{+}}$, ${S}_{{P}_{10}}^{{BT}^{+}}$, ${S}_{{P}_{20}}^{{BT}^{+}}$ | ${P}_{5}$, ${P}_{10}$, ${P}_{20}$ | BT${}^{+}$ | |

${S}_{{P}_{5}}^{Int}$, ${S}_{{P}_{10}}^{Int}$, ${S}_{{P}_{20}}^{Int}$ | ${P}_{5}$, ${P}_{10}$, ${P}_{20}$ | Interout | |

${S}_{{P}_{5}}^{{Int}^{+}}$, ${S}_{{P}_{10}}^{{Int}^{+}}$, ${S}_{{P}_{20}}^{{Int}^{+}}$ | ${P}_{5}$, ${P}_{10}$, ${P}_{20}$ | Int${}^{+}$ | |

Short | ${S}_{{P}_{5}}^{{E}_{3}}$, ${S}_{{P}_{5}}^{{E}_{4}}$ | ${P}_{5}$ | Synthetic |

${S}_{{P}_{10}}^{{E}_{3}}$, ${S}_{{P}_{10}}^{{E}_{4}}$ | ${P}_{10}$ | Synthetic | |

${S}_{{P}_{20}}^{{E}_{3}}$, ${S}_{{P}_{20}}^{{E}_{4}}$ | ${P}_{20}$ | Synthetic |

**Table 5.**Total average cost to revenue for all solved requests in all long simulation run scenarios.

Scheme | Total Number of Solved Requests | $\mathbf{AR}$ | ${\mathbf{R}}_{\mathit{c}/\mathit{r}}$ |
---|---|---|---|

DcPSM | 128,528 | 47.46% | 0.3629 |

DSBM | 128,528 | 56.21% | 1.0775 |

ILP-A | 59,639 | 100% | 0.5461 |

ILP-P | 122,417 | 100% | 0.5299 |

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## Share and Cite

**MDPI and ACS Style**

Raddwan, B.; AL-Wagih, K.; Al-Baltah, I.A.; Alrshah, M.A.; Al-Maqri, M.A.
Path Mapping Approach for Network Function Virtualization Resource Allocation with Network Function Decomposition Support. *Symmetry* **2019**, *11*, 1173.
https://doi.org/10.3390/sym11091173

**AMA Style**

Raddwan B, AL-Wagih K, Al-Baltah IA, Alrshah MA, Al-Maqri MA.
Path Mapping Approach for Network Function Virtualization Resource Allocation with Network Function Decomposition Support. *Symmetry*. 2019; 11(9):1173.
https://doi.org/10.3390/sym11091173

**Chicago/Turabian Style**

Raddwan, Basheer, Khalil AL-Wagih, Ibrahim A. Al-Baltah, Mohamed A. Alrshah, and Mohammed A. Al-Maqri.
2019. "Path Mapping Approach for Network Function Virtualization Resource Allocation with Network Function Decomposition Support" *Symmetry* 11, no. 9: 1173.
https://doi.org/10.3390/sym11091173