# A Multi-Dimension Spatial Method for Topology Awareness and Multipath Generating

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Background and Problem Statement

#### 2.1. Multipath Transmission on Overlay Networks and SDSON

#### 2.2. Topology Awareness

#### 2.3. Multipath Diversity

#### 2.3.1. Diversity of Underlay Network

#### 2.3.2. Enhancing Multipath Diversity

## 3. Constructing Multi-Dimensional Topology View

#### 3.1. Constructing Independent Views

#### 3.2. Merging Topology Views

Algorithm 1 Embedding exchange points |

Input:MM(N,N), N is the number of RSes ${T}_{W}$, W is the number of autonomous systems DT, LT Output:${L}_{M}(N,N)$, M is the number of locations (cities) $N{B}_{M}(R{S}_{P},R{S}_{Q})$, P,Q are the numbers of neighbor RSes. C(N,N), coordinate of exchange point, center of two RSes 1: while ${T}_{i}\in {T}_{W}\mathbf{and}{T}_{J}\in {T}_{W}$ do2: while ${L}_{c}\in {L}_{M}\mathbf{and}{L}_{d}\in {L}_{M}\mathbf{and}0\le NB({L}_{c},{L}_{d})\le DT$ do3: while $R{S}_{f}\in {T}_{i}\mathbf{and}R{S}_{f}\in {L}_{c}\mathbf{and}R{S}_{g}\in {T}_{j}\mathbf{and}R{S}_{g}\in {L}_{d}$ do4: MM(f,g) ≤ LT and Get top h minimum MM(f,g) 5: $N{B}_{k}\left(\right)\leftarrow (R{S}_{f},R{S}_{g}),{L}_{k}(f,g)=1$ (k= c or d or c-d) 6: $C(f,g)\leftarrow center({C}_{f},{C}_{g})$ 7: end while8: end while9: end while |

## 4. Multipath Generating

#### 4.1. Spatial Multipath Diversity

#### 4.2. Exploiting Underlay Diversity

Algorithm 2 Generating multiple paths with MDSM |

Input:$R{S}_{i}\in {L}_{s},R{S}_{j}\in {L}_{t},R{S}_{i}\in {T}_{u},R{S}_{j}\in {T}_{v}$ ${T}_{N}$, N is the number of autonomous systems ${L}_{M}$, M is the number of locations (cities) $NB(M,M),N{B}_{M}(P,P)$, P is the number of RSes Output:MP(i,j), multiple paths from $R{S}_{i}$ to $R{S}_{j}$ Origin(i,j), Dest(i,j), candidate RSes near two ARSes 1: while ${L}_{k}\in {L}_{M}\mathbf{and}0\le NB(k,s)\le 1$ do2: while ${T}_{d}\in {T}_{N}\mathbf{and}{L}_{k}(u,d)=1\mathbf{and}{L}_{k}\in TS(i,j)$ do3: Add(Origin(i,j), d, k) 4: while ${L}_{r}\in {L}_{set}\mathbf{and}0\le NB(r,t)\le 1$ do5: while ${T}_{w}\in {T}_{set}\mathbf{and}{L}_{r}(v,w)=1\mathbf{and}{L}_{r}\in TS(i,j)$ do6: Add(Dest(i,j), w, r) 7: if ${T}_{w}={T}_{d}$ then8: Add(MP(i,j), k, r, 1) 9: else if ${L}_{b}(w,d)=1\mathbf{and}{L}_{b}\in TS(w,d)$ then10: Add(MP(i,j), k, b, r, 2) 11: end if12: end while13: end while14: end while15: end while |

