Bank Office
Queue problems are common-place application of discrete event simulation.
Often there are multiple solutions for a model. Here we model similar problems - a customer queue - differently using resources, states and queues in various configurations and interaction patterns.
Simple Bank Office (1 clerk)
Lets start with a bank office where customers are arriving in a bank, where there is one clerk. This clerk handles the customers in a first in first out (FIFO) order.
We see the following processes:
- The customer generator that creates the customers, with an inter-arrival time of
uniform(5,15) - The customers
- The clerk, which serves the customers in a constant time of 30 (overloaded and non steady state system)
We need a queue for the customers to wait for service.
The model code is:
////Bank1clerk.kt
package org.kalasim.examples.bank.oneclerk
import org.kalasim.*
import org.kalasim.misc.printThis
import org.kalasim.plot.kravis.canDisplay
import org.kalasim.plot.kravis.display
import org.koin.core.component.inject
import kotlin.time.Duration
import kotlin.time.Duration.Companion.minutes
class Customer(
val waitingLine: ComponentQueue<Customer>,
val clerk: Clerk
) : Component() {
override fun process() = sequence {
waitingLine.add(this@Customer)
if(clerk.isPassive) clerk.activate()
passivate()
}
}
class Clerk(val serviceTime: Duration = 10.minutes) : Component() {
val waitingLine: ComponentQueue<Customer> by inject()
override fun process() = sequence {
while(true) {
while(waitingLine.isEmpty()) passivate()
val customer = waitingLine.poll()
hold(serviceTime) // bearbeitungszeit
customer.activate()
}
}
}
class CustomerGenerator : Component() {
override fun process() = sequence {
while(true) {
Customer(get(), get())
hold(uniform(5.minutes, 15.minutes).sample())
}
}
}
fun main() {
val deps = declareDependencies {
dependency { Clerk() }
dependency { ComponentQueue<Customer>("waiting line") }
}
val env = createSimulation(dependencies = deps) {
enableComponentLogger()
CustomerGenerator()
}
env.run(50.0)
val waitingLine: ComponentQueue<Customer> = env.get()
waitingLine.statistics.printThis()
if(canDisplay()) {
waitingLine.queueLengthTimeline.display()
waitingLine.lengthOfStayStatistics.display()
}
}
Let's look at some details (marked in yellow for convenience).
With:
waitingLine.add(this@Customer)
the customer places itself at the tail of the waiting line.
Then, the customer checks whether the clerk is idle, and if so, activates him immediately.:
if (clerk.isPassive) clerk.activate()
Once the clerk is active (again), it gets the first customer out of the waitingline with:
val customer = waitingLine.poll()
and holds for 30 time units with:
hold(10.0)
After that hold the customer is activated and will terminate:
customer.activate()
In the main section of the program, we create the CustomerGenerator, the Clerk and a ComponentQueue called waitingline. Here the customer generator is implemented as a custom instance of Component for educational puroposes. Using the provided ComponentGenerator API would be more concise.
hold(uniform(5.0, 15.0).sample())
will do the statistical sampling and wait for that time till the next customer is created.
