基于耦合强度的双层网络数据传输能力

马金龙; 杜长峰; 隋伟; 许向阳

doi:10.7498/aps.69.20200181

摘要

为了降低网络拥塞, 提升网络传输性能, 对双层网络之间的耦合机理进行研究, 层间关系依据度度相关性分成三种耦合方式: 随机耦合、异配耦合、同配耦合. 在基于最短路径路由策略和基于度的权重路由策略条件下, 分析网络数据包的传输过程, 并研究双层网络的耦合方式及其适合的路由策略对网络传输容量的影响. 采用双层无标度网络进行仿真实验, 分析在路由策略约束下传输容量和耦合方式之间的关系, 依据双层网络之间耦合方式的特点, 找出适合每一种路由策略的最佳耦合方式以提升网络的传输容量. 经过仿真发现, 采用最短路径路由策略时, 异配耦合方式最佳; 采用基于度的静态权重路由策略时, 同配耦合方式最佳. 路由策略在匹配的耦合方式下使得网络流量分配均匀, 有利于网络传输容量的提升. 本研究为实际网络设计和传输性能优化提供了理论基础.

关键词:

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:

作者及机构信息

1.
河北科技大学信息科学与工程学院, 石家庄　050018

2.
通信网信息传输与分发技术重点实验室, 石家庄　050081

通信作者: 马金龙, mzjinlong@163.com

基金项目: 河北省高等学校科学技术研究项目(批准号: QN2019081)、石家庄市科学技术研究与发展计划(批准号: 195790055A)和河北省社会科学发展研究项目(批准号: 2019041201007)资助的课题

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)

文章全文 : translate this paragraph

参考文献

[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
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施引文献

图 1 双层网络模型示意图

Fig. 1. Legend of the two-layer networks model

下载: 全尺寸图片幻灯片

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

Fig. 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

下载: 全尺寸图片幻灯片

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

Fig. 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

下载: 全尺寸图片幻灯片

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

Fig. 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

下载: 全尺寸图片幻灯片

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

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

下载: 全尺寸图片幻灯片

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

Fig. 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

下载: 全尺寸图片幻灯片

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

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

下载: 全尺寸图片幻灯片

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

Fig. 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

下载: 全尺寸图片幻灯片

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,

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

下载: 全尺寸图片幻灯片

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

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

下载: 全尺寸图片幻灯片

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

Fig. 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

下载: 全尺寸图片幻灯片

map

[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 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 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 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 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 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 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 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 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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基于耦合强度的双层网络数据传输能力