The Paradox of Adding More

Unintended Consequences of "addition" in Traffic, Technology, and Nature

Who likes traffic? Whether it's in London, Toronto, or Bengaluru, nobody enjoys being stuck on crowded roads. A quick fix might seem to be building more roads. The idea is simple: more roads, more routes, less congestion. That would seem to work, except it does not.

Surprisingly, more roads can slow down traffic. I know what you are thinking! Well here is an arrangement: if no one uses the new road, traffic stays the same—no better, no worse. So, how could it get worse? It's all about human behavior and Game Theory.

Setting up the Problem

Imagine we have a road network where 4,000 drivers want to go from Start to End. The Start-A route's travel time is always 45 minutes. The Start-B route travel time is the number of drivers (N) divided by 100. A-End is again the number of drivers (N) divided by 100. B-End always takes 45mins.

In ideal case, drivers split evenly between Start-A-End and Start-B-End, which means each route takes 65 minutes. It's a balance—if one route were quicker, drivers would switch, disrupting the equilibrium.

Now, introduce a new A-B road that takes almost no time. If one driver tries it, his journey drops to just over 40 minutes.

As more drivers follow, the time savings vanish. When 2,500 use the new route, everyone's back to 65 minutes.

But the remaining 1,500 on the original route now take 77.5 minutes due to increased congestion.

The drivers on original route are tempted to switch to the faster route, so now all drivers end up taking 80 minutes, worse than the original 65. If drivers collectively avoided the A-B shortcut, or if it were closed, they'd all save 15 minutes.

This is called Braess's Paradox.

A Client-Server Setup

The idea that more isn't always better extends far beyond the realm of traffic management, touching every system where resources and demand interact.

Imagine a network where clients are connected to servers, each server assigned based on its proximity to ensure the fastest possible response time for the client. This design is meant to optimize efficiency, reducing latency and making the system responsive.

Each of the servers have roughly same number of clients.

Now, introduce a new server into the heart of this network. At first glance, this seems like a straightforward improvement: a new server means more capacity, theoretically distributing the load more evenly and reducing the strain on individual servers.

The new server becomes overloaded due to excess demand.

However, the reality is counterintuitive. Most clients, seeking the shortest possible path to their data, reroute to the new, centrally located server. This sudden shift in demand can easily overwhelm the new server, leading to delays that affect not just those connected to it but potentially reverberating across the entire network.

What was intended as an enhancement ends up complicating the system further.

Let's try this in a shopping mall. Picture a three-storey shop. The first floor has the fewest items but houses all the checkout counters. The third floor is where you'll find the most shoppers. In an effort to ease congestion and enhance the shopping experience, the owner introduces a new checkout counter on the third floor. Does it solve the problem?

Old Arrangement vs New Arrangement

It might seem like a smart move. But soon, as word spreads among third-floor shoppers about the new counter, it becomes overwhelmed. Despite intentions to streamline checkouts, the counter quickly gets too crowded, leading to longer wait times. Some shoppers might opt to head back to the first floor to avoid the crowd, but the overall effect is a more congested third floor, making the situation there even less efficient than before.

Analogy in Physical Systems

Physics shows us similar paradoxes. Take springs, for example. Imagine a setup with two springs and three ropes. When you cut the red rope linking the springs, the weight unexpectedly moves up, not down. Why? It's about the shift from series to parallel.

In series, the two springs stretch twice as much as one would alone, bearing the full weight together. Cutting the red rope switches them to parallel, where each spring supports only half the weight. This shows how restructuring by removing support elements can actually improve the situation.

For a deeper dive into how this works with electric currents, check out this link.

Nature's Flow

Is it possible that the dynamics we see in traffic and networks also play out in nature? Consider the concept of traffic flow applied to an ecosystem's food web. Picture a system with six species labeled A through F, organized in two linear chains: C eats B, which eats A, and separately, F eats E, who eats D. This setup represents a balanced, stable ecosystem where each species has a clear role and source of sustenance.

Now, introduce a twist: a new species, G, that creates a bridge by eating B and being eaten by E. This insertion might seem minor but has profound implications. G hunts B more effectively than C did, disrupting C's food supply. Simultaneously, G becomes a preferred prey for E over D, sidelining it, who relied on E not just as food but also as a partner in ecological processes like seed dispersal. E's inability to consume D and fulfil this ecological role due to G's interference illustrates a cascading effect through the food web, causing significant disruptions for both C and D.

This example, though simplified, hints at the intricate and often unpredictable interactions within natural ecosystems. The introduction of a new species can trigger a series of chain reactions, reshaping relationships and dependencies. For a more in-depth exploration of such complex interactions in nature, have a look here.

And what did we learn…

Whether it's drivers choosing a new road, clients connecting to a server, shoppers flocking to a new checkout counter, or species within a food web, the introduction of a new element can disrupt the balance, leading to unforeseen consequences.

These insights challenge us to think critically about solutions to congestion and efficiency problems, reminding us that sometimes, less can indeed be more, and the best solution might involve simplification rather than addition.

That's all for this week, see you again with a new topic next week. Till then you can read how removing six-lane highway in Seoul, South Korea improved the traffic flow.