Since logging is enabled when creating the simulation with createSimulation the following log trace is being produced
time current component action info
--------- ------------------------ -------------------------------------------- ----------------------------------
.00 main create
.00 main
.00 Clerk.1 create
.00 Clerk.1 activate scheduled for .00
.00 CustomerGenerator.1 create
.00 CustomerGenerator.1 activate scheduled for .00
.00 main run +50.00 scheduled for 50.00
.00 Clerk.1
.00 Clerk.1 passivate
.00 CustomerGenerator.1
.00 Customer.1 create
.00 Customer.1 activate scheduled for .00
.00 CustomerGenerator.1 hold +11.95 scheduled for 11.95
.00 Customer.1
.00 Customer.1 entering waiting line
.00 Clerk.1 activate scheduled for .00
.00 Customer.1 passivate
.00 Clerk.1
.00 Customer.1 leaving waiting line
.00 Clerk.1 hold +10.00 scheduled for 10.00
10.00 Clerk.1
10.00 Customer.1 activate scheduled for 10.00
10.00 Clerk.1 passivate
10.00 Customer.1
10.00 Customer.1 ended
11.95 CustomerGenerator.1
11.95 Customer.2 create
11.95 Customer.2 activate scheduled for 11.95
11.95 CustomerGenerator.1 hold +7.73 scheduled for 19.68
11.95 Customer.2
11.95 Customer.2 entering waiting line
11.95 Clerk.1 activate scheduled for 11.95
11.95 Customer.2 passivate
11.95 Clerk.1
11.95 Customer.2 leaving waiting line
11.95 Clerk.1 hold +10.00 scheduled for 21.95
19.68 CustomerGenerator.1
19.68 Customer.3 create
19.68 Customer.3 activate scheduled for 19.68
19.68 CustomerGenerator.1 hold +10.32 scheduled for 30.00
19.68 Customer.3
19.68 Customer.3 entering waiting line
19.68 Customer.3 passivate
21.95 Clerk.1
21.95 Customer.2 activate scheduled for 21.95
21.95 Customer.3 leaving waiting line
21.95 Clerk.1 hold +10.00 scheduled for 31.95
21.95 Customer.2
21.95 Customer.2 ended
30.00 CustomerGenerator.1
30.00 Customer.4 create
30.00 Customer.4 activate scheduled for 30.00
30.00 CustomerGenerator.1 hold +10.63 scheduled for 40.63
30.00 Customer.4
30.00 Customer.4 entering waiting line
30.00 Customer.4 passivate
31.95 Clerk.1
31.95 Customer.3 activate scheduled for 31.95
31.95 Customer.4 leaving waiting line
31.95 Clerk.1 hold +10.00 scheduled for 41.95
31.95 Customer.3
31.95 Customer.3 ended
40.63 CustomerGenerator.1
40.63 Customer.5 create
40.63 Customer.5 activate scheduled for 40.63
40.63 CustomerGenerator.1 hold +5.31 scheduled for 45.95
40.63 Customer.5
40.63 Customer.5 entering waiting line
40.63 Customer.5 passivate
41.95 Clerk.1
41.95 Customer.4 activate scheduled for 41.95
41.95 Customer.5 leaving waiting line
41.95 Clerk.1 hold +10.00 scheduled for 51.95
41.95 Customer.4
41.95 Customer.4 ended
45.95 CustomerGenerator.1
45.95 Customer.6 create
45.95 Customer.6 activate scheduled for 45.95
45.95 CustomerGenerator.1 hold +12.68 scheduled for 58.63
45.95 Customer.6
45.95 Customer.6 entering waiting line
45.95 Customer.6 passivate
50.00 main
After the simulation is finished, the statistics of the queue are presented with:
waitingLine.stats.print()
The statistics output looks like
{
"queue_length": {
"all": {
"duration": 50,
"min": 0,
"max": 1,
"mean": 0.15,
"standard_deviation": 0.361
},
"excl_zeros": {
"duration": 7.500540828621098,
"min": 1,
"max": 1,
"mean": 1,
"standard_deviation": 0
}
},
"name": "waiting line",
"length_of_stay": {
"all": {
"entries": 5,
"ninety_pct_quantile": 3.736,
"median": 1.684,
"mean": 1.334,
"ninetyfive_pct_quantile": 3.736,
"standard_deviation": 1.684
},
"excl_zeros": {
"entries": 3,
"ninety_pct_quantile": 3.736,
"median": 1.645,
"mean": 2.223,
"ninetyfive_pct_quantile": 3.736,
"standard_deviation": 1.645
}
},
"type": "QueueStatistics",
"timestamp": 50
}
Bank Office with 3 Clerks
Now, let's add more clerks:
add { (1..3).map { Clerk() } }
And, every time a customer enters the waiting line, we need to make sure at least one passive clerk (if any) is activated:
for (c in clerks) {
if (c.isPassive) {
