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Traffic congestion in interconnected complex networks
Fei Tan, Jiajing Wu, Yongxiang Xia, Chi K. Tse
TL;DR
Traffic congestion in coupled networks is less explored than in isolated networks, despite the interdependence of modern infrastructures. The paper models packet traffic in interconnected BA networks and Internet AS-level graphs, finding that assortative coupling is most favorable under node-usage-based capacity allocation, while coupling preferences perform similarly under uniform capacity.
Problem
Traffic congestion in coupled communication networks remains underexplored despite the interaction and dependence among modern networked infrastructures.
Source: §I · pp. 1–2Method
The paper studies packet traffic under different coupling preferences, coupling probabilities, routing criteria, and node-capacity allocations in interconnected BA networks and South Korean-Japanese Internet AS-level graphs.
Source: §I · p. 2Results
Assortative coupling outperforms disassortative and random coupling under NUP allocation, has an optimal coupling probability, while all three preferences achieve almost the same capacity under UNI allocation.
Source: A. Interconnected BA scale-free networks · pp. 4–5Takeaways & Limitations
Interconnection patterns and processing-capacity allocation can be used to optimize traffic performance in interconnected networks.
Source: §I · p. 2, A. Interconnected BA scale-free networks · pp. 4–5, B. Interconnected Internet AS-level… · pp. 6–7
Abstract
from arXiv · showhide
Traffic congestion in isolated complex networks has been investigated extensively over the last decade. Coupled network models have recently been developed to facilitate further understanding of real complex systems. Analysis of traffic congestion in coupled complex networks, however, is still relatively unexplored. In this paper, we try to explore the effect of interconnections on traffic congestion in interconnected BA scale-free networks. We find that assortative coupling can alleviate traffic congestion more readily than disassortative and random coupling when the node processing capacity is allocated based on node usage probability. Furthermore, the optimal coupling probability can be found for assortative coupling. However, three types of coupling preferences achieve similar traffic performance if all nodes share the same processing capacity. We analyze interconnected Internet AS-level graphs of South Korea and Japan and obtain similar results. Some practical suggestions are presented to optimize such real-world interconnected networks accordingly.
I. INTRODUCTION
Traffic congestion research has largely treated networks as isolated, despite modern infrastructures being coupled. This paper addresses the gap by studying how interconnections affect packet traffic in coupled networks and real interconnected Internet graphs.
- Prior work has mainly studied isolated networks, emphasizing network structure, routing algorithms, and node-resource allocation as congestion-mitigation approaches.Source: §I · p. 1
- Traffic congestion in coupled communication networks remains comparatively underexplored even though modern infrastructures interact and depend on one another.Source: §I · pp. 1–2
- The paper examines how coupling preference and coupling probability affect traffic in interconnected Barabási-Albert scale-free networks.Source: §I · p. 2
- It also analyzes interconnected Internet AS-level graphs from South Korea and Japan to suggest ways of optimizing links between the two countries.Source: §I · p. 2
II. MODEL
The model couples two equal-size BA scale-free networks and evaluates packet traffic under alternative routing, coupling, and processing-capacity configurations. Congestion is characterized through the order parameter and its critical generation rate.
Network construction
- Two equal-size BA scale-free networks are connected with coupling probability P, while each node has at most one interconnection.Source: §II · p. 2
Coupling preferences
- The study compares assortative, disassortative, and random coupling by connecting nodes according to descending load, opposite load rankings, or random selection.Source: §II · p. 2
Resource allocation
- Node processing capacity is allocated either uniformly as UNI or proportionally to algorithmic betweenness and node usage probability as NUP.Source: §II · pp. 2–3
Traffic process
- Packets are generated with random sources and destinations, routed through queued nodes under FIFO processing, and removed upon reaching their destinations.Source: §II · p. 3
Traffic measure
- The order parameter distinguishes free flow from jamming, with the critical generation rate Rc serving as a measure of traffic capacity.Source: §II · p. 3
Routing criteria
- Shortest-path and efficient-routing criteria are studied because shortest paths pair with NUP allocation, whereas efficient routing redistributes load from hubs under UNI allocation.Source: §II · p. 3
III. RESULTS
The analysis extends traffic-capacity estimates from isolated networks to interconnected networks by using algorithmic betweenness and node processing capacities after coupling. It separately formulates estimates for NUP and UNI allocation scenarios.
- The isolated-network traffic-capacity expression is applied to interconnected networks because interconnection links provide routes between the two networks.Source: §III · p. 3
- Under NUP allocation, traffic capacity is estimated using the post-coupling algorithmic betweenness of nodes in networks A and B.Source: §III · p. 3
- Under UNI allocation, every node has processing capacity one, and traffic capacity is estimated from algorithmic betweenness in the newly interconnected network.Source: §III · p. 3
A. Interconnected BA scale-free networks
For interconnected BA scale-free networks, traffic capacity depends jointly on coupling preference, coupling probability, routing, and resource allocation. Assortative coupling is most advantageous with node-usage-based capacities, while coupling preferences perform similarly under uniform capacities.
