Data traffic capability of double-layer network based on coupling strength

Ma Jin-Long; Du Chang-Feng; Sui Wei; Xu Xiang-Yang

doi:10.7498/aps.69.20200181

Abstract

The two-layer network model offers us a new viewpoint to observe the traffic dynamics of multilayer network systems. An efficient coupling mechanism is of great importance for alleviating the traffic congestion on two-layer networks. In order to reduce the network congestion and improve network transmission performance, the coupling mechanism between two layers of network and three coupling methods, which are random coupling, disassortative coupling and assortative coupling, are studied based on degree correlation. The packet transmission process is analyzed with both the shortest path routing strategy and degree-based weight routing strategy. The influences of the coupling mode and its corresponding routing strategy on the traffic capacity of the two-layer network are studied. In this paper, two scale-free networks are used to construct the two-layer network for simulation experiments. The network scale is in a range from 200 to 2400 with the value of average degree being 8. We focus on the traffic dynamics of two-layer network, and analyze the relationship between the traffic capacity and the three coupling modes, which are random coupling, disassortative coupling and assortative coupling, under the constraints of the shortest path routing strategy and the weight-based routing strategy. According to the characteristics of the coupling connection between the two layers of network, the best coupling method which is suitable for a certain routing strategy should be investigated. The suitable coupling connection between the two layers can effectively increase the traffic capacity. Both numerical result and analytical result show that the packet generation rate, average transmission time, and average throughput can be obviously improved under the shortest path routing strategy with the disassortative coupling method. When the degree-based static weight routing strategy is used, the traffic performance parameters such as packet generation rate, average transmission time, and average throughput can reach the optimal values with the assortative coupling method. It makes the traffic flow uniform that the routing strategy is chosen with the most suitable coupling method on the two-layer network, and the network traffic capacity may be effectively enhanced. More generally, the results indicate that the coupling modes can give rise to traffic behavior that relies subtly on the routing strategy on the two-layer network. Our work may shed some light on the design and optimization of some real traffic or communication networks.

Keywords:

Authors and contacts

1.
School of Information Science and Engineering, Hebei University of Science and Technology, Shijiazhuang 050018, China
2.
Science and Technology on Communication Networks Laboratory, Shijiazhuang 050081, China

Corresponding author: Ma Jin-Long, mzjinlong@163.com

Funds: Project supported by the Science and Technology Research Project of Hebei Higher Education Institutions, China (Grant No. QN2019081), the Science and Technology Research and Development Plan Project of Shijiazhuang, China (Grant No. 195790055A), and the Research Projects on Social Science Development in Hebei Province, China (Grant No. 2019041201007)

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References

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[40]	杨先霞, 濮存来, 许忠奇, 陈荣斌, 吴洁鑫, 李伦波 2016 物理学报 65 248901 Google Scholar Yang X X, Pu C L, Xu Z Q, Chen R B, Wu J X, Li L B 2016 Acta Phys. Sin. 65 248901 Google Scholar

Cited By

图 1 双层网络模型示意图

Figure 1. Legend of the two-layer networks model

DownLoad: Full-Size Img PowerPoint

图 2 采用SPR策略AC, DC, RC 这三种耦合方式有序参数$ \eta $与数据包产生率$ R $的关系　(a) BA-BA模型; (b) ER-ER模型; (c) SF-SF模型; (d) BA-ER模型; (e) BA-SF模型; (f) ER-SF模型

Figure 2. Used the SPR strategy, the relationship between ordered parameters $ \eta $ and packet generation rate $ R $ under the three coupling modes of AC, DC and RC: (a) BA-BA model; (b) ER-ER model; (c) SF-SF model; (d) BA-ER model; (e) BA-SF model; (f) ER-SF model

DownLoad: Full-Size Img PowerPoint

图 3 采用DWR策略AC, DC, RC 这三种耦合方式$ R $与控制参数$ \alpha $的关系　(a) BA-BA模型; (b) ER-ER模型; (c) SF-SF模型; (d) BA-ER模型; (e) BA-SF模型; (f) ER-SF模型

Figure 3. Used the SPR strategy, the relationship between $ R $ and control parameter $ \alpha $ under the three coupling modes of AC, DC and RC: (a) BA-BA model; (b) ER-ER model; (c) SF-SF model; (d) BA-ER model; (e) BA-SF model; (f) ER-SF model

DownLoad: Full-Size Img PowerPoint

图 4 采用DWR策略AC, DC, RC 这三种耦合方式序参数$ \eta $与数据包产生率$ R $的关系　(a) BA-BA模型; (b) ER-ER模型; (c) SF-SF模型; (d) BA-ER模型; (e) BA-SF模型; (f) ER-SF模型