c.activate()
break // activate at max one clerk
}
}
The complete source of a three clerk post office:
////Bank3Clerks.kt
package org.kalasim.examples.bank.threeclerks
import org.kalasim.*
import org.kalasim.plot.kravis.canDisplay
import org.kalasim.plot.kravis.display
import org.koin.core.component.inject
import kotlin.time.Duration.Companion.minutes
class CustomerGenerator : Component() {
override fun process() = sequence {
while(true) {
Customer(get())
hold(uniform(5.0, 15.0).minutes.sample())
}
}
}
class Customer(val waitingLine: ComponentQueue<Customer>) : Component() {
private val clerks: List<Clerk> by inject()
override fun process() = sequence {
waitingLine.add(this@Customer)
for(c in clerks) {
if(c.isPassive) {
c.activate()
break // activate at max one clerk
}
}
passivate()
}
}
class Clerk : Component() {
private val waitingLine: ComponentQueue<Customer> by inject()
override fun process() = sequence {
while(true) {
if(waitingLine.isEmpty())
passivate()
val customer = waitingLine.poll()
hold(30.minutes) // bearbeitungszeit
customer.activate() // signal the customer that's all's done
}
}
}
fun main() {
createSimulation {
dependency { ComponentQueue<Customer>("waitingline") }
dependency { State(false, "worktodo") }
dependency { CustomerGenerator() }
dependency { (1..3).map { Clerk() } }
run(50000.0)
val waitingLine: ComponentQueue<Customer> = get()
if(canDisplay()) {
// waitingLine.lengthOfStayMonitor.printHistogram()
// waitingLine.queueLengthMonitor.printHistogram()
waitingLine.queueLengthTimeline.display()
waitingLine.lengthOfStayStatistics.display()
}
// waitingLine.stats.toJson().toString(2).printThis()
waitingLine.printSummary()
}
}
Bank Office with Resources
kalasim contains another useful concept for modelling: Resources. Resources have a limited capacity and can be claimed by components and released later.
In the model of the bank with the same functionality as the above example, the clerks are defined as a resource with capacity 3.
The model code is:
////Bank3ClerksResources.kt
package org.kalasim.examples.bank.resources
import org.kalasim.*
import org.kalasim.plot.kravis.canDisplay
import org.kalasim.plot.kravis.display
import kotlin.time.Duration.Companion.minutes
class Customer(private val clerks: Resource) : Component() {
override fun process() = sequence {
request(clerks)
hold(30.minutes)
release(clerks) // not really required
}
}
fun main() {
val env = createSimulation {
dependency { Resource("clerks", capacity = 3) }
ComponentGenerator(iat = uniform(5.0, 15.0)) { Customer(get()) }
}
env.run(3000)
env.get<Resource>().apply {
printSummary()
if(canDisplay()) {
claimedTimeline.display()
requesters.queueLengthTimeline.display()
}
printStatistics()
}
}
Let's look at some details.:
add { Resource("clerks", capacity = 3) }
This defines a resource with a capacity of 3.
Each customer tries to claim one unit (=clerk) from the resource with:
request(clerks)
B default 1 unit will be requested. If the resource is not available, the customer needs to wait for it to become available (in order of arrival).
In contrast with the previous example, the customer now holds itself for 30 time units (clicks). After this time, the customer releases the resource with:
release(clerks)
The effect is that kalasim then tries to honor the next pending request, if any.
In this case the release statement is not required, as resources that were claimed are automatically released when a process terminates).`
The statistics are maintained in two system queues, called clerk.requesters and clerk.claimers.
The output is very similar to the earlier example. The statistics are exactly the same.
Bank Office with Balking and Reneging
Now, we assume that clients are not going to the queue when there are more than 5 clients waiting (balking). On top of that, if a client is waiting longer than 50, he/she will leave as well (reneging).
