How to visualise queue wait time

Question

Suppose I have a process that works as follows:

• collect all outstanding requests
• process all of them, which takes time
• commit all results in one transaction
• repeat

I get a data point (start, duration) from each cycle:

00:00: 1h, 01:00: 1h, 02:00: 2h30m, 04:30: 2h, 06:30: 1h, 07:30: 1h

Below is the best I've come up with so far, boxes ;-)

It shows a "slow" batch @2:00 where:

• all users had to wait, 2h30min for their results
• this "sloweness" lasted just as long, 2h30min

I this visualisation good? Is there a canonical visualisation for time spent in queue?

How can I show multiple similar processes on same plot, e.g. requests from Germany (own process), France (-"-), UK (-"-)?

Answer 1

I'm sure that many plots could be beneficial. One of my favourites is to plot the waiting times against the arrival times. It can be quite diagnostic of what is happening.

For example, let's say my customers start reneging away from my service. I would expect to see the waiting times cap. Note that other effects could lead to capping, but it is a good start.

import ciw
import matplotlib.pyplot as plt
import pandas as pd

ciw.seed(2018)

N = ciw.create_network(
    arrival_distributions=[ciw.dists.Exponential(5)],
    service_distributions=[ciw.dists.Exponential(2)],
    number_of_servers=[1],
    reneging_time_distributions=[ciw.dists.Deterministic(5)]
)


Q = ciw.Simulation(N)
Q.simulate_until_max_time(30)
df = pd.DataFrame(
    Q.get_all_records()
    )

plt.scatter(df.arrival_date, df.waiting_time)
plt.xlabel('Arrival Time')
plt.ylabel('Waiting Time')
plt.show()

The same process without the reneging would just show the waiting times getting longer:

import ciw
import matplotlib.pyplot as plt
import pandas as pd

ciw.seed(2018)

N = ciw.create_network(
    arrival_distributions=[ciw.dists.Exponential(5)],
    service_distributions=[ciw.dists.Exponential(2)],
    number_of_servers=[1],
)


Q = ciw.Simulation(N)
Q.simulate_until_max_time(30)
df = pd.DataFrame(
    Q.get_all_records()
    )

plt.scatter(df.arrival_date, df.waiting_time)
plt.xlabel('Arrival Time')
plt.ylabel('Waiting Time')
plt.show()

Or maybe I am only 'just' meeting demand on average, leading to some random walk behaviour:

import ciw
import matplotlib.pyplot as plt
import pandas as pd

ciw.seed(2018)

N = ciw.create_network(
    arrival_distributions=[ciw.dists.Exponential(5)],
    service_distributions=[ciw.dists.Exponential(5)],
    number_of_servers=[1],
)


Q = ciw.Simulation(N)
Q.simulate_until_max_time(30)
df = pd.DataFrame(
    Q.get_all_records()
    )

plt.scatter(df.arrival_date, df.waiting_time)
plt.xlabel('Arrival Time')
plt.ylabel('Waiting Time')
plt.show()

Or maybe we've got substantially more supply than demand. Some customer don't even need to wait!

import ciw
import matplotlib.pyplot as plt
import pandas as pd

ciw.seed(2018)

N = ciw.create_network(
    arrival_distributions=[ciw.dists.Exponential(5)],
    service_distributions=[ciw.dists.Exponential(10)],
    number_of_servers=[1],
)


Q = ciw.Simulation(N)
Q.simulate_until_max_time(30)
df = pd.DataFrame(
    Q.get_all_records()
    )

plt.scatter(df.arrival_date, df.waiting_time)
plt.xlabel('Arrival Time')
plt.ylabel('Waiting Time')
plt.show()

To be clear, I'm not saying these plots are the end-all-be-all. They're just helpful in diagnosing system behaviour (in conjunction with other tools).