How Multiplex Design Will Power Faster, More Resilient Networks of the Future

Image: Matt E/Flickr

We’re surrounded by networks, all straining to move their constituent things—products, data, people—as efficiently as possible in the face of ever-growing demand. Yet even as the tubes get more crowded, and continue to do so, we expect them to move faster and more reliably. So what’s the super-fast, ultra-resilient internet or subway of the future going to look like?

The key to preventing disruptions isn’t to simply add more pipes to the network—the network must be diverse as well. Think of mass transit: Normally, buses and the subway act as an interconnected compliment to each other, but when a train breaks down, buses aren’t stuck waiting on the tracks.

It may seem intuitive, but actually quantifying how such multilayer networks really work is far from simple. A paper from a mathematicians at the Universitat Rovira i Virgili in Spain successfully tested a new model for tracking network effects, and it has the potential to profoundly affect the way we design the cities, telecom networks, and even healthcare of the future.

The team used London’s mass transit system to study the value of using so-called “random walk” models to test network resilience to random disruptions, such as a train delay. The concept is fascinating: Normally, you’d expect that the best way to travel between nodes is to take the shortest route, and modeling such behavior is relatively straightforward.

Maps of London’s rail networks from the study.

But what happens when the train gets stuck underground in a station and you don’t know where to go next?

“In the presence of random failures it is not possible to have real-time information about the subsequent congestion,” the authors write in PNAS. “Moreover, the catastrophic cascade of failures, which might follow because of the interdependence of transport systems, is likely to propagate along shortest paths affecting the vertices with highest betweenness.”

Basically, when it all hits the fan, knowing the optimal solution while you’re in transit isn’t easy, and that confusion, multiplied across all the people moving through a network, will compound congestion. To test the resilience of a network to disruption, the authors write that “random walks represent a good choice to overcome this problem, and a good proxy to the real scenario.” 

So what exactly is a random walk? Essentially, random walk models serve as a mathematical proxy for a series of random steps, whether it’s the movement of gas molecules in a container, an animal through its habitat, or stock prices over time. (Wolfram Alpha has good references for background, as well as a model you can play with.) 

But for the wide variety of disciplines that random walk theory has been applied to, using it to study multilayered networks is pretty novel. How exactly does that work? Let’s take the London rail system, which features three different sets of rail networks, as our guide:

In aggregate, London’s rail lines work as a singular network, but each layer also works independently. So if a section of the Tube goes down, the Overground and DLR are likely to keep moving. A random walk model for a scenario like that, in which a person basically bumbles their way to their destination, would look like this:

The authors call this a multiplex network, in which an object can traverse multiple individual networks, or monoplexes. When multiple networks are connected into a multiplex, a curious thing happens: After a disruption, objects moving across those networks tend to balance themselves out as they search for optimal paths.

“When a vertex fails in a single transportation layer, it cannot be traversed by any path. However, if that vertex is part of an interconnected network it can still be reach on other layers. This intrinsic feature of multiplexes enhances the resilience of the system with respect to monoplexes,” the authors write.

The above graph shows the results of the team’s model of the London transit system. Over time, the entire, diverse network was more resilient than any individual part. 

“We have shown, theoretically and by means of extensive simulations, how the whole system is more resilient to random failures than its individual layers separately,” the authors write. “Indeed, interconnected networks introduce additional dimensions that can help to find paths from apparently isolated parts of single layers, enhancing the resilience to random failures, and we provide a way to quantify this.”

Knowing how such a model can be studied is crucial to developing more efficient network designs in the real world, and the list of applications is long. From the authors:

The results can be used to design optimal searching strategies, for instance, to characterize the cyclic structure of the multiplex, to infer gene regulatory pathways, to coarse grain the network structure, to assess the PageRank in these topologies, or to identify genes associated with hereditary disorders in protein–protein interaction networks, providing a step for further development of searching and navigability strategies in real interconnected systems.

Being able to quantify the benefits of multiplex networks is huge, as knowing those benefits can drive adoption. That means that, in the future, an emphasis on building networks that have multiple layers for people and things to pass through could help free up congestion and lower network downtime. It’s already happening, to a degree: One London ISP is already building out a separate network just for the Internet of Things, which doesn’t need the full power of broadband networks to function.

The concept can potentially apply to just about anything you think of. Mass transit is one obvious case, but what if we applied it to all infrastructure, from road networks to architecture? Of course, we already do intuitively—buildings that have elevators also have stairs, just in case—but being able to reliably test that design is crucial, and will lead to better, more reliable networks in the future.