Bus Route Simulator

What you just saw

Even with identical buses, identical stops, and identical passenger arrival rates, buses end up bunched. Why? A bus running slightly late picks up more waiting passengers at each stop, which makes it later. A bus running slightly early finds fewer passengers and catches up. This positive feedback is fundamental to any headway-based transit system — and explains why real bus routes need active control (skip-stop, holding, short-turning) to stay on schedule.

The science behind it

The bus bunching phenomenon was formalized by Newell and Potts (1964) and has been studied continuously since. It is the archetypal example of why transit operations can't rely on static timetables alone. Modern agent-based transit models (MATSim, SUMO public transport) extend this with network topology, transfer penalties, and demand response — but the bunching dynamic on a single route is always the first thing they reproduce.

Try these experiments

1. 1. Under-supplied

   Settings: num_buses=2 passenger_arrival_rate=2

   What to look for: Massive wait times, buses overloaded, obvious bunching within one or two cycles.

2. 2. Well-supplied

   Settings: num_buses=6 passenger_arrival_rate=1

   What to look for: Stable headways, short waits. The bunching feedback is too weak to compound.

3. 3. Demand spike

   Settings: passenger_arrival_rate=4

   What to look for: Even a large fleet struggles; dwell times explode at high-demand stops.

from scirouter import SciRouter
client = SciRouter(api_key="sk-sci-...")
result = client.simulation.run(
    model="bus_route",
    params={"num_buses": 5, "bus_capacity": 40,
            "passenger_arrival_rate": 1.5},
    steps=3600, seed=42,
)
print(result.metrics["avg_wait_time"])