Implementing a D/M/1 Queue in Ciw

Introduction

Ciw is a Python package for simulating queueing networks.

Simulation

A D/M/1 queue can be implemented and simulated using Ciw in the following way.

import ciw

ciw.seed(2018)

ARRIVAL_TIME = 1
SERVICE_TIME = 1 / 2
HORIZON = 365

network = ciw.create_network(
    arrival_distributions = [ciw.dists.Deterministic(ARRIVAL_TIME)],
    service_distributions = [ciw.dists.Exponential(SERVICE_TIME)],
    number_of_servers = [1]
    )

simulation = ciw.Simulation(network)
simulation.simulate_until_max_time(HORIZON)
records = simulation.get_all_records()

Results

We can tabulate the results.

from IPython.display import Markdown, display
import pandas as pd
records = pd.DataFrame(records)
display(
    Markdown(
        records
        [['waiting_time', 'service_time', 'queue_size_at_arrival', 'queue_size_at_departure']]
        .describe()
        .to_markdown()
        )
    )

	waiting_time	service_time	queue_size_at_arrival	queue_size_at_departure
count	183	183	183	183
mean	71.9111	1.96964	36.8087	73.3607
std	51.243	1.8815	25.7219	51.6083
min	0	0.0229044	0	0
25%	19.1338	0.676208	13.5	20
50%	75.1552	1.28472	34	76
75%	111.045	2.53828	61	112
max	175.985	9.49261	80	179

We can plot the arrival times against the waiting times.

records.plot(x='arrival_date', y='waiting_time')

We can plot the service start times against the service times.

records.plot(x='service_start_date', y='service_time')

We can plot the arrival dates against the length of the queue when the customer arrived.

records.plot(x='arrival_date', y='queue_size_at_arrival')

We can plot the departure dates against the length of the queue when the customer departed.

records.plot(x='exit_date', y='queue_size_at_departure')