Figure 4. Used the DWR strategy, the relationship between ordered parameters $ \eta $ and generation rate $ R $ under the three coupling modes of AC, DC and RC: (a) BA-BA model; (b) ER-ER model; (c) SF-SF model; (d) BA-ER model; (e) BA-SF model; (f) ER-SF model

DownLoad: Full-Size Img PowerPoint

图 5 耦合强度系数$P_{\rm r}$与$ R_{\rm c} $的关系

Figure 5. Relationship between coupling correlation coefficient $ P_r $ and $ R_{\rm c} $

DownLoad: Full-Size Img PowerPoint

图 6 DWR策略不同网络规模$ R_{\rm c} $与控制参数$ \alpha $的关系　(a) RC耦合方式; (b) DC 耦合方式; (c) AC耦合方式

Figure 6. Relationship between $ R_{\rm c} $ and control parameter $ \alpha $ under different network scales of DWR strategy: (a) RC Coupling; (b) DC Coupling; (c) AC Coupling

DownLoad: Full-Size Img PowerPoint

图 7 DWR策略不同网络规模$ R $与控制参数$ \alpha $的关系　(a) AC耦合方式; (b) DC 耦合方式; (c) RC耦合方式

Figure 7. Relationship between $ R $ and control parameter $ \alpha $ under different network scales of DWR strategy: (a) AC Coupling; (b) DC Coupling; (c) RC Coupling

DownLoad: Full-Size Img PowerPoint

图 8 两种路由策略不同耦合方式平均吞吐量$ \left\langle N_t \right\rangle $ 与$ R $的关系　(a) SPR策略; (b) DWR策略

Figure 8. Relationship between average information flow $ \left\langle N_t \right\rangle $ and $ R $ under two routing strategies with different coupling: (a) SPR; (b) DWR

DownLoad: Full-Size Img PowerPoint

图 9 采用两种路由策略不同耦合方式平均传输时间$ \left\langle T \right\rangle $与$ R $的关系　(a) SPR策略; (b) DWR策略,

Figure 9. Relationship between average transmission time $ \left\langle T \right\rangle $ and $ R $ under two routing strategies with different coupling: (a) SPR; (b) DWR

DownLoad: Full-Size Img PowerPoint

图 10 两种路由策略三种耦合方式$ R_{\rm c} $随网络规模N的变化　(a) SPR策略; (b) DWR策略

Figure 10. Relationship between network size N and $ R_{\rm c} $ under two routing strategies with different coupling: (a) SPR; (b) DWR

DownLoad: Full-Size Img PowerPoint

图 11 两种路由策略三种耦合方式平均路径长度$ \left\langle L \right\rangle $与网络规模N的关系　(a) SPR策略; (b) DWR 策略

Figure 11. Relationship between average path length $ \left\langle L \right\rangle $ and network size N under two routing strategies with different coupling: (a) SPR; (b) DWR

