simulator.rb

n_shards = 128
n_simulations = 1_000_000
processed_booted_for_minimum_two_per_shard = []

n_simulations.times do |i| # Number of simulations
  booted = 0
  booted_by_shard = [0] * n_shards
  done = [false] * n_shards
  done_count = 0

  until done_count == n_shards
    shard = rand(n_shards) # 'roll the die', or 'boot the process'
    booted += 1
    if (booted_by_shard[shard] += 1) >= 2 && !done[shard]
      done[shard] = true
      done_count += 1
    end
  end

  processed_booted_for_minimum_two_per_shard << booted
end

processed_booted_for_minimum_two_per_shard.sort!
booted = processed_booted_for_minimum_two_per_shard

puts "Max: #{booted.max}"
puts "Min: #{booted.min}"
puts "P50: #{booted[booted.size / 2]}"
puts "P99: #{booted[(booted.size / 100 * 99.0).to_i]}"
puts "P999: #{booted[(booted.size / 100 * 99.9).to_i]}"
puts "P9999: #{booted[(booted.size / 100 * 99.99).to_i]}"

# Max: 2829
# Min: 507
# P50: 939
# P99: 1532
# P999: 1849
# P9999: 2167