Review Paper on Routing and Networks Using Hybrid AI

Abstract

In recent years, the engineering and physical sciences have been more interested in traffic dynamics. In order to increase the transportation efficiency of a scale-free network, we propose a routing strategy by building a cost function based on the ratio of degree to closeness centrality. In this brief, we concentrate on the traffic capacity that can be measured by the critical point of phase transition from free flow to congestion. Simulations are used to examine the average route length, traffic load, and maximum node betweenness. To further analyze the traffic distribution, load variance, load mean, and load decrease rate are added. Our approach outperforms the efficient routing (ER) technique by achieving a notable increase in traffic capacity and more equitable load distribution.

Introduction

1. Background and Motivation

• Real-world networks like biological, communication, and power grids face increasing congestion due to growing traffic.

• Traditional routing methods (e.g., Shortest Path (SP), Efficient Routing (ER)) often direct traffic through hub nodes, making them prone to congestion.

• Goal: Improve network traffic capacity by avoiding overloaded nodes using more intelligent routing strategies.

2. Related Work

• ER Strategy: Avoids hub nodes by minimizing the sum of node degrees.

• Probability Routing (PR): Considers packet waiting probability based on node degree.

• Betweenness-based Methods: Use centrality metrics to avoid congested nodes.

• Hybrid Methods: Combine structural (static) and dynamic info, e.g., traffic-aware routing, gravitation theory, and Reinforcement Learning (RL) approaches.

3. Proposed Strategy: Improved Optimum (IO) Routing

• Introduces a new cost function based on the ratio of node degree to closeness centrality, enabling smarter avoidance of congested hub nodes.

• Control parameter α adjusts the influence of this ratio:

  • α > 0: Prefers nodes with low degree/closeness ratio (avoids hubs).

  • α < 0: Prefers hubs.

  • α = 0: Reduces to traditional SP routing.

• Goal: Identify an optimal α value that maximizes traffic capacity.

4. Models Used

• Network Model: Barabási-Albert (BA) scale-free network, which mimics real-world network growth via preferential attachment.

• Traffic Model: At each time step, R packets are generated randomly. Congestion occurs when R exceeds a critical threshold Rc.

5. Performance Metrics

• Traffic Capacity (Rc): Maximum packet generation rate before congestion occurs.

• Efficient Betweenness Centrality (Bmax): Measures node traffic load. Lower is better.

• Average Path Length (⟨L⟩): Indicates routing efficiency.

• Load Metrics:

  • Load Reduction Rate: Improvement of IO over ER.

  • Load Average: Mean number of packets per node.

  • Load Variance: Traffic distribution uniformity.

6. Simulation Results (via MATLAB)

• Optimal α = 1.1 for IO routing yields highest Rc across network sizes.

• IO routing outperforms ER and PR in traffic capacity for networks with N < 800.

• When N > 900, IO’s traffic capacity drops below PR.

Conclusion

In complicated networks, traffic congestion has led researchers to develop a number of solutions. An efficient route plan is one way to do this. By using degree and closeness centrality, respectively, the network is examined from a local and global viewpoint. We used the two indications to offer an IO routing technique. Regardless of network size, our routing system has a higher critical packet generation rate (Rc) than the ER technique. When network size is modest, our strategy\'s traffic capacity is superior to that of PR strategies. Regardless of the network size, our strategy\'s average path length is shorter than that of ER and PR techniques. Three more indices—load reduction rate, load mean, and load variance—were added to the load distribution diagram of nodes in order to conduct a thorough analysis of the load situation. The outcomes demonstrate that our approach not only lessens the network\'s overall load but also improves the distribution of that load. Ultimately, simulation results consistently show that the proposed technique has certain advantages in terms of traffic capacity, maximum node betweenness, average path length, and traffic load of scale-free networks.

