-
-
Notifications
You must be signed in to change notification settings - Fork 42
/
simmer-04-bank-2.Rmd
698 lines (555 loc) · 22.6 KB
/
simmer-04-bank-2.Rmd
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
---
title: "The Bank Tutorial: Part II"
author: "Duncan Garmonsway"
date: "`r Sys.Date()`"
output:
rmarkdown::html_vignette:
toc: yes
vignette: >
%\VignetteIndexEntry{04. The Bank Tutorial: Part II}
%\VignetteEngine{knitr::rmarkdown}
%\VignetteEncoding{UTF-8}
---
```{r, cache = FALSE, include=FALSE}
knitr::opts_chunk$set(collapse = T, comment = "#>",
fig.width = 6, fig.height = 4, fig.align = "center")
required <- c("simmer.plot")
if (!all(sapply(required, requireNamespace, quietly = TRUE)))
knitr::opts_chunk$set(eval = FALSE)
```
## Introduction
This tutorial is adapted from a tutorial for the Python 2 package 'SimPy',
[here](https://pythonhosted.org/SimPy/Tutorials/TheBank2.html). Users familiar
with SimPy may find this tutorial helpful for transitioning to `simmer`. Some
very basic material is not covered. Beginners should first read
[_The Bank Tutorial: Part I_](simmer-04-bank-1.html).
## Priority customers
In many situations there is a system of priority service. Those customers with
high priority are served first, those with low priority must wait. In some
cases, preemptive priority will even allow a high-priority customer to interrupt
the service of one with a lower priority.
Simmer implements priority requests with an extra integer priority argument to
`add_generator()`. By default, priority is zero; higher integers have higher
priority. For this to operate, the resource must have been created with
`preemptive = TRUE`.
### Priority customers without preemption
In the first example, we modify the program with random arrivals, one counter,
and a fixed service time (like _One Service counter_ in _The Bank Tutorial: Part
I_) to process a high priority customer.
Here, we give each customer a priority. Since the default is `priority = 0` this
is easy for most of them.
To observe the priority in action, while all other customers have the default
priority of 0, we create and activate one special customer, Guido, with priority
1 who arrives at time 23. This is to ensure that he arrives after Customer2.
Since the activity trace does not produce the waiting time by default, this is
calculated and appended using the `transform` function.
```{r, message = FALSE}
library(simmer)
set.seed(1933)
bank <- simmer()
customer <-
trajectory("Customer's path") %>%
set_attribute("start_time", function() {now(bank)}) %>%
log_(function() {
paste("Queue is", get_queue_count(bank, "counter"), "on arrival")
}) %>%
seize("counter") %>%
log_(function() {paste("Waited", now(bank) - get_attribute(bank, "start_time"))}) %>%
timeout(12) %>%
release("counter") %>%
log_("Completed")
bank <-
simmer("bank") %>%
add_resource("counter") %>%
add_generator("Customer", customer, function() {c(0, rexp(4, 1/10), -1)}) %>%
add_generator("Guido", customer, at(23), priority = 1)
bank %>% run(until = 400)
bank %>%
get_mon_arrivals() %>%
transform(waiting_time = end_time - start_time - activity_time)
```
The output above displays the number of customers in the queue just as each one
arrives. That count does not include any customer in service.
Reading carefully one can see that when Guido arrives Customer0 has been served
and left at 12, Customer1 is in service and two (customers 2 and 3) are
queueing. Guido has priority over those waiting and is served before them at 24.
When Guido leaves at 36, Customer2 starts service.
### Priority customers with preemption
Now we allow Guido to have preemptive priority. He will displace any customer in
service when he arrives. That customer will resume when Guido finishes (unless
higher priority customers intervene). It requires only a change to one line of
the program, adding the argument, `preemptive = TRUE` to the `add_resource`
function call.
```{r, message = FALSE}
library(simmer)
set.seed(1933)
bank <- simmer()
customer <-
trajectory("Customer's path") %>%
set_attribute("start_time", function() {now(bank)}) %>%
log_(function() {
paste("Queue is", get_queue_count(bank, "counter"), "on arrival")
}) %>%
seize("counter") %>%
log_(function() {paste("Waited", now(bank) - get_attribute(bank, "start_time"))}) %>%
timeout(12) %>%
release("counter") %>%
log_("Completed")
bank <-
simmer("bank") %>%
add_resource("counter", preemptive = TRUE) %>%
add_generator("Customer", customer, function() {c(0, rexp(4, 1/10), -1)}) %>%
add_generator("Guido", customer, at(23), priority = 1)
bank %>% run(until = 400)
bank %>%
get_mon_arrivals() %>%
transform(waiting_time = end_time - start_time - activity_time)
```
Though Guido arrives at the same time, 23, he no longer has to wait and
immediately goes into service, displacing the incumbent, Customer1. That
customer had already completed 23 - 12 = 11 minutes of his service. When Guido
finishes at 35, Customer1 resumes service and takes 36 - 35 = 1 minutes to
finish. His total service time is the same as before (12 minutes).
