Queue Analysis
Gert Janssenswillen
2022-07-10
library(edeaR)
library(dplyr)
#>
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#>
#> filter, lag
#> The following objects are masked from 'package:base':
#>
#> intersect, setdiff, setequal, union
Calculate queueing times
The function calculate_queueing_times can be used to calculate for
each activity instance in the log when it was started, and since when it
was queued. (That is, each activity instance except the first one for
each case).
For example, for the sepsis event log
library(eventdataR)
calculate_queuing_times(sepsis) -> queuing_times
The result is the following:
queuing_times
#> # A tibble: 14,164 x 7
#> case_id activity activity_instance_id resource started
#> <chr> <fct> <chr> <fct> <dttm>
#> 1 XJ ER Triage 3835 C 2013-11-07 08:29:18
#> 2 XJ ER Sepsis Triage 3836 A 2013-11-07 08:37:32
#> 3 XJ CRP 3839 B 2013-11-07 08:51:00
#> 4 XJ LacticAcid 3837 B 2013-11-07 08:51:00
#> 5 XJ Leucocytes 3838 B 2013-11-07 08:51:00
#> 6 XJ IV Liquid 3840 A 2013-11-07 09:05:57
#> 7 XJ IV Antibiotics 3841 A 2013-11-07 10:05:58
#> 8 XJ Admission NC 3842 I 2013-11-07 11:11:34
#> 9 XJ Leucocytes 3843 B 2013-11-08 08:00:00
#> 10 I ER Triage 106 C 2013-11-09 09:34:28
#> # ... with 14,154 more rows, and 2 more variables: in_queue_since <dttm>,
#> # time_in_queue <drtn>
We can use the output to compare the times time in queue for
different activities, for example.
library(ggplot2)
#> Warning: package 'ggplot2' was built under R version 3.6.3
queuing_times %>%
ggplot(aes(activity, time_in_queue)) +
geom_boxplot()
#> Don't know how to automatically pick scale for object of type difftime. Defaulting to continuous.
Or between different resources:
queuing_times %>%
ggplot(aes(resource, time_in_queue)) +
geom_boxplot()
#> Don't know how to automatically pick scale for object of type difftime. Defaulting to continuous.
If we remove the “?” resource:
queuing_times %>%
filter(resource != "?") %>%
ggplot(aes(resource, time_in_queue)) +
geom_boxplot()
#> Don't know how to automatically pick scale for object of type difftime. Defaulting to continuous.
Calculate queue length
Based on the information about queuing times, we can also compute the
length of the queue. This can be done using the function
calculate_queue_length. For this, we need to decide at which time
interval we want to compute the length of the queue. For example, we can
compute the length of the queue for each day, each week, each month,
etc. The sepsis data covers approximately 1.5 years. Computing the queue
for each week will thus give us about 75 different observations.
queuing_times %>%
calculate_queuing_length(time_interval = "week")
#> # A tibble: 83 x 2
#> date queue_length
#> <date> <int>
#> 1 2013-11-07 0
#> 2 2013-11-14 5
#> 3 2013-11-21 11
#> 4 2013-11-28 15
#> 5 2013-12-05 17
#> 6 2013-12-12 19
#> 7 2013-12-19 21
#> 8 2013-12-26 27
#> 9 2014-01-02 32
#> 10 2014-01-09 36
#> # ... with 73 more rows
The first observation is the data above will always be the first
timestamp for which an event was recorded. At this point, the queue will
always be zero. The second observation is the queue length after one
week, etc. We can plot this data to see the evolution of the queue over
time.
queuing_times %>%
calculate_queuing_length(time_interval = "week") %>%
ggplot(aes(date, queue_length)) +
geom_line()
Of course, you need to be careful when interpreting both extremes of
this time range, because we only have complete cases. At the start of
the time range, the process is “building up” activity, and the queue
goes up. At the end of the time range, the last cases are being
finished, and the queue gradually empties. It takes some knowledge about
the data to decide on a time frame that is proper for analysis.
By resource or activity
The length of the queue shown above refers to all queued activity
instances in the process. We can also look at queue length by either
activity or by resource. This can be done by changing the level argument
in the calculation function.
queuing_times %>%
calculate_queuing_length(time_interval = "week", level = "resource")
#> # A tibble: 258 x 3
#> date resource queue_length
#> <date> <fct> <int>
#> 1 2013-11-14 ? 1
#> 2 2013-11-14 B 3
#> 3 2013-11-14 E 1
#> 4 2013-11-21 ? 4
#> 5 2013-11-21 B 6
#> 6 2013-11-21 E 1
#> 7 2013-11-28 ? 5
#> 8 2013-11-28 B 6
#> 9 2013-11-28 E 3
#> 10 2013-11-28 I 1
#> # ... with 248 more rows
queuing_times %>%
calculate_queuing_length(time_interval = "week", level = "activity")
#> # A tibble: 340 x 3
#> date activity queue_length
#> <date> <fct> <int>
#> 1 2013-11-14 CRP 3
#> 2 2013-11-14 Release A 1
#> 3 2013-11-14 Return ER 1
#> 4 2013-11-21 CRP 5
#> 5 2013-11-21 Leucocytes 1
#> 6 2013-11-21 Release A 1
#> 7 2013-11-21 Return ER 4
#> 8 2013-11-28 Admission NC 1
#> 9 2013-11-28 CRP 5
#> 10 2013-11-28 Leucocytes 1
#> # ... with 330 more rows
Again, these can be plotted conveniently (we ignore the unknown
resource):
queuing_times %>%
filter(resource != "?") %>%
calculate_queuing_length(time_interval = "week", level = "resource") %>%
ggplot(aes(date, queue_length, color = resource)) +
geom_line()
The impact of the time interval
If we increase the time interval, the queue length is calculated
after longer periods of time, so the data becomes more sparse. For
example, calculating after a month instead of a week:
queuing_times %>%
filter(resource != "?") %>%
calculate_queuing_length(time_interval = "month", level = "resource") %>%
ggplot(aes(date, queue_length, color = resource)) +
geom_line()
We can set it to a integer number to indicate an interval of x days.
For example, every 3 days:
queuing_times %>%
filter(resource != "?") %>%
calculate_queuing_length(time_interval = 3, level = "resource") %>%
ggplot(aes(date, queue_length, color = resource)) +
geom_line()
The time interval should be chosen carefully. Note that a very small
interval (the smallest possible is “day”) can be computationally
expensive if your event log covers a long time period.