Traffic capacity under NUP allocation
- Assortative coupling outperforms disassortative and random coupling as P increases under node-usage-based capacity allocation, with an optimal P maximizing Rc.For assortative coupling, Rc first rises sharply and then declines slightly; disassortative and random coupling show continuously increasing Rc.Source: A. Interconnected BA scale-free networks · p. 4
- Similar processing capacities at the two ends of interconnected links help balance cross-network load, explaining assortative coupling’s advantage in equal-size, equal-degree BA networks.The model uses two networks with NA = NB = 600 and ⟨kA⟩= ⟨kB⟩= 4.Source: A. Interconnected BA scale-free networks · p. 4
Mechanism
- Under assortative coupling, increasing P first distributes load away from high-capacity nodes, but eventually shifts more load onto low-capacity nodes and increases congestion.For disassortative and random coupling, more links facilitate a more even traffic-load distribution because high-capacity nodes are rarely interconnected.Source: A. Interconnected BA scale-free networks · pp. 4–5
Traffic capacity under UNI allocation
- With uniform node capacities, all three coupling preferences achieve nearly identical Rc, which increases continuously with P.More interconnections create additional paths between the originally isolated networks and reduce the maximum traffic load.Source: A. Interconnected BA scale-free networks · p. 5
Routing and allocation comparison
- Under node-usage-based allocation, NUP outperforms UNI for both routing criteria, while shortest path beats efficient routing only with NUP; UNI reverses that routing comparison.The result shows that routing comparisons require the resource-allocation strategy to be specified.Source: A. Interconnected BA scale-free networks · p. 5
Validation
- The theoretical estimates based on Eqs. (5) and (6) agree with corresponding simulations on interconnected BA scale-free networks.The theoretical and simulation analyses use the same interconnected-network setting described for Fig. 1.Source: Figure 1 · p. 4, A. Interconnected BA scale-free networks · p. 5
B. Interconnected Internet AS-level graphs of South Korea and Japan
The South Korea–Japan Internet AS-level networks provide a real-world test of how coupling, routing, resource allocation, and link pruning affect traffic capacity. Assortative coupling is favored under node-usage-based allocation, while coupling preference has little effect under uniform allocation; selective pruning can further improve capacity.
Network data
- The analyzed networks contain 677 South Korean and 509 Japanese nodes, differ in average internal degree, exhibit power-law internal-link distributions, and are connected by fourteen external edges.The networks are labeled SK and JP; their average internal degrees are approximately 3.65 and 4.40, respectively.Source: B. Interconnected Internet AS-level… · pp. 5–6, Figure 2 · p. 5, Table I · p. 5
Routing and resource allocation
- Shortest-path routing with node-usage-probability allocation achieves the highest traffic capacity, whereas shortest-path routing with uniform allocation performs worst.The real-world result agrees with the idealized interconnected BA-network analysis.Source: B. Interconnected Internet AS-level… · p. 6, Figure 4 · p. 7
Coupling preference and probability
- Assortative coupling outperforms disassortative and random coupling when node processing capacity follows node usage probability, despite irregular real-network trends.Super high-degree nodes and differences in network size and average degree contribute to deviations from the idealized model.Source: B. Interconnected Internet AS-level… · pp. 5–6, Figure 4 · p. 7
Uniform allocation
- Under uniform processing capacity, traffic capacity is unaffected by coupling preference, and the established fourteen links produce similar performance despite lacking a single coupling pattern.Capacity rises sharply at first and then remains steady or increases slowly as coupling probability grows.Source: B. Interconnected Internet AS-level… · p. 6, Figure 4 · p. 7
Link pruning
- Pruning interconnected links is beneficial because the fourteen established links are not optimal, but capacity depends on both the number and positions of retained links.For shortest path, the largest capacity uses five remaining links after pruning nine; efficient routing achieves its largest capacity with two remaining links after pruning twelve.Source: B. Interconnected Internet AS-level… · pp. 6–7, Figure 5 · p. 7
Link-efficiency objective
- The quantity Q decreases monotonically with the number of interconnected links, making one link optimal from the perspective of maximizing capacity per link.The retained links labeled 4 and 9 are indispensable for shortest-path and efficient-routing protocols, respectively.Source: B. Interconnected Internet AS-level… · pp. 7–8
IV. CONCLUSIONS
The paper studies traffic congestion in interconnected complex networks. It finds that assortative coupling is most effective under node-usage-based capacity allocation, while coupling preferences perform similarly under uniform capacity allocation.
- For interconnected BA scale-free networks, assortative coupling alleviates congestion more effectively than disassortative or random coupling when capacity follows node usage probability.Source: §IV · p. 8
- When all nodes have the same processing capacity, the three coupling preferences achieve similar traffic performance.Source: §IV · p. 8