## Balking and reneging customers
Balking occurs when a customer refuses to join a queue if it is too long.
Reneging (or, better, abandonment) occurs if an impatient customer gives up
while still waiting and before being served.
### Balking customers
Another term for a system with balking customers is one where “blocked
customers” are “cleared”, termed by engineers a BCC system. This is very
convenient analytically in queueing theory and formulae developed using this
assumption are used extensively for planning communication systems. The easiest
case is when no queueing is allowed.
As an example let us investigate a BCC system with a single server but the
waiting space is limited. We will estimate the rate of balking when the maximum
number in the queue is set to 1. On arrival into the system the customer must
first check to see if there is room. If there is not enough room, the customer
balks.
To get the balking rate, we first count the number of arrivals that didn't
finish, using the data given by `get_mon_arrivals()`. Then we divide it by the
current model time from `now(bank)`.
```{r}
library(simmer)
timeInBank <- 12 # mean, minutes
ARRint <- 10 # mean, minutes
numServers <- 1 # servers
maxInSystem <- 2 # customers
maxInQueue <- maxInSystem - numServers
maxNumber <- 8
maxTime <- 400 # minutes
set.seed(59098)
bank <- simmer()
customer <-
trajectory("Customer's path") %>%
log_("Here I am") %>%
set_attribute("start_time", function() {now(bank)}) %>%
seize("counter",
continue = FALSE,
reject =
trajectory("Balked customer") %>%
log_("BALKING")) %>%
log_(function() {paste("Waited", now(bank) - get_attribute(bank, "start_time"))}) %>%
timeout(function() {rexp(1, 1/timeInBank)}) %>%
release("counter") %>%
log_("Finished")
bank <-
simmer("bank") %>%
add_resource("counter",
capacity = numServers,
queue_size = maxInQueue) %>%
add_generator("Customer",
customer,
at(c(0, cumsum(rexp(maxNumber - 1, 1 / ARRint)))))
bank %>% run(until = maxTime)
number_balked <- sum(!get_mon_arrivals(bank)$finished)
paste("Balking rate is", number_balked / now(bank), "customers per minute.")
```
When Customer2 arrives, Customer0 is already in service and Customer1 is
waiting. There is no room, so Customer2 balks. By the vagaries of exponential
random numbers, Customer0 takes a very long time to serve (22.7358 minutes) so
the first one to find room is number Customer6 at 25.5339.
### Reneging (or abandoning) customers
Often in practice an impatient customer will leave the queue before being
served. Simmer can model this reneging behaviour using the `renege_in()`
function in a trajectory. This defines the maximum time that a customer will
wait before reneging, as well as an 'out' trajectory for them to follow when
they renege.
If the customer reaches the server before reneging, then their impatience must
be cancelled with the `renege_abort()` function.
```{r, message = FALSE}
library(simmer)
timeInBank <- 15 # mean, minutes
ARRint <- 10 # mean, minutes
numServers <- 1 # servers
maxNumber <- 5
maxTime <- 400 # minutes
maxWaitTime <- 12 # minutes, maximum time to wait before reneging
set.seed(59030)
bank <- simmer()
customer <-
trajectory("Customer's path") %>%
log_("Here I am") %>%
set_attribute("start_time", function() {now(bank)}) %>%
renege_in(maxWaitTime,
out = trajectory("Reneging customer") %>%
log_(function() {
paste("Waited", now(bank) - get_attribute(bank, "start_time"), "I am off")
})) %>%
seize("counter") %>%
renege_abort() %>% # Stay if I'm being attended within maxWaitTime
log_(function() {paste("Waited", now(bank) - get_attribute(bank, "start_time"))}) %>%
timeout(function() {rexp(1, 1/timeInBank)}) %>%
release("counter") %>%
log_("Completed")
bank <-
simmer("bank") %>%
add_resource("counter",
capacity = numServers) %>%
add_generator("Customer",
customer,
at(c(0, cumsum(rexp(maxNumber - 1, 1 / ARRint)))))
bank %>% run(until = maxTime)
```
Customer1 arrives after Customer0 but has only 12 minutes patience. After that
time in the queue (at time 28.5058) he abandons the queue to leave Customer2 to
take his place. Customer2 and Customer3 also renege. Customer4 is served within
12 minutes.
