On a virtual network functions placement and routing problem: Some properties and a comparison of two formulations

Addis, Bernardetta; Carello, Giuliana; Gao, Meihui

doi:10.1002/net.21915

Cited by 12 publications

(15 citation statements)

References 16 publications

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“…Constraint (10) bounds the number of needed service instances. In [2] the value of the bound

{VNF}_{LB}

is set equal to

⌈\frac{\sum_{k \in D} d_{k}}{q}⌉

. We further improve the formulation by computing the value of

{VNF}_{LB}

as the optimal solution of the following Bin‐Packing‐like Problem (BPP), which uses the same parameters and variables summarized in Table 1:

\begin{align} false(BPP false) & \min \sum_{i \in N} y_{i} \\ \sum_{i \in N} z_{i}^{k} = 1 & \forall k \in D \\ \sum_{k \in D} d_{k} z_{i}^{k} \leq \overset{q_{i}}{true} y_{i} & \forall i \in N . \end{align}

…”

Section: Problem Description and Formulationmentioning

confidence: 99%

“…Due to its relevance from the application point of view, the problem has been widely addressed in the telecommunication literature, where the solution proposed have been mainly models and heuristics. However, only in [2], is there a comparison between formulations. Even the most promising formulation proposed in [2] cannot deal with large size instances.…”

Section: Introductionmentioning

confidence: 99%

“…However, only in [2], is there a comparison between formulations. Even the most promising formulation proposed in [2] cannot deal with large size instances. The goal of this work is therefore to develop and compare heuristics based on mathematical models to tackle large size instances.…”

Section: Introductionmentioning

confidence: 99%

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ILP‐based heuristics for a virtual network function placement and routing problem

2021

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Thanks to the increased availability of computing capabilities in data centers, the recently proposed virtual network function paradigm can be used to keep up with the increasing demand for network services as internet and its applications grow. The problem arises then of managing the virtual network functions, that is, to decide where to instantiate the functions and how to route the demands to reach them. While it arises in an application field, the Virtual Network Function placement and routing problem combines location and routing aspects in an interesting, challenging problem. In this paper, we propose several ILP‐based heuristics and compare them on a dataset that includes instances with different sizes, network topologies, and service capacity. The heuristics prove effective in tackling even large size instances, with up to 50 nodes and more than 80 arcs.

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“…Constraint (10) bounds the number of needed service instances. In [2] the value of the bound

{VNF}_{LB}

is set equal to

⌈\frac{\sum_{k \in D} d_{k}}{q}⌉

. We further improve the formulation by computing the value of

{VNF}_{LB}

as the optimal solution of the following Bin‐Packing‐like Problem (BPP), which uses the same parameters and variables summarized in Table 1:

\begin{align} false(BPP false) & \min \sum_{i \in N} y_{i} \\ \sum_{i \in N} z_{i}^{k} = 1 & \forall k \in D \\ \sum_{k \in D} d_{k} z_{i}^{k} \leq \overset{q_{i}}{true} y_{i} & \forall i \in N . \end{align}

…”

Section: Problem Description and Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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ILP‐based heuristics for a virtual network function placement and routing problem

2021

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“…NFV-FGE is also the central problem of NFV-RA accompanying with Virtual Network Functions (VNFs) chain composition (known as service function chaining) and VNFs scheduling [9]. In fact, VNE is assumed to be even more complicated than NFV-FGE in some specific cases and topologies [10], [11].…”

Section: List Of Symbolsmentioning

confidence: 99%

“…4.2f due to least remapping. Inspired by this idea, we present a heuristic conciliation algorithm to handle this problem as detailed in Algorithm 5 where lines [10][11][12][13][14][15][16][17][18][19][20][21][22] attempt to quantify potential nodes for re-mapping. For better understanding, let take an example in Fig.…”

mentioning

confidence: 99%

Distributed and Parallel Metaheuristic-based Algorithms for Online Virtual Resource Allocation

Nguyen¹

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I would like to express my sincere gratitude to my supervisor, Prof. Changcheng Huang, for his support, guidance, and encouragement. It is my privilege to have a great opportunity to work with him. His invaluable advice and patient guidance help me how to conduct a scientific research, and explore new research topics independently. He consistently motivates me to do my best, or encourages me when I have a challenging time during research. His profound supervision pushes me beyond my expectations. I would have never been able to accomplish my dissertation without his tremendous support.During the long journey of a PhD student, it has been a great pleasure to work with faculty, staff, alumni, colleagues and students at Carleton University. I would like to thank Qiao Lu, Steve Drew, Pei Jin, Hieu Le and other colleagues in laboratory for their support, precious advice and stimulating discussions on my work.Finally, I would like to appreciate the unconditional support, patience and encouragement from my wife Trang Pham, my daughter Helen Nguyen, our families, Tung Pham, Tin Vo and other friends throughout my PhD journey.

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Two extended formulations for the virtual network function placement and routing problem

et al. 2023

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Given a bi‐directed graph modeling a telecommunication network, and a set of origin‐destination pairs representing traffic requests (commodities) along with their associated Service Function Chains (SFCs), the Virtual Network Function Placement and Routing Problem (VNFPRP) aims to find, for each commodity, one latency‐constrained routing path that visits the required Virtual Network Functions in a specific order. The function installation costs together with the node activation costs have to be minimized. In this paper, we present two extended Mixed Integer Programming (MIP) formulations to model the VNFPRP. For each formulation we define the master problem, the pricing problem, the associated Lagrangian bound and a specific branching scheme, in order to derive an efficient Branch‐and‐Price algorithm. We also provide several families of valid inequalities to strengthen the LP‐relaxation bounds. Computational results are reported comparing the performance of the two Branch‐and‐Price algorithms with a compact MIP formulation and its Branch‐and‐Benders‐cut implementation on a set of SNDlib instances representing telecommunication networks.

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On a virtual network functions placement and routing problem: Some properties and a comparison of two formulations

Cited by 12 publications

References 16 publications

ILP‐based heuristics for a virtual network function placement and routing problem

ILP‐based heuristics for a virtual network function placement and routing problem

Distributed and Parallel Metaheuristic-based Algorithms for Online Virtual Resource Allocation

Two extended formulations for the virtual network function placement and routing problem

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