The model code is:
////Bank3ClerksReneging.kt
package org.kalasim.examples.bank.reneging
import org.kalasim.*
import org.kalasim.misc.printThis
import org.kalasim.monitors.printHistogram
import org.koin.core.component.inject
import kotlin.time.Duration.Companion.minutes
//**{todo}** use monitors here and maybe even inject them
//to inject use data class Counter(var value: Int)
var numBalked: Int = 0
var numReneged: Int = 0
class CustomerGenerator : Component() {
override fun process() = sequence {
while(true) {
Customer(get())
hold(uniform(5.0, 15.0).minutes.sample())
}
}
}
class Customer(val waitingLine: ComponentQueue<Customer>) : Component() {
private val clerks: List<Clerk> by inject()
override fun process() = sequence {
if(waitingLine.size >= 5) {
numBalked++
log("balked")
cancel()
}
waitingLine.add(this@Customer)
for(c in clerks) {
if(c.isPassive) {
c.activate()
break // activate only one clerk
}
}
hold(50.minutes) // if not serviced within this time, renege
if(waitingLine.contains(this@Customer)) {
// this@Customer.leave(waitingLine)
waitingLine.remove(this@Customer)
numReneged++
log("reneged")
} else {
// if customer no longer in waiting line,
// serving has started meanwhile
passivate()
}
}
}
class Clerk : Component() {
private val waitingLine: ComponentQueue<Customer> by inject()
override fun process() = sequence {
while(true) {
if(waitingLine.isEmpty())
passivate()
val customer = waitingLine.poll()
customer.activate() // get the customer out of it's hold(50)
hold(30.minutes) // bearbeitungszeit
customer.activate() // signal the customer that's all's done
}
}
}
fun main() {
val env = createSimulation {
enableComponentLogger()
// register components needed for dependency injection
dependency { ComponentQueue<Customer>("waitingline") }
dependency { (0..2).map { Clerk() } }
// register other components to be present when starting the simulation
CustomerGenerator()
val waitingLine: ComponentQueue<Customer> = get()
waitingLine.lengthOfStayStatistics.enabled = false
run(1500.0)
waitingLine.lengthOfStayStatistics.enabled = true
run(500.0)
// with console
waitingLine.lengthOfStayStatistics.printHistogram()
waitingLine.queueLengthTimeline.printHistogram()
// with kravis
// waitingLine.queueLengthMonitor.display()
// waitingLine.lengthOfStayMonitor.display()
waitingLine.statistics.toJson().toString(2).printThis()
println("number reneged: $numReneged")
println("number balked: $numBalked")
}
}
Let's look at some details.
cancel()
This makes the current component (a customer) a DATA component (and be subject to garbage collection), if the queue length is 5 or more.
The reneging is implemented after a hold of 50. If a clerk can service a customer, it will take the customer out of the waitingline and will activate it at that moment. The customer just has to check whether he/she is still in the waiting line. If so, he/she has not been serviced in time and thus will renege.
hold(50.0)
if (waitingLine.contains(this@Customer)) {
waitingLine.leave(this@Customer)
numReneged++
printTrace("reneged")
} else {
passivate()
}
All the clerk has to do when starting servicing a client is to get the next customer in line out of the queue (as before) and activate this customer (at time now). The effect is that the hold of the customer will end.
hold(30.0)
customer.activate() // signal the customer that's all's done
Bank Office with Balking and Reneging (resources)
Now we show how balking and reneging can be implemented with resources.
The model code is:
////Bank3ClerksRenegingResources.kt
package org.kalasim.examples.bank.reneging_resources
import org.kalasim.*
import org.kalasim.monitors.printHistogram
import kotlin.time.Duration.Companion.minutes
//var numBalked = LevelMonitoredInt(0)
var numBalked = 0
var numReneged = 0
class Customer(val clerks: Resource) : Component() {
override fun process() = sequence {
if(clerks.requesters.size >= 5) {
numBalked++
log("balked")
cancel()
}
request(clerks, failDelay = 50.minutes)
if(failed) {
numReneged++
log("reneged")
} else {
hold(30.minutes)
release(clerks)
}
}
}
fun main() {
declareDependencies {
dependency { Resource("clerks", capacity = 3) }
}.createSimulation {
// register other components to be present when starting the simulation
ComponentGenerator(iat = uniform(5.0, 15.0)) {
Customer(get())
}
run(50000.minutes)
val clerks = get<Resource>()
// with console
clerks.requesters.queueLengthTimeline.printHistogram()
clerks.requesters.lengthOfStayStatistics.printHistogram()
// with kravis
// clerks.requesters.queueLengthMonitor.display()
// clerks.requesters.lengthOfStayMonitor.display()
println("number reneged: $numReneged")
println("number balked: $numBalked")
}
}
As you can see, the balking part is exactly the same as in the example without resources.