## Interrupting a process
Klaus goes into the bank to talk to the manager. For clarity we ignore the
counters and other customers. During his conversation his cellphone rings. When
he finishes the call he continues the conversation.
In this example, the call is another trajectory, whose only activities are to
send a signal (the ringing of the phone), and to write that event to the log.
In Klaus' trajectory, the `trap` activity causes him to listen for the phone to
ring. Supposing the phone doesn't ring, then his trajectory would continue to
the `timeout` activity, where he would do his banking business for 20 minutes,
and then finish.
Supposing the phone _does_ ring, then Klaus would enter the sub-trajectory
defined within the `trap` function as a 'handler'. In that trajectory, he makes
his excuses, answers the phone, then returns to business. At the end of the
trajectory, he continues the original trajectory at the next step _following_
the original `timeout`, without spending the rest of the 20 minutes on his
banking.
To make Klaus spend a full 20 minutes banking, we add a `timeout` activity to
the end of the 'handler', but first we have to calculate how much time remains
after the interruption. This is done by storing the 'start' time in an
attribute, and calculating how much time is left when the phone rings.
By default, interruptions can themselves be interrupted, as illustrated in this
example by the phone ringing twice. This could be avoided by setting
`interruptible = FALSE` in the `trap` activity.
```{r, message = FALSE}
library(simmer)
timeInBank <- 20
timeOfCall <- 9
onphone <- 3
maxTime <- 100
bank <- simmer()
customer <-
trajectory("Customer's path") %>%
trap("phonecall",
handler = trajectory() %>%
log_("Excuse me") %>%
set_attribute(
"timeleft", function() {
sum(get_attribute(bank, c("timeleft", "start"))) - now(bank)
}) %>%
log_("Hello! I'll call back") %>%
timeout(onphone) %>%
log_("Sorry, where were we?") %>%
set_attribute("start", function() {now(bank)}) %>%
log_(function() {paste("Time left:", get_attribute(bank, "timeleft"))}) %>%
timeout_from_attribute("timeleft")
) %>%
log_("Here I am") %>%
set_attribute("timeleft", timeInBank) %>%
set_attribute("start", function() {now(bank)}) %>%
timeout(timeInBank) %>%
log_("Completed")
phone <-
trajectory("Phone") %>%
log_("Ringgg!") %>%
send("phonecall")
bank <-
simmer("bank") %>%
add_generator("Klaus", customer, at(0)) %>%
add_generator("Phone", phone, at(timeOfCall, timeOfCall + 7))
bank %>% run(until = maxTime)
```
As this has no random numbers the results are reasonably clear: the first
interrupting call occurs at 9. It takes Klaus 3 minutes to listen to the message
and he resumes the conversation with the bank manager at 12. The phone rings
again at 16, he listens for three more minutes, and resumes the conversation at
19, finally finishing at 26. The total time of conversation is 9 + 4 + 7 = 20
minutes, the same as it would have been if the interrupt had not occurred.
## Wait until the bank door opens
Customers arrive at random, some of them getting to the bank before the door is
opened by a doorman. They wait for the door to be opened and then rush in and
queue to be served.
This model defines the door as a resource, just like the counter. The capacity
of the door is defined according to the `schedule` function, so that it has zero
capacity when it is shut, and infinite capacity when it is open. Customers
'seize' the door and must then wait until it has capacity to 'serve' them. Once
it is available, all waiting customers are 'served' immediately (i.e. they pass
through the door). There is no `timeout` between 'seizing' and 'releasing' the
door.
For the sake of announcing in the log that the door has been opened, a doorman
trajectory is defined.
```{r, message = FALSE}
library(simmer)
maxTime = 400
set.seed(393937)
bank <- simmer()
customer <-
trajectory("Customer's path") %>%
log_(function()
if (get_capacity(bank, "door") == 0)
"Here I am but the door is shut."
else "Here I am and the door is open."