## 5. Evaluation and Analysis

#### 5.1. Accuracy of Topology Awareness

#### 5.2. Diversity of Multipath Generating

#### 5.3. Performance of Multipath Transmission

## 6. Related Work

#### 6.1. Topology Awareness

#### 6.2. Multipath Diversity

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- 3GPP. TS 23.107 (V15) Quality of service (qos) concept and architecture. 2018. Available online: http://www.3gpp.org/DynaReport/23107.htm (accessed on 14 May 2019).
- Cidon, I.; Rom, R.; Shavitt, Y. Analysis of multi-path routing. IEEE/ACM Trans. Netw.
**1999**, 7, 885–896. [Google Scholar] [CrossRef] - Han, H.; Shakkottai, S.; Hollot, C.V.; Srikant, R.; Towsley, D. Multi-path tcp: A joint congestion control and routing scheme to exploit path diversity in the internet. IEEE/ACM Trans. Netw.
**2006**, 14, 1260–1271. [Google Scholar] [CrossRef] - Güven, T.; La, R.J.; Shayman, M.A.; Bhattacharjee, B. A unified framework for multipath routing for unicast and multicast traffic. IEEE/ACM Trans. Netw.
**2008**, 16, 1038–1051. [Google Scholar] [CrossRef] - Jiang, J.; Das, R.; Ananthanarayanan, G.; Chou, P.A.; Padmanabhan, V.; Sekar, V.; Zhang, H. Via: Improving internet telephony call quality using predictive relay selection. In Proceedings of the 2016 ACM SIGCOMM Conference, Florianopolis, Brazil, 22–26 August 2016; pp. 286–299. [Google Scholar]
- Jones, N.M.; Paschos, G.S.; Shrader, B.; Modiano, E. An overlay architecture for throughput optimal multipath routing. IEEE/ACM Trans. Netw.
**2017**, 25, 2615–2628. [Google Scholar] [CrossRef] - Liao, J.; Wang, J.; Li, T.; Zhu, X. Introducing multipath selection for concurrent multipath transfer in the future internet. Comput. Netw.
**2011**, 55, 1024–1035. [Google Scholar] [CrossRef] - Wang, B.; Wei, W.; Guo, Z.; Towsley, D. Multipath live streaming via tcp:scheme, performance and benefits. ACM Trans. Multimedia Comput. Commun. Appl.
**2009**, 5, 25. [Google Scholar] [CrossRef] - Guan, Y.; Lei, W.; Zhang, W.; Li, H.; Zhang, S. SGMR: A spatial geometry–based multipath routing method on overlay networks. Int. J. Commun. Syst.
**2019**, 32, e3894. [Google Scholar] [CrossRef] - Pietzuch, P.; Ledlie, J.; Mitzenmacher, M.; Seltzer, M. Network-aware overlays with network coordinates. In Proceedings of the 26th IEEE International Conference on Distributed Computing Systems Workshops, Lisboa, Portugal, 4–7 July 2006; p. 12. [Google Scholar]
- Xie, H.; Yang, Y.R.; Krishnamurthy, A.; Liu, Y.G.; Silberschatz, A. P4P: Provider portal for applications. In Proceedings of the ACM SIGCOMM Computer Communication Review, Barcelona, Spain, 16–21 August 2008; pp. 351–362. [Google Scholar]
- Sun, Y.; Yang, Y.R.; Zhang, X.; Guo, Y.; Li, J.; Salamatian, K. Thash: A practical network optimization scheme for dht-based p2p applications. IEEE J. Sel. Areas Commun.
**2013**, 31, 379–390. [Google Scholar] [CrossRef] - Helbing, D.; Brockmann, D.; Chadefaux, T.; Donnay, K.; Blanke, U.; Woolley-Meza, O.; Perc, M. Saving Human Lives: What Complexity Science and Information Systems can Contribute. J. Stat. Phys.
**2015**, 158, 735–781. [Google Scholar] [CrossRef] - Jalili, M.; Perc, M. Information cascades in complex networks. J. Complex Netw.
**2017**, 5, 665–693. [Google Scholar] [CrossRef] - Bui, V.; Zhu, W.; Bui, L.T. Optimal relay placement for maximizing path diversity in multipath overlay networks. In Proceedings of the IEEE GLOBECOM 2008–2008 IEEE Global Telecommunications Conference, New Orleans, LA, USA, 30 November–4 December 2008; pp. 1–6. [Google Scholar]
- Yang, X.; Wetherall, D. Source selectable path diversity via routing deflections. ACM SIGCOMM Comput. Commun. Rev.
