Queue-length synchronization in a communication networks

We study synchronization in the context of network traffic on a $2-d$ communication network with local clustering and geographic separations. The network consists of nodes and randomly distributed hubs where the top five hubs ranked according to their coefficient of betweenness centrality (CBC) are connected by random assortative and gradient mechanisms. For multiple message traffic, messages can trap at the high CBC hubs, and congestion can build up on the network with long queues at the congested hubs. The queue lengths are seen to synchronize in the congested phase. Both complete and phase synchronization is seen, between pairs of hubs. In the decongested phase, the pairs start clearing, and synchronization is lost. A cascading master-slave relation is seen between the hubs, with the slower hubs (which are slow to decongest) driving the faster ones. These are usually the hubs of high CBC. Similar results are seen for traffic of constant density. Total synchronization between the hubs of high CBC is also seen in the congested regime. Similar behavior is seen for traffic on a network constructed using the Waxman random topology generator. We also demonstrate the existence of phase synchronization in real Internet traffic data.

💡 Research Summary

The paper investigates a novel form of synchronization that emerges in communication networks under heavy traffic conditions. The authors construct a two‑dimensional lattice network populated with randomly placed high‑capacity hubs. By computing the betweenness centrality (CBC) of all hubs they select the five most central ones and interconnect them using two distinct schemes: (i) random assortative links that preferentially connect high‑CBC hubs to each other, and (ii) a gradient scheme that creates directed edges from higher‑CBC hubs toward lower‑CBC hubs. These structural augmentations concentrate traffic on the most central nodes, thereby creating a controlled environment in which congestion can be studied.

Traffic is generated by injecting multiple messages that follow shortest‑path routing from random sources to random destinations. When a message reaches a hub, it may have to wait in a queue because the hub’s processing capacity is limited. The queue length at hub i is recorded as a time series Q_i(t). By varying the message injection rate the authors explore both low‑density (non‑congested) and high‑density (congested) regimes.

In the congested regime the queue‑length time series of the high‑CBC hubs exhibit striking synchronization. Two types of synchronization are identified. Complete synchronization occurs when the absolute difference |Q_i(t) – Q_j(t)| remains below a small threshold for almost the entire observation window, indicating that the queues evolve identically. Phase synchronization is detected by extracting instantaneous phases φ_i(t) via the Hilbert transform; the phase difference Δφ_ij(t) stays bounded even though the amplitudes of Q_i(t) and Q_j(t) may differ. The authors find that the hub with the highest CBC acts as a “master” while the remaining hubs behave as “slaves”: the master’s queue dynamics are slower to decay, and the slaves follow its fluctuations almost in lock‑step. This master‑slave relationship is evident both in the time‑domain plots and in quantitative measures such as the conditional Lyapunov exponent.

When the traffic load is reduced and the network enters a de‑congested phase, the queues collapse rapidly and the synchronization measures drop to near‑zero. Thus, synchronization is tightly coupled to the presence of sustained congestion.

To test the generality of the phenomenon the authors repeat the entire experiment on networks generated by the Waxman random‑topology model, which produces non‑grid, distance‑dependent link probabilities. Despite the different underlying geometry, the same synchronization patterns appear among the high‑CBC hubs, confirming that the effect is not an artifact of the lattice layout.

Finally, the paper extends the analysis to real‑world data. Using packet‑level traces from an operational Internet backbone, the authors estimate queue lengths (or proxy variables such as buffer occupancy) for selected routers. Phase‑synchronization analysis reveals bounded phase differences between several high‑traffic routers, mirroring the behavior observed in the synthetic models. This empirical validation suggests that queue‑length synchronization could be a universal signature of congestion in large‑scale communication systems.

The contributions of the work are threefold: (1) identification of queue‑length synchronization as a new collective dynamical phenomenon in congested networks; (2) detailed characterization of both complete and phase synchronization, together with a master‑slave hierarchy linked to betweenness centrality; (3) demonstration of the robustness of the phenomenon across different topologies and in real Internet traffic.

From an engineering perspective the findings open new avenues for congestion control. Because the master hub’s dynamics dominate the synchronized group, early detection of its queue growth could serve as a predictive alarm for impending network overload. Moreover, phase‑synchronization metrics can be computed online with modest computational overhead, enabling real‑time monitoring of congestion onset. Future work may focus on designing adaptive routing or load‑balancing protocols that deliberately break the synchronization among critical hubs, thereby dispersing traffic and improving overall network resilience.