M/M/1 Queue Simulation Server

""" Metrics calculation and comparison utilities """ from typing import Dict, Tuple import numpy as np def calculate_error(simulated: float, theoretical: float) -> Tuple[float, float]: """ Calculate absolute and relative error between simulated and theoretical values Args: simulated: Simulated value theoretical: Theoretical value Returns: Tuple of (absolute_error, relative_error_percentage) """ absolute_error = abs(simulated - theoretical) relative_error = (absolute_error / abs(theoretical)) * 100 if theoretical != 0 else float('inf') return absolute_error, relative_error def compare_metrics(simulated_metrics: Dict[str, float], theoretical_metrics: Dict[str, float]) -> Dict[str, Dict[str, float]]: """ Compare simulated metrics with theoretical values Args: simulated_metrics: Dictionary of simulated metric values theoretical_metrics: Dictionary of theoretical metric values Returns: Dictionary with comparison results for each metric """ comparison = {} for key in simulated_metrics: if key in theoretical_metrics: sim_value = simulated_metrics[key] theo_value = theoretical_metrics[key] abs_err, rel_err = calculate_error(sim_value, theo_value) comparison[key] = { 'simulated': sim_value, 'theoretical': theo_value, 'absolute_error': abs_err, 'relative_error_pct': rel_err, 'acceptable': rel_err < 10.0 # 10% threshold } return comparison def calculate_confidence_interval(data: list, confidence: float = 0.95) -> Tuple[float, float, float]: """ Calculate confidence interval for a dataset Args: data: List of values confidence: Confidence level (default 0.95 for 95%) Returns: Tuple of (mean, lower_bound, upper_bound) """ if not data: return 0.0, 0.0, 0.0 mean = np.mean(data) std = np.std(data, ddof=1) n = len(data) # Calculate standard error se = std / np.sqrt(n) # Z-score for confidence level from scipy import stats z = stats.norm.ppf((1 + confidence) / 2) margin = z * se return mean, mean - margin, mean + margin