**2006**, 36, 159–170. [Google Scholar] [CrossRef] - Zhang, W.; Lei, W.; Liu, S.; Li, G. A general framework of multipath transport system based on application-level relay. Comput. Commun.
**2014**, 51, 70–80. [Google Scholar] [CrossRef] - Guan, Y.; Lei, W.; Zhang, W.; Liu, S.; Li, H. Scalable orchestration of software defined service overlay network for multipath transmission. Comput. Netw.
**2018**, 137, 132–146. [Google Scholar] [CrossRef] - Zhang, W.; Lei, W.; Guan, Y.; Li, G.; Yang, L. Considerations for application-layer multipath transport control. Int. J. Commun. Syst.
**2017**, 30, e3343. [Google Scholar] [CrossRef] - Zhang, W.; Ning, Z.; Lei, W.; Chen, Z. A topology and application-aware relay path allocation scheme in multipath transport system based on application-level relay. Int. J. Commun. Syst.
**2016**, 30, e3245. [Google Scholar] [CrossRef] - Shang, Y.; Ruml, W. Improved MDS-based localization. IEEE INFOCOM 2004
**2004**, 4, 2640–2651. [Google Scholar] - Jesi, G.P.; Montresor, A.; Babaoglu, O. Proximity-aware superpeer overlay topologies. In IEEE International Workshop on Self-Managed Networks, Systems, and Services; Springer: Berlin/Heidelberg, Germanuy, 2006; pp. 43–57. [Google Scholar]
- Shang, Y.; Ruml, W.; Zhang, Y.; Fromherz, M.P. Localization from mere connectivity. In Proceedings of the 4th ACM international symposium on Mobile ad hoc networking computing, Annapolis, MD, USA, 1–3 June 2003; pp. 201–212. [Google Scholar]
- Ng, T.E.; Zhang, H. Predicting Internet network distance with coordinates-based approaches. In Proceedings of the Twenty-First, Annual Joint Conference of the IEEE Computer and Communications Societies, New York, NY, USA, 23–27 June 2002; pp. 170–179. [Google Scholar]
- Medina, A.; Lakhina, A.; Matta, I.; Byers, J. BRITE: An approach to universal topology generation. In Proceedings of the Ninth International Symposium on Modeling, Analysis and Simulation of Computer and Telecommunication Systems, Cincinnati, OH, USA, 15–18 August 2001; pp. 346–353. [Google Scholar]
- Costa, M.; Castro, M.; Rowstron, R.; Key, P. PIC: Practical Internet coordinates for distance estimation. In Proceedings of the 24th International Conference on Distributed Computing Systems, Tokyo, Japan, 24–26 March 2004; pp. 178–187. [Google Scholar]
- Bessani, A.; Neves, N.F.; Veríssimo, P.; Dantas, W.; Fonseca, A.; Silva, R.; Correia, M. JITeR: Just-in-time application-layer routing. Comput. Netw.
**2016**, 104, 122–136. [Google Scholar] [CrossRef] - Dahlin, M.; Chandra, B.B.V.; Gao, L.; Nayate, A. End-to-end WAN service availability. IEEE/ACM Trans. Netw.
**2003**, 11, 300–313. [Google Scholar] [CrossRef] - Li, Z.; Yuan, L.; Mohapatra, P.; Chuah, C.N. On the analysis of overlay failure detection and recovery. Comput. Netw.
**2007**, 51, 3828–3843. [Google Scholar] [CrossRef] - Markopoulou, A.; Iannaccone, G.; Bhattacharyya, S.; Chuah, C.N.; Ganjali, Y.; Diot, C. Characterization of failures in an operational ip backbone network. IEEE/ACM Trans. Netw.
**2008**, 16, 749–762. [Google Scholar] [CrossRef] - Ren, S.; Guo, L.; Zhang, X. ASAP: An AS-aware peer-relay protocol for high quality VoIP. In Proceedings of the 26th IEEE International Conference on Distributed Computing Systems, Lisboa, Portugal, 4–7 July 2006; p. 70. [Google Scholar]
- Guo, D.; Jin, H.; Chen, T.; Wu, J.; Lu, L.; Li, D.; Zhou, X. Partial probing for scaling overlay routing. IEEE Trans. Parallel Distrib. Syst.
**2013**, 24, 2261–2272. [Google Scholar] [CrossRef]

