Ciw is a Python package for simulating queueing networks.
Since G in M/G/1 can be any distribution with non-negative support, we will use a gamma distribution for the sake of example. A gamma distribution is the result of a sum of independent exponentially-distributed random variables, and thus for this example we have an interpretation that the servicing is implicitly a multi-step process where each step has an exponentially-distributed completion time.
An M/G/1 queue as described can be implemented and simulated using Ciw in the following way.
"""M/G/1 queue simulation logic."""
import ciw
def run_simulation(
arrival_time=1,
service_shape=6 / 10,
service_scale=12 / 10,
horizon=365,
seed=2018,
):
"""Run M/G/1 queue simulation and return simulation object and records."""
ciw.seed(seed)
network = ciw.create_network(
arrival_distributions=[ciw.dists.Exponential(arrival_time)],
service_distributions=[ciw.dists.Gamma(shape=service_shape, scale=service_scale)],
number_of_servers=[1],
)
simulation = ciw.Simulation(network)
simulation.simulate_until_max_time(horizon)
records = simulation.get_all_records()
return simulation, records
def main():
"""Main entry point for the simulation."""
_, records = run_simulation()
for record in records[:10]:
print(record)
if __name__ == "__main__":
main()