Kind of city

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07:30

Everyone’s day. Pale blocks are what they are doing; solid bars are trips. Tap a trip to open it, or anywhere else to set the clock.

Nuvia is made up; its people are composites. Household types follow published figures (see “This kind of city”). Times and costs are illustrative. © 2026 The Moving Dot · CC BY 4.0Labs · 20 questions to ask your modeller

Nuvia · behind the day

The model

Fourteen parts. Lit ones you have found.

© 2026 The Moving Dot · CC BY 4.0Labs · 20 questions

Labs

Play with congestion

Four small live models behind the day in Nuvia.

Lab 1

One road: the last cars cost the most

Traffic doesn't slow down evenly. Far below capacity, extra cars barely matter. Near capacity, each extra car slows everyone.

0
your trip, 10 km
0
average speed
0
delay you add to everyone else

Understand

The curve is flat, then steep. That is why school holidays feel so different: take away five or ten percent of traffic from a road near capacity and the queue largely disappears.

It also explains the strangest number on the panel. When you join a busy road, you feel your own delay. You don't feel the delay you add to everyone behind you, and near capacity that hidden cost is larger than your own trip time saving from driving at all. Economists call this an externality. It is the core argument for road pricing.

For a decision: a scheme that removes a small share of traffic from a congested corridor can be worth far more than its traffic numbers suggest. A scheme that adds a small share can cost far more.

Mechanics

Most strategic models use a volume-delay function. The classic one, from the US Bureau of Public Roads in 1964, is what this panel runs:

t(v) = t₀ × (1 + α × (v / c)^β) t₀ = free-flow time (10 min for 10 km here) c = capacity (1,800 veh/h, one lane) α = 0.15, β = 4 (the textbook defaults)

The delay one more car adds to all others is v × dt/dv = t₀ × α × β × (v/c)^β. At capacity that is 6 vehicle-minutes, more than half of a free-flow trip.

Real models tune α and β by road type, and many use other curve shapes (Akçelik, conical). Choosing them is a quiet but important modelling decision: it sets how sharply the model punishes extra traffic.

Reflect

A model can tell you how slow a road gets. It cannot tell you whether that is acceptable. Congestion is a price paid in time instead of money, and it falls on whoever has no other option. Deciding how much of it a city should tolerate is a political choice, not a technical one. A good modeller makes that choice visible instead of hiding it inside a "do-minimum" scenario.

Lab 2

Two routes: everyone ends up waiting the same

Drivers keep switching routes until no one can save time by switching. Models call that point equilibrium, and it is what they search for.

Ring roadlonger, 3,000/h capacity
Through townshorter, 1,200/h capacity

Understand

Try to beat the drivers: set any split by hand and someone on the slower route can always do better by switching. Only one split is stable, where both routes take the same time. Real traffic finds that point by itself, through millions of small daily choices.

This is why you can't judge a scheme by looking at one road. Improve the town route and traffic moves onto it from the ring road until the times are equal again. The benefit spreads across the network, and so do the problems.

Mechanics

This is Wardrop's first principle (1952): at user equilibrium, all used routes between two places have equal and minimal travel time. Assignment software finds it by iterating: load the network, recompute times, shift some traffic to faster routes, repeat until the gap closes.

Wardrop also described a second state, the system optimum, where total travel time is lowest. Drivers don't reach it on their own, because each one ignores the delay they add to others (see the One road lab).

0
average time, drivers choose
0
average time, best for everyone
0
cost of everyone choosing alone

Reflect

Equilibrium is a convenient fiction. Real drivers don't know every route's time, and habits matter more than seconds. Yet it remains the backbone of nearly every strategic model, because the alternative is to say nothing about how a network responds. Knowing which simplifications a model makes, and when they stop being safe, is most of the craft.

Lab 3

The free shortcut that makes everyone slower

4,000 drivers go from S to E. We open a new link from A to B that takes no time at all. Before you press the button: will the average trip get faster or slower?

Your guess:
0
trip time without shortcut
?
trip time with shortcut
Make a guess, then open the shortcut.

Understand

The shortcut tempts every driver onto the two busy links, S to A and B to E, because each driver only sees their own saving. They all take it, so those links get congested, and everyone ends up slower than before. Nobody can do better by going back, so the bad outcome is stable.

Now move the number of drivers. The paradox only appears between 3,000 and 9,000 drivers. Below that the shortcut helps, above it it makes no difference. The same scheme can be good or bad depending on demand, which is exactly the kind of answer intuition can't give you and a model can.

This is not only theory. Closing roads has sometimes improved traffic, and road closures for events or works often cause less chaos than feared.

Mechanics

Link times: S→A and B→E take drivers/100 minutes; A→E and S→B take a fixed 45 minutes; A→B takes 0. Without the shortcut, drivers split evenly: 2,000/100 + 45 = 65 minutes. With it, the route S→A→B→E costs 40 + 0 + 40 = 80 minutes, and the old routes cost 40 + 45 = 85, so no one switches back.

Shortcut route alone: 2D/100 (for D ≤ 4,500) Old routes, no link: D/200 + 45 Paradox when 2D/100 > D/200 + 45 → D > 3,000

The panel solves it with path-based equilibrium assignment, the same family of methods that commercial software uses on networks with millions of links. Dietrich Braess described the effect in 1968.

Reflect

Intuition about networks is unreliable, including the intuition of experienced engineers. That is the strongest argument for modelling. It is also a reason for humility: a model's structure is itself an intuition, written in code, and it can be wrong in ways that are just as hard to see.

The Moving Dot view

A model result without the question it was built to answer is just a number. Start from the question; pick the simplest model that answers it.

Lab 4

Widen the road, and traffic grows into it

Faster journeys make travel more attractive. More people drive, at different times, to further places. Part of the time saving disappears.

0
today, 2 lanes
0
promised, same traffic
0
what you get
0
traffic growth

Understand

This is induced demand. A model that keeps traffic fixed will overstate the benefit of every road scheme, sometimes by a lot. In the UK, the 1994 SACTRA report made this official: appraisals must allow traffic to respond to the scheme.

It works both ways. Take capacity away, and some traffic disappears too: people change time, route, mode or destination, or don't travel.

For a decision: ask whether the model's demand responds to travel time and cost. If it doesn't, treat the time savings as an upper bound.

Mechanics

The panel finds the point where demand and travel time agree:

demand D = D₀ × (t / t_today)^(−e) time t = BPR(D / capacity) solve for t where both hold (e = elasticity)

Full models do this with a demand model (trip generation, destination and mode choice) looping with assignment until they converge. The size of the response depends on the time horizon: small in the first year, larger after people move house or change jobs. Try e = 0 to see the fixed-demand answer.

Reflect

For forty years, much of planning followed "predict and provide": forecast traffic, then build roads to carry it. Induced demand shows why that loop never closes. The newer approach, often called "vision and validate", starts from the place you want to be and uses models to test which paths get you there across several possible futures. The models are the same; the question you ask them is different.

Toolkit

Twenty questions to ask your modeller

Bring these to the inception meeting, the calibration review and the final presentation. A good modeller will be glad you asked.