) %>%
seize("door") %>%
log_("I can go in!") %>%
release("door") %>%
seize("counter") %>%
timeout(function() {rexp(1, 1/10)}) %>%
release("counter")
openTime <- rexp(1, 1/10)
door_schedule <- schedule(c(0, openTime), c(0, Inf))
doorman <-
trajectory() %>%
timeout(openTime) %>%
log_("Ladies and Gentlemen! You may all enter.")
bank <-
simmer("bank") %>%
add_resource("door", capacity = door_schedule) %>%
add_resource("counter") %>%
add_generator("Customer",
customer,
at(c(0, cumsum(rexp(5 - 1, 0.1))))) %>%
add_generator("Doorman", doorman, at(0))
bank %>% run(until = maxTime)
bank %>%
get_mon_arrivals() %>%
transform(waiting_time = end_time - start_time - activity_time)
```
The output above programs shows how the first two customers have to wait until
the door is opened.
# Wait for the doorman to give a signal
Customers arrive at random, some of them getting to the bank before the door is
open. This is controlled by an automatic machine called the doorman which opens
the door only at intervals of 30 minutes (it is a very secure bank). The
customers wait for the door to be opened and all those waiting enter and proceed
to the counter. The door is closed behind them.
There are at least two ways to implement this model. The first example uses a
schedule, and the second uses batching.
The principle behind the schedule is that the door is modelled as a server with
zero capacity for 30 minutes, then infinite capacity for zero minutes, then
repeat the 30-minute cycle. In the moment that it has infinite capacity, all
the customers will pass through the door (i.e. they will be 'served').
For the sake of announcing in the log that the door has been opened, a doorman
trajectory is defined. The doorman has a `rollback` step so that it keeps
opening and shutting the door every 30 minutes for ever.
```{r, message = FALSE}
library(simmer)
maxTime = 150
customer <-
trajectory("Customer's path") %>%
log_("Here I am, but the door is shut.") %>%
set_attribute("start_time", function() {now(bank)}) %>%
seize("door") %>%
log_("The door is open!") %>%
log_(function() {paste("Waited", now(bank) - get_attribute(bank, "start_time"))}) %>%
release("door") %>%
seize("counter") %>%
timeout(function() {rexp(1, 1/10)}) %>%
release("counter") %>%
log_("Finished.")
door_schedule <- schedule(c(30, 30), c(Inf, 0), period = 30)
doorman <-
trajectory("Doorman") %>%
timeout(30) %>%
log_("You may enter.") %>%
rollback(2, times = Inf)
set.seed(393939)
bank <- simmer("bank")
bank %>%
add_resource("door", capacity = door_schedule) %>%
add_resource("counter") %>%
add_generator("Customer",
customer,
at(c(0, cumsum(rexp(5 - 1, 0.1))))) %>%
add_generator("Doorman", doorman, at(0))
bank %>% run(until = maxTime)
bank %>%
get_mon_arrivals() %>%
transform(waiting_time = end_time - start_time - activity_time)
```
The output run for this program shows how the first two customers have to wait
until the door is opened, and then the next three have to wait.
The second method is batching. Customers can be collected into batches of a
given size, or for a given time, or whichever occurs first. Here, they are
collected for periods of 30, and the number of customers in each batch is
unrestricted.
After the batch is created with `batch`, usually the customers will all be
processed together by a server, before separating with `separate`. In this
example, there is no need for a server -- the door is modelled by the batch
itself -- so the customers are separated immediately after the batch.
```{r, message = FALSE}
library(simmer)
maxTime = 150
customer <-
trajectory("Customer's path") %>%
log_("Here I am, but the door is shut.") %>%
set_attribute("start_time", function() {now(bank)}) %>%
batch(n = Inf, timeout = 30) %>%
separate() %>%
log_("The door is open!") %>%
log_(function() {paste("Waited", now(bank) - get_attribute(bank, "start_time"))}) %>%
seize("counter") %>%
timeout(function() {rexp(1, 1/10)}) %>%
release("counter") %>%
log_("Finished.")
doorman <-
trajectory("Doorman") %>%
timeout(30) %>%
log_("You may enter.") %>%
rollback(2, times = Inf)
set.seed(393939)
bank <- simmer("bank")
bank %>%
add_resource("door") %>%
add_resource("counter") %>%
add_generator("Customer",
customer,
at(c(0, cumsum(rexp(5 - 1, 0.1))))) %>%
add_generator("Doorman", doorman, at(0))
bank %>% run(until = maxTime)
bank %>%
get_mon_arrivals() %>%
transform(waiting_time = end_time - start_time - activity_time)
```
This second method gives the same output as the first.
