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Simulation Examples

Monte Carlo and discrete event simulation patterns in pure Java 17+.

Contents

Class Pattern Key Concepts
MonteCarloSimulation Monte Carlo method Parallel streams, Welford's online variance, confidence intervals, option pricing
DiscreteEventSimulation Discrete Event Simulation Priority-queue event loop, M/M/1 queuing model, exponential distributions

Monte Carlo Simulation

A generic engine that runs N independent stochastic trials and aggregates results using Welford's online algorithm for numerically stable mean/variance computation.

Examples included

  • Pi estimation — random points in the unit square; ratio inside the unit circle converges to π/4
  • European call option pricing — geometric Brownian motion with discounted payoff (Black-Scholes Monte Carlo)
// Estimate Pi with 2M parallel trials
var result = MonteCarloSimulation.run(2_000_000, true, MonteCarloSimulation::piTrial);
System.out.printf("Pi ≈ %.6f (95%% CI: ±%.6f)%n",
        result.mean(), result.confidenceInterval95());

// Price a European call option
var trial = MonteCarloSimulation.europeanCallTrial(
        100,   // spot price
        105,   // strike
        0.05,  // risk-free rate
        0.2,   // volatility
        1.0    // time to expiry (years)
);
var price = MonteCarloSimulation.run(1_000_000, true, trial);

Design decisions

  • DoubleSupplier as the trial interface — composable, works with lambdas and method references
  • ThreadLocalRandom for thread-safe parallel execution without contention
  • Single-pass Welford's algorithm avoids storing all trial results in memory

Discrete Event Simulation

A priority-queue-based DES engine where events are (time, name, action) tuples processed in chronological order.

M/M/1 Queue example

Models a single-server queue with Poisson arrivals (rate λ) and exponential service times (rate μ):

var sim = new DiscreteEventSimulation();
var queue = new DiscreteEventSimulation.MM1Queue(sim, 0.8, 1.0); // λ=0.8, μ=1.0
queue.scheduleArrival(0.0);
sim.runUntil(100_000);
queue.printStats();

Outputs server utilization, average system time, and max queue length — values converge to the theoretical M/M/1 results as simulation time increases.

Extending the engine

Schedule custom events by providing a time and a Runnable:

var sim = new DiscreteEventSimulation();
sim.schedule(0.0, "init", () -> {
    System.out.println("Simulation started at t=" + sim.clock());
    sim.scheduleDelay(5.0, "check", () ->
        System.out.println("Checkpoint at t=" + sim.clock()));
});
sim.runUntil(100);

How to Run

# From project root
./mvnw -pl examples/simulation compile

# Run Monte Carlo demo
./mvnw -pl examples/simulation exec:java -Dexec.mainClass=com.example.template.simulation.MonteCarloSimulation

# Run DES demo
./mvnw -pl examples/simulation exec:java -Dexec.mainClass=com.example.template.simulation.DiscreteEventSimulation

When to Use Each Approach

Technique Best For Not Ideal For
Monte Carlo Estimating expected values, risk analysis, integration Deterministic problems, real-time systems
Discrete Event Simulation Queuing systems, process modeling, resource allocation Continuous dynamics (use ODE solvers instead)

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