For the renenging, all we have to do is add a failDelay:
request(clerks, failDelay = 50.asDist())
If the request is not honored within 50 time units (ticks), the process continues after that request statement. We check whether the request has failed with the built-in Component property:
iff (failed)
numReneged++
This example shows clearly the advantage of the resource solution over the passivate/activate method, in former example.
Bank Office with States
Another useful concept for modelling are states. In this case, we define a state called worktodo.
The model code is:
////Bank3ClerksState.kt
package org.kalasim.examples.bank.state
import org.apache.commons.math3.distribution.UniformRealDistribution
import org.kalasim.*
import org.koin.core.component.inject
import kotlin.time.Duration.Companion.minutes
class CustomerGenerator : Component() {
override fun process() = sequence {
while(true) {
Customer(get(), get())
hold(UniformRealDistribution(env.rg, 5.0, 15.0).minutes.sample())
}
}
}
class Customer(val workTodo: State<Boolean>, val waitingLine: ComponentQueue<Customer>) : Component() {
override fun process() = sequence {
waitingLine.add(this@Customer)
workTodo.trigger(true, max = 1)
passivate()
}
}
class Clerk : Component() {
val waitingLine: ComponentQueue<Customer> by inject()
val workTodo: State<Boolean> by inject()
override fun process() = sequence {
while(true) {
if(waitingLine.isEmpty())
wait(workTodo, true)
val customer = waitingLine.poll()
hold(32.minutes) // bearbeitungszeit
customer.activate()
}
}
}
fun main() {
val env = declareDependencies {
// register components needed for dependency injection
dependency { ComponentQueue<Customer>("waitingline") }
dependency { State(false, "worktodo") }
}.createSimulation {
enableComponentLogger()
// register other components to be present
// when starting the simulation
repeat(3) { Clerk() }
CustomerGenerator()
}
env.run(500.0)
println(env.get<ComponentQueue<Customer>>().statistics)
env.get<State<Boolean>>().printSummary()
// val waitingLine: ComponentQueue<Customer> = env.get()
// waitingLine.stats.print()
// waitingLine.queueLengthMonitor.display()
}
Let's look at some details.
add { State(false, "worktodo") }
This defines a state with an initial value false and registers it as a dependency.
In the code of the customer, the customer tries to trigger one clerk with:
workTodo.trigger(true, max = 1)
The effect is that if there are clerks waiting for worktodo, the first clerk's wait is honored and that clerk continues its process after:
wait(workTodo, true)
Note that the clerk is only going to wait for worktodo after completion of a job if there are no customers waiting.
Bank Office with Standby
The kalasim package contains yet another powerful process mechanism, called standby. When a component is in STANDBY mode, it will become current after each event. Normally, the standby will be used in a while loop where at every event one or more conditions are checked.
The model with standby is:
////Bank3ClerksStandby.kt
import org.kalasim.*
import org.kalasim.plot.kravis.display
import org.koin.core.component.inject
import kotlin.time.Duration.Companion.minutes
class Customer(val waitingLine: ComponentQueue<Customer>) : Component() {
override fun process() = sequence {
waitingLine.add(this@Customer)
passivate()
}
}
class Clerk : Component() {
val waitingLine: ComponentQueue<Customer> by inject()
override fun process() = sequence {
while(true) {
while(waitingLine.isEmpty())
standby()
val customer = waitingLine.poll()
hold(32.minutes) // bearbeitungszeit
customer.activate()
}
}
}
fun main() {
val env = declareDependencies {
dependency { ComponentQueue<Customer>("waitingline") }
}.createSimulation {
enableComponentLogger()
repeat(3) { Clerk() }
ComponentGenerator(uniform(5, 15)) { Customer(get()) }
}
env.run(500.0)
env.get<ComponentQueue<Customer>>().apply {
printSummary()
println(statistics)
lengthOfStayStatistics.display()
}
}
In this case, the condition is checked frequently with:
while(waitingLine.isEmpty())
standby()
The rest of the code is very similar to the version with states.
Warning
It is very important to realize that this mechanism can have significant impact on the performance, as after EACH event, the component becomes current and has to be checked. In general, it is recommended to try and use states or a more straightforward passivate/activate construction.