## Monitors
Monitors record events in a simulation. Unlike SimPy, Simmer does this by
default, so the records are available after -- in fact, even during -- a
simulation. Data that is collected by monitors is available from the following
functions:
```{r, eval = FALSE}
get_capacity
get_mon_arrivals
get_mon_attributes
get_mon_resources
get_n_activities
get_n_generated
get_queue_count
get_queue_size
get_server_count
```
The `get_mon_*()` functions return a data frame (which is growing during the
simulation, so that, although possible, it is computationally expensive to call
them from inside a trajectory). The others return a numeric value.
### Plotting a histogram of monitor results
A histogram of the amount of time that customers spend in the
bank can be plotted by taking some basic information -- start and end time of
each customer -- from the `get_mon_arrivals()` function, and then calculating
the elapsed time. This example draws the plot with the `ggplot2` package, but
other plotting packages, and base R graphics, could do something similar.
```{r}
library(simmer)
library(simmer.plot)
# library(ggplot2) # (automatically loaded with simmer.plot)
bank <- simmer()
customer <-
trajectory("Customer's path") %>%
seize("counter") %>%
timeout(12) %>%
release("counter")
set.seed(393939)
bank <-
simmer("bank") %>%
add_resource("counter") %>%
add_generator("Customer",
customer,
at(c(0, cumsum(rexp(20 - 1, 0.1)))))
bank %>% run(400)
bank %>%
get_mon_arrivals %>%
ggplot(aes(end_time - start_time)) +
geom_histogram() +
xlab("Time spent in the system") +
ylab("Number of customers")
```
### Monitoring a resource
Now consider observing the number of customers waiting or active in a Resource.
`get_mon_resources()` returns a table of states and times for the counter.
Whenever a customer enters/leaves a queue/counter, a new row is created
recording the number of customers in the queue, the counter and the system as a
whole. We call this the 'state'. The amount of time that the state lasts is
the difference in time between one state and the next, which we calculate with
the `diff()` function. Finally, we multiply the number of customers in each
state by the duration of the state, and divide by the duration of the simulation
(the time at the end) to get the average.
```{r, message = FALSE}
library(simmer)
set.seed(1234)
bank <- simmer()
customer <-
trajectory("Customer's path") %>%
log_("Arrived") %>%
set_attribute("start_time", function() {now(bank)}) %>%
seize("counter") %>%
log_("Got counter") %>%
log_(function() {paste("Waited", now(bank) - get_attribute(bank, "start_time"))}) %>%
timeout(12) %>%
release("counter") %>%
log_("Finished")
bank <-
simmer("bank") %>%
add_resource("counter") %>%
add_generator("Customer", customer, function() {c(0, rexp(4, 1/10), -1)})
bank %>% run(until = 400)
customer_monitor <-
get_mon_arrivals(bank) %>%
transform(wait = end_time - start_time - activity_time)
mean_waiting_time <- mean(customer_monitor$wait)
resource_monitor <- get_mon_resources(bank)
queue_state <- head(resource_monitor$queue, -1)
server_state <- head(resource_monitor$server, -1)
time_state_lasted <- diff(resource_monitor$time)
time_at_end <- max(resource_monitor$time)
mean_active_customers <- sum(server_state * time_state_lasted) / time_at_end
mean_waiting_customers <- sum(queue_state * time_state_lasted) / time_at_end
cat(" Average waiting = ", mean_waiting_customers, "\n",
"Average active = ", mean_active_customers, "\n")
```
### Plotting from resource monitors
All the `get_mon_*()` return information that enables us to graph the output.
Alternative plotting packages can be used; here we use the `simmer.plot`
package just to graph the number of customers waiting for the counter.
The `simmer.plot` package is imported at line 2. The function
`get_mon_resources()` is not called because the function `plot()` calles
`get_mon_resources()` itself. The `plot()` function has arguments to specifiy
what to plot.
```{r, message = FALSE}
library(simmer)
library(simmer.plot)
timeInBank <- 12 # mean, minutes
set.seed(1234)
bank <- simmer()
customer <-
trajectory("Customer's path") %>%
set_attribute("start_time", function() {now(bank)}) %>%
seize("counter") %>%
timeout(function() {rexp(1, 1/timeInBank)}) %>%
release("counter")
bank <-
simmer("bank") %>%
add_resource("counter") %>%
add_generator("Customer", customer, function() {c(0, rexp(19, 1/10), -1)})
bank %>% run(until = 400)
plot(bank,
what = "resources",
metric = "usage",
names = "counter",
items = "system",
steps = TRUE)
```