sim.py

import random

DEVICES = 32
WINDOW_US = 100
FIXED_ROUND_DELAY_SEC = 0.003

# Less than 8 is bad
WINDOWS = 8

print(f"{DEVICES} devices, {WINDOW_US}us per window, {FIXED_ROUND_DELAY_SEC * 1000}ms delay each round")
print("Time Slots, Average Rounds Taken, Average time taken (ms)")

while WINDOWS <= 1024:
    rounds_taken = []
    for x in range(4096):
        registered = 0
        rounds = 0


        while registered < DEVICES:
            rounds += 1
            slots = []
            collisions = []
            unique = []
            to_register = DEVICES - registered
            for i in range(to_register):
                slots.append(random.randrange(WINDOWS))

            # print(f"slots: {slots}")

            for i in slots:
                if i in collisions:
                    pass
                elif i in unique:
                    collisions.append(i)
                    while i in unique:
                        unique.remove(i)
                else:
                    unique.append(i)

            registered += len(unique)

            # print("Round ended.")
            # print(f"Registered: {len(unique)}")
            # print(f"Unique collisions: {len(collisions)}")
            # print(f"remaining: {DEVICES - registered}")

        # print(f"complete. Rounds: {rounds}")
        rounds_taken.append(rounds)

    avg_rounds = sum(rounds_taken)/len(rounds_taken)
    print(f"{WINDOWS}, {avg_rounds:0.03f}, {(((WINDOW_US / 1000000) * avg_rounds) + (avg_rounds * FIXED_ROUND_DELAY_SEC)) * 1000:0.03f}")
    WINDOWS *= 2

32 devices, 100us per window, 3.0ms delay each round
Time Slots, Average Rounds Taken, Average time taken (ms)
8, 23.432, 72.638
16, 6.638, 20.578
32, 3.773, 11.697
64, 2.707, 8.390
128, 2.152, 6.671
256, 1.893, 5.867
512, 1.626, 5.042
1024, 1.389, 4.307