DownLoad: Full-Size Img PowerPoint

[1]	Janaki T M, Gupte N 2003 Phy. Rev. E 67 021503 Google Scholar
[2]	Albert R, Jeong H, Barabási A L 1999 Nature 401 130 Google Scholar
[3]	刘宏鲲, 周涛 2007 物理学报 56 106 Google Scholar Liu H K, Zhou T 2007 Acta Phys. Sin. 56 106 Google Scholar
[4]	Ohira T, Sawatari R 1998 Phy. Rev. E 58 193 Google Scholar
[5]	Solé R V, Valverde S 2001 Physica A 289 595 Google Scholar
[6]	Guimerà R, Arenas A, Díaz G A, Giralt F 2002 Phy. Rev. E 66 026704 Google Scholar
[7]	Woolf M, Arrowsmith D K, Mondragón C R J, Pitts J M 2002 Phy. Rev. E 66 046106 Google Scholar
[8]	Arenas A, Díaz G A, Guimerà R 2001 Phys. Rev. Lett. 86 3196 Google Scholar
[9]	Du W B, Wu Z X, Cai K Q 2013 Physica A 392 3505 Google Scholar
[10]	陈华良, 刘忠信, 陈增强, 袁著祉 2009 物理学报 58 6068 Google Scholar Chen H L, Liu Z X, Chen Z Q, Yuan Z Z 2009 Acta Phys. Sin. 58 6068 Google Scholar
[11]	Zhou J, Yan G, Lai C H 2013 EPL-Europhys. Lett. 102 28002 Google Scholar
[12]	Kurant M, Thiran P, Hagmann P 2007 Phys. Rev. E 76 026103 Google Scholar
[13]	Du W B, Zhou X L, Chen Z, Cai K Q, Cao X B 2014 Chaos, Solitons Fractals 68 72 Google Scholar
[14]	Tan F, Wu J J, Xia Y X, Tse C K 2014 Phys. Rev. E 89 062813 Google Scholar
[15]	Kurant M, Thiran P 2006 Phys. Rev. Lett. 96 138701 Google Scholar
[16]	Morris R G, Barthelemy M 2012 Phys. Rev. Lett. 109 128703 Google Scholar
[17]	Chen S Y, Huang W, Cattani C, Altieri G 2012 Math. Prob. Eng. 2012 256 Google Scholar
[18]	Fortz B, Thorup M 2002 IEEE J. Sel. Areas Commun. 20 756 Google Scholar
[19]	Zhuo Y, Peng Y F, Yang X L, Long K 2011 Phys. Scr. 84 055802 Google Scholar
[20]	卓越 2011 计算机应用研究 28 3411 Google Scholar Zhuo Y 2011 Appl. Res. Comput. 28 3411 Google Scholar
[21]	Zhang S, Liang M G, Li H J 2014 Can. J. Phys. 92 1599 Google Scholar
[22]	Zhang S, Liang M G, Jiang Z Y, Li Z Y 2015 Int. J. Mod. Phys. C 26 1550001 Google Scholar
[23]	Ma J L, Han W Z, Guo Q, Zhang S, Wang J F, Wang Z H 2016 Int. J. Mod. Phys. C 27 1650044 Google Scholar
[24]	Pu C L, Li S Y, Yang X X, Yang J, Wang K 2016 Physica A 447 261 Google Scholar
[25]	Wang W, Tang M, Yang H, Do Y, Lai Y C, Lee G W 2014 Sci. Rep. 4 5097 Google Scholar
[26]	Lee K M, Kim J Y, Cho W K, Goh K L, Kim I M 2012 New J. Phys. 14 033027 Google Scholar
[27]	Cho W K, Min B, Goh K I 2010 Phys. Rev. E 81 066109 Google Scholar
[28]	Gu C G, Zou S R, Xu X L, Qu Y Q, Jiang Y M, He D R, Liu H K, Zhou T 2011 Phy. Rev. E 84 026101 Google Scholar
[29]	Wang K, Zhang Y F, Zhou S Y, Pei W J, Wang S P, Li T 2011 Physica A 390 2593 Google Scholar
[30]	Zhuo Y, Peng Y F, Liu C, Liu Y K, Long K 2011 Physica A 390 2401 Google Scholar
[31]	Yang S J 2005 Phy. Rev. E 71 016107 Google Scholar
[32]	Zou S R, Zhou T, Liu A F, Xu X L, He D R 2010 Phys. Lett. A 374 4406 Google Scholar
[33]	王丹, 于灏, 井元伟, 姜囡, 张嗣瀛 2009 物理学报 58 6802 Google Scholar Wang D, Yu H, Jing Y W, Jiang N, Zhang S Y 2009 Acta Phys. Sin. 58 6802 Google Scholar
[34]	李涛, 裴文江, 王少平 2009 物理学报 58 5903 Google Scholar Li T, Pei W J, Wang S P 2009 Acta Phys. Sin. 58 5903 Google Scholar
[35]	濮存来, 裴文江 2010 物理学报 59 3841 Google Scholar Pu C L, Pei W J 2010 Acta Phys. Sin. 59 3841 Google Scholar
[36]	Zhao L, Lai Y C, Park K, Ye N 2005 Phys. Rev. E 71 026125 Google Scholar
[37]	Boccaletti S, Bianconi G, Criado R, Genio C L, Gómez G J, Romance M, Sendiña Nadal I, Wang Z, Zanin M 2014 Phys. Rep. 544 1 Google Scholar
[38]	刘伟彦, 刘斌 2014 物理学报 63 248901 Google Scholar Liu W Y, Liu B 2014 Acta Phys. Sin. 63 248901 Google Scholar
[39]	李世宝, 娄琳琳, 陈瑞祥, 洪利 2014 物理学报 63 028901 Google Scholar Li S B, Lou L L, Chen R X, Hong L 2014 Acta Phys. Sin. 63 028901 Google Scholar
[40]	杨先霞, 濮存来, 许忠奇, 陈荣斌, 吴洁鑫, 李伦波 2016 物理学报 65 248901 Google Scholar Yang X X, Pu C L, Xu Z Q, Chen R B, Wu J X, Li L B 2016 Acta Phys. Sin. 65 248901 Google Scholar

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