**Figure 1.**The framework of Software-Defined Service Overlay Network (SDSON) built on bearing networks. The bottom plane consists of underlay bearing networks. The middle plane is the forwarding plane, which consists of Relay Servers (relay forwarding nodes). The top plane is the control plane, which consists of Relay Controller (control node).

**Figure 3.**The underlay bearing networks consisting of multiple autonomous systems in different locations. (

**a**) shows the underlay networks with three different autonomous systems (represented by three layers), and in each autonomous systems, forwarding nodes are deployed in several locations (represented by dotted rectangles); (

**b**) shows the independent topology view of each autonomous systems and (

**c**) shows the merged topology view of three independent views.

**Figure 4.**Sample topologies consist of overlay nodes and different autonomous systems. (

**a**) shows a coordinate-based view of Relay Serves and solid circles represent the coordinates of Relay Servers; (

**b**) shows the underlay bearing networks consisting of various autonomous systems deployed in different locations (L1–L6).

**Figure 5.**The network topology of the scale-free topology feature generated with BRITE. Nodes with different colours mean they belong to different autonomous systems.

**Figure 6.**The backbone topology of practically deployed bearing networks from ChinaNet, CMNet. (

**a**) shows the topology of one underlay network and circles represent the backbone routers; (

**b**) shows the integrated topology of underlay networks belonging to ChinaNet and CMNet; the bold lines are exchange points between them.

**Figure 7.**The CDF (cumulative distribution function) of multipath stretch calculated from different multipath generating methods. (

**a**) shows the CDF of multipath stretch in bearing networks generated with BRITE with scale-free feature in Figure 5; (

**b**) shows the CDF of multipath stretch in practically deployed bearing networks from Internet Service Providers in Figure 6.

**Figure 8.**Evaluation of multipath transmission performance with injected congestion traffic and link failure. (

**a**) depicts the sending rate from origin hosts; (

**b**) depicts the total bandwidth of traffic injected into bearing networks as congestion; (

**c**) depicts the aggregating rates from destination host using different transmission methods.

Notation | Definition and Description |
---|---|

${T}_{set}=\{{T}_{1}\sim {T}_{n}\}$ | topology view set, ${T}_{i}$ denotes the view of $A{S}_{i}$ |

${T}_{i}=\{R{S}_{1}\sim R{S}_{m}\}$ | ${T}_{i}$ has m RSes |

${L}_{set}=\{{L}_{1}\sim {L}_{p}\}$ | location set, city is the basic unit of location |

$R{S}_{i}^{j}\in {L}_{j}$ | $R{S}_{i}$ is deployed in ${L}_{j}$ |

$NB(i,j)$ | distance between ${L}_{i}$ and ${L}_{j}$, or $R{S}_{i}$, and $R{S}_{j}$ |

${L}_{k}(p,q)=1$ | ${T}_{p}$ and ${T}_{q}$ have SPs in ${L}_{k}$ |

$MP(i,j)=\{{P}_{1}\sim {P}_{q}\}$ | q multiple paths between $R{S}_{i}$ and $R{S}_{j}$ |

$R{S}_{i}\in {P}_{j}$ | $R{S}_{i}$ is on ${P}_{j}$ |

${P}_{j}\subseteq {T}_{k}$ | $\forall R{S}_{i}\in {P}_{j},R{S}_{i}\in {T}_{k}$ |

$MPD(i,j)$ | the multipath diversity of $MP(i,j)$ |

**Table 2.**Geometric items and descriptions referring to Figure 4.

Item | Definition and Description |
---|---|

Transmission Direction (TD) | Vector from the coordinate of origin-ARS to that of destination-ARS, TD of 7-9 is TD(7,9) |

Transmission Surface (TS) | The candidate RSes are restricted within the surface, which is enclosed with constrained criteria, TS of 7-9 is TS(7,9), which includes rectangle surface ABCD, ellipse EF |

Deviation Angle (DA) | The angle between the link and TD, $\alpha $ is the deviation angle of 7-2 and 7-9, $\beta $ the 7-12 and 7-9, Then, the angle of 7-2 and 7-12 is DA(7-2,7-12)=$\left|\alpha \right|+\left|\beta \right|$ |

Node Quantity | MDSM | MDS-MAP | GNP | Vivaldi |
---|---|---|---|---|

30 | 0.163 | 0.215 | 0.231 | 0.230 |

50 | 0.175 | 0.227 | 0.245 | 0.251 |

70 | 0.183 | 0.232 | 0.255 | 0.257 |

© 2019 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/).

## Share and Cite

**MDPI and ACS Style**

Guan, Y.; Lei, W.; Zhang, W.; Zhan, Y.; Li, H.; Zhang, S.
A Multi-Dimension Spatial Method for Topology Awareness and Multipath Generating. *Symmetry* **2019**, *11*, 870.
https://doi.org/10.3390/sym11070870

**AMA Style**

Guan Y, Lei W, Zhang W, Zhan Y, Li H, Zhang S.
A Multi-Dimension Spatial Method for Topology Awareness and Multipath Generating. *Symmetry*. 2019; 11(7):870.
https://doi.org/10.3390/sym11070870

**Chicago/Turabian Style**

Guan, Yunchong, Weimin Lei, Wei Zhang, Yuzhuo Zhan, Hao Li, and Songyang Zhang.
2019. "A Multi-Dimension Spatial Method for Topology Awareness and Multipath Generating" *Symmetry* 11, no. 7: 870.
https://doi.org/10.3390/sym11070870