Mexico National Team — FIFA World Cup 2026
FIFA World Cup 2026 · Ticket Queue Simulation · IE 4510

When millions queue, data decides who waits.

A discrete-event simulation of the FIFA World Cup 2026 ticketing platform — modeling the exact moment millions of fans flood the site simultaneously. Six scenarios. Live queue dynamics. Real decisions.

Open Dashboard ↗ Run the Model
Scroll
NHPP Arrival Model Non-homogeneous Poisson
6 Scenarios Baseline + 5 strategies
30+ Replications Monte Carlo · Student-t CI
95% Confidence Student-t intervals, df=n−1
Six strategies · Live model

Real scenarios.
Real consequences.

Each scenario models a different server and inventory allocation strategy. Click any card to jump directly to the simulator with that configuration loaded.

Ready to run the model?
Adjust parameters, choose a scenario, and see queue dynamics live.
Open Dashboard ↗
WC 2026 · 48 Nations
Live System · Fan Flow Network

Every fan
is a particle.

Watch queue dynamics unfold in real time. Each particle traces the exact path a fan takes — arriving, waiting, buying, balking, or reneging — weighted by live simulation probabilities.

Balk Renege Success Sellout
Increase Peak λ and watch red (balk) particles surge — the queue overwhelms arrivals before they can even join.
Live Dashboard

Simulation control room

Adjust parameters, run replications, and watch every metric update in real time. Each run streams results so you can observe the Law of Large Numbers.

Ready · 0 reps
ServersMaps to simpy.Resource(capacity=n). Higher values reduce renege rate but accelerate inventory depletion because throughput rises. 10
Peak λ /minMax NHPP arrival rate at t=0. Decays as λ(t)=λ_max·e^{-αt}. Represents how many fans hit the platform the instant tickets go live. 200
Patience (min)Mean of the Exponential patience distribution. Each fan draws their own from Exp(1/μ). If wait exceeds patience → renege. 5
Balk queueMax visible queue length before new arrivals balk and never join. 120
Decay αExponential decay constant. Large α = demand spike fades fast. Small α = sustained high demand. 0.05
Reps 40
Success Rate
—
Fraction completing a purchase
What it means: Of every fan who tried, this fraction succeeded. Balks + reneges + sellouts all reduce it.
Avg Wait Time
—
Minutes in queue before server
What it means: Time between joining the queue and reaching a purchase slot. More servers reduces it.
Balk Rate
—
Left on arrival, never joined
What it means: Pre-queue failure. Staggered inventory is most effective at reducing this.
Renege Rate
—
Abandoned while waiting
What it means: In-queue failure. A race between the server request and an Exponential patience timer.
Monte Carlo Possibility Cloud
Each dot = one independent replication. Horizontal = avg wait, vertical = success rate. Crosshair marks the empirical mean. Cluster tightness = outcome predictability.
Reading it: Dots upper-left (low wait, high success) = best outcomes. Wide scatter = high variance = policy risk.
Monte Carlo · 30+ Replications

30 runs.
One truth.

Run the simulation 30 independent times. Each replication samples from the same distributions but produces a unique outcome. The cloud of possibilities is the only honest answer to a stochastic system.

Student-t · 95% Confidence

Certainty
lives in the
interval.

A single number is a guess. An interval is honest. If we ran 100 more batches, 95 would produce a mean inside the filled bar. That is what confidence actually means — not certainty, but calibrated doubt.

95% Confidence Intervals — Student-t, df=n−1
Dot = mean · filled bar = 95% CI · ghost bar = full observed range.
Success rate—
Avg wait (min)—
Balk rate—
Renege rate—
Half-width: — pp. Below ±3pp = publication-ready for policy comparison.
Output Distributions (KDE)
Smoothed probability density over all replications. IQR shaded.
Estimate Convergence (LLN)
Each point = batch mean. Watch lines stabilise as replications accumulate.
Law of Large Numbers · KDE

The law of
large
numbers.

Add replications and watch the estimates stabilize. The distribution smooths. The confidence interval tightens. This is the mathematical foundation every policy decision rests on — not faith, just convergence.

Interactive Model

Configure and
run the model

Wire to your FastAPI backend to execute the real SimPy model in Python. The frontend uses a validated approximation while offline.

Backend endpoint
POST http://localhost:8000/simulate
{"servers":10,"tickets":3000,
 "lMax":200,"alpha":0.05,
 "scenario":"baseline","nReps":30}
Simulation Parameters
● Complete · 30 replications
—
Success Rate
—
Avg Wait
—
Balk Rate
—
Renege Rate
All Scenarios

Cross-scenario comparison

Means across 30 replications. Student-t CI, df=29.

ScenarioServersAvg Wait95% CISuccessBalkRenegeSelloutVerdict
Baseline104.7 min[4.1–5.3]63%18%12%11 minReference
Staggered103.5 min[3.0–4.0]71%12%9%28 minBetter
Servers ×3302.8 min[2.4–3.2]74%15%7%9 minBetter
Servers ×5502.1 min[1.8–2.4]78%13%5%8 minBest Wait
Priority VIP102.6 min*[2.2–3.1]69%19%11%10 minFairness ↓
Hold-Release104.2 min[3.7–4.7]68%17%11%14 minFairness ↑

* VIP subset only. Regular fan wait under Priority is 5.8 min [5.2–6.4].