loom.py

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

# 1. Set up parameter ranges
# Global injection rate from 10k to 90k TPS
Lambdas = np.linspace(10000, 90000, 20)
# Service times from 5 us to 150 us
S_FJ = np.linspace(0.000005, 0.000150, 20)
S_IO = np.linspace(0.000005, 0.000150, 20)

# Create 3D grid
L, FJ, IO = np.meshgrid(Lambdas, S_FJ, S_IO)
L_flat, FJ_flat, IO_flat = L.flatten(), FJ.flatten(), IO.flatten()

# 2. System 1: 8 FJ + 8 EL pairs
lambda_pair = L_flat / 8.0
# Doubled for Req + Res signals
lambda_signal_pair = lambda_pair * 2 

rho_FJ = lambda_signal_pair * FJ_flat
rho_IO = lambda_signal_pair * IO_flat

P_idle_FJ = 1 - rho_FJ
P_idle_IO = 1 - rho_IO

ctx_sw_FJ_total = 8 * (lambda_signal_pair * P_idle_FJ)
ctx_sw_IO_total = 8 * (lambda_signal_pair * P_idle_IO)
total_CS_FJ_IO = ctx_sw_FJ_total + ctx_sw_IO_total

# 3. System 2: 16 Custom Scheduler instances
lambda_custom = L_flat / 16.0
# Doubled for Req + Res signals
lambda_signal_custom = lambda_custom * 2 

S_Custom = FJ_flat + IO_flat
rho_C = lambda_signal_custom * S_Custom

P_idle_C = 1 - rho_C

total_CS_Custom = 16 * (lambda_signal_custom * P_idle_C)

# 4. Masking to prevent queue buildup (rho < 0.9 for all queues)
mask = (rho_FJ < 0.9) & (rho_IO < 0.9) & (rho_C < 0.9)

# 5. Calculate the Ratio
ratio = total_CS_FJ_IO[mask] / total_CS_Custom[mask]

# 6. Plotting
fig = plt.figure(figsize=(10, 8))
ax = fig.add_subplot(111, projection='3d')

# Color 'c' is mapped to the ratio
scatter = ax.scatter(L_flat[mask], FJ_flat[mask] * 1e6, IO_flat[mask] * 1e6, 
                     c=ratio, cmap='viridis', alpha=0.8, marker='o')

cbar = fig.colorbar(scatter, ax=ax, shrink=0.5, aspect=5)
cbar.set_label('Ratio (FJ+IO Context Switches / Custom Context Switches)')

ax.set_xlabel('Global Injection Rate ($\Lambda$)')
ax.set_ylabel('FJ Service Time ($\mu s$)')
ax.set_zlabel('IO Service Time ($\mu s$)')
ax.set_title('Ratio of Total Context Switches\n(Traditional vs Custom)')

plt.tight_layout()

# Print the min and max to the console to prove it's a constant
print(f"Minimum Ratio calculated: {np.min(ratio)}")
print(f"Maximum Ratio calculated: {np.max(ratio)}")

plt.show()