Simplex Algorithm

TypeScript implementation of the Simplex algorithm for linear programming optimization.

Structure

type Table = {
    header: string[],
    rows: TableRow[],
    z_row: number[]
}

Usage

const problem: Table = {
    header: ["x1", "x2", "x3", "x4", "x5", "b"],
    rows: [
        { basic_var: "x3", coefficients: [5, 3, 1, 0, 0, 30] },
        { basic_var: "x4", coefficients: [2, 3, 0, 1, 0, 24] },
        { basic_var: "x5", coefficients: [1, 3, 0, 0, 1, 18] }
    ],
    z_row: [-8, -6, 0, 0, 0, 0]
}
const solution = solve_simplex(problem);

Algorithm

1. Find entering variable (most negative in z-row)
2. Minimum ratio test → leaving variable
3. Pivot and normalize
4. Repeat until optimal

Functions

• verify_z_negative() / verify_z_positive() - Select entering variable
• verify_row_and_perform_header_swap() - Minimum ratio test
• compute_row_reduction() - Gauss-Jordan elimination
• solve_simplex() - Main solver

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M/M/s Queue (Erlang-C)

TypeScript implementation for capacity planning and server sizing. Useful to determine needs for load balancers during high frequency trading.

Structure

interface QueueMetrics {
  lambda: number;  // arrival rate (transactions/hour)
  mu: number;      // service rate per server (transactions/hour)
  s: number;       // number of servers
}

Usage

// Example: 1200 trades/hour, 3 seconds per trade, 2 workers
const lambda = 1200;
const mu = 1200;  // 1/(3/3600) transactions/hour per server
const s = 2;

const rho = compute_utilization(lambda, mu, s);  // 0.5
const decision = should_scale(lambda, mu, s);

Algorithm

1. Calculate ρ = λ / (s × μ)
2. If ρ > 0.7 → add servers
3. If ρ < 0.3 → remove servers
4. Target: 0.5 ≤ ρ ≤ 0.7

Functions

• compute_utilization() - Calculate ρ
• should_scale() - Auto-scaling decision
• factorial() - Helper for Erlang-C