References

[1] G. Chen, Z. Y. Dong, D. J. Hill, G. H. Zhang, and K. Q. Hua, “Attack structural vulnerability of power grids: A hybrid approach based on complex networks,” Physica A Stat. Mech. Appl., vol. 389, no. 3, pp. 595–603, 2010. [2] J.-P. Onnela et al., “Structure and tie strengths in mobile communication networks,” Proc. Natl. Acad. Sci., vol. 104, no. 18, pp. 7332–7336, 2007. [3] Y. Han, J. Z. Ji, and C. C. Yang, “Functional module detection based on multi-label propagation mechanism in protein-protein interaction networks,” Int. J. Pattern Recognit. Artif. Intell., vol. 29, no. 6, pp. 548–557, 2016. [4] P. P. Sun et al., “Protein function prediction using function associations in protein-protein interaction network,” IEEE Access, vol. 6, pp. 30892–30902, 2018. [5] M. Ericsson, M. G. C. Resende, and P. Pardalos, “A genetic algorithm for the weight setting problem in OSPF routing,” J. Comb. Optim., vol. 6, pp. 299–333, Sep. 2002. [6] B. Fortz and M. Thorup, “Optimizing OSPF/IS-IS weights in a changing world,” IEEE J. Sel. Areas Commun., vol. 20, no. 4, pp. 756–767, May 2002. [7] F. Tan and Y. X. Xia, “Hybrid routing on scale-free networks,” Physica A Stat. Mech. Appl., vol. 392, no. 18, pp. 4146–4153, 2013. [8] G. Yan, T. Zhou, B. Hu, Z.-Q. Fu, and B.-H. Wang, “Efficient routing on complex networks,” Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 73, no. 2, 2006, Art. no. 46108. [9] B. Danila, Y. Yu, J. A. Marsh, and K. E. Bassler, “Optimal transport on complex networks,” Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 74, no. 4, 2006, Art. no. 46106. [10] L. Chen, J. C. Chen, Z. H. Guan, X.-H. Zhang, and D.-X. Zhang, “Optimization of transport protocols in complex networks,” Physica A Stat. Mech. Appl., vol. 391, no. 11, pp. 3336–3341, 2012. [11] Z. Y. Jiang, M. G. Liang, J.-L. Huang, and Q. Li, “An efficient weighted routing strategy for scale-free networks,” Mod. Phys. Lett. B, vol. 26, no. 29, 2012, Art. no. 50195. [12] X. J. Zhang, Z. S. He, Z. He, and R.-B. Lez, “Probability routing strategy for scale-free networks,” Physica A Stat. Mech. Appl., vol. 392, no. 4, pp. 953–958, 2013. [13] W. X. Wang, C. Y. Yin, G. Yan, and B. Wang, “Integrating static and dynamic information for routing traffic,” Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 74, Jul. 2006, Art. no. 016101. [14] X. Ling, M. B. Hu, R. Jiang, and Q. S. Wu, “Global dynamic routing for scale-free networks,” Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 81, Jan. 2010, Art. no. 16113. [15] K. Li, X. F. Gong, S. G. Guan, and C.-H. Lai, “Analysis of traffic flow on complex networks,” Int. J. Mod. Phys. B, vol. 25, no. 10, pp. 1419–1428 ,2012. [16] X. Gao et al., “Global hybrid routing for scale-free networks,” IEEE Access, vol. 7, pp. 19782–19791, 2019. [17] X. P. Wang, G. Yu, and H. T. Lu, “A local information-based routing strategy on the scale-free network,” Mod. Phys. Lett. B, vol. 23 , no. 10, pp. 1291–1301, 2009. [18] G. Liu and Y. S. Li, “Routing strategy for complex networks based on gravitation field theory,” Acta Physica Sinica, vol. 61, no. 24, 2012, Art. no. 248901. [19] G. Liu and Y.-S. Li, “Study on the congestion phenomena in complex network based on gravity constraint,” Acta Physica Sinica, vol. 61, no. 10, 2012, Art. no. 108901. [20] G. Liu, Y.-S. Li, and X.-P. Zhang, “Analysis of network traffic flow dynamics based on gravitational field theory,” Chin. Phys. B, vol. 22, no. 6, 2013, Art. no. 68901. [21] Z. Liu, M.-B. Hu, R. Jiang, W.-X. Wang, and Q.-S. Wu, “Method to enhance traffic capacity for scale-free networks,” Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 76, Sep. 2007, Art. no. 37101. [22] G.-Q. Zhang, D. Wang, and G.-J. Li, “Enhancing the transmission efficiency by edge deletion in scale-free networks,” Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 76, Jul. 2007, Art. no. 17101. [23] Z. Y. Chen and X. F. Wang, “Effects of network structure and routing strategy on network capacity,” Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 73, Mar. 2006, Art. no. 36107. [24] M. Tang, Z. H. Liu, X. M. Liang, and P. M. Hui, “Self-adjusting routing schemes for time-varying traffic in scale-free networks,” Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 80, Aug. 2009, Art. no. 26114. [25] C. L. Pu, S.-Y. Zhou, K. Wang, Y.-F. Zhang, and W. J. Pei, “Efficient and robust routing on scale-free networks,” Physica A Stat. Mech. Appl., vol. 391, no. 3, pp. 866–871, 2012. [26] S.-C. Kao, C.-H. H. Yang, P.-Y. Chen, X. L. Ma, and T. Krishna, “Reinforcement learning based interconnection routing for adaptive traffic optimization,” in Proc. 13th IEEE/ACM Int. Symp. Networks-on-Chip (NOCS), New York, NY, USA, 2019, pp. 1–2, doi: 10.1145/3313231.3352369. [27] A. L. Barabási and R. Albert, “Emergence of scaling in random networks,” Science, vol. 286, no. 5439, pp. [28] H. Liu and J. Zhang, “Research on network fixed point theory based on the correlation of nodes,” Acta Physica Sinica, vol. 56, no. 4, pp. 1952–1957, 2007. [29] J. L. Ma, M. Li, and H.-J. Li, “Traffic dynamics on multilayer networks with different speeds,” IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 69, no. 3, pp. 1697–1701, Mar. 2022. [30] A. Arenas, A. Díaz-Guilera, and R. Guimerà, “Communication in networks with hierarchical branching,” Phys. Rev. Lett., vol. 86, pp. 3196–3199, Apr. 2001. [31] A. Bavelas, “Communication patterns in task? Oriented groups,” J. Acoust. Soc. America, vol. 22, pp. 725–730, Aug. 1950. [32] R. Goldstein and M. S. Vitevitch, “The influence of closeness centrality on lexical processing,” Front. Psychol., vol. 8, p. 1683, Sep. 2017. [33] L. C. Freeman, “A set of measures of centrality based on betweenness,” Sociometry, vol. 40, no. 1, pp. 35–41, 1977. [34] R. Guimerà, A. Díaz-Guilera, F. Vega-Redondo, A. Cabrales, and A. Arenas, “Optimal network topologies for local search with congestion,” Phys. Rev. Lett., vol. 89, no. 4, 2002, Art. no. 248701. [35] F. Xia et al., “User popularity-based packet scheduling for congestion control in ad-hoc social networks,” J. Comput. Syst. Sci., vol. 82, no. 1, pp. 93–112, 2015.

Copyright

Copyright © 2025 Deepmala Sharma, Jitendra Ahir, Laxmi Singh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.