simmer
Discrete-Event Simulation for R
Iñaki Úcar, postdoctoral fellow @ UC3M-Santander Big Data Institute (IBiDat)
Bart Smeets, founder & data scientist @ dataroots.io

XI Jornadas de Usuarios de R, Madrid, November 14-16, 2019
1 / 20

Introduction

Simulation

From R. Shannon (1975), simulation is

the process of designing a model of a real system and conducting experiments with this model for the purpose either of understanding the behavior of the system or of evaluating various strategies [...] for the operation of the system.

2 / 20

Introduction

Simulation

From R. Shannon (1975), simulation is

the process of designing a model of a real system and conducting experiments with this model for the purpose either of understanding the behavior of the system or of evaluating various strategies [...] for the operation of the system.

Taxonomy, from Law and Kelton (2000):

deterministic vs. stochastic
(time component?) static vs. dynamic
(if dynamic) continuous vs. discrete

2 / 20

Introduction

Simulation

From R. Shannon (1975), simulation is

the process of designing a model of a real system and conducting experiments with this model for the purpose either of understanding the behavior of the system or of evaluating various strategies [...] for the operation of the system.

Taxonomy, from Law and Kelton (2000):

deterministic vs. stochastic
(time component?) static vs. dynamic
(if dynamic) continuous vs. discrete

Examples:

deterministic + dynamic + continuous = Dynamical Systems
stochastic + static = Monte Carlo Simulation
stochastic + dynamic + discrete = Discrete-Event Simulation (DES)

2 / 20

Introduction

Simulation

DES

What can be modelled as a Discrete-Event Simulation (DES)?

An event is an instantaneous occurrence that may change the state of the system
The number of events is countable
Between events, all the state variables remain constant
Output: snapshots of the state of the system over time

3 / 20

Introduction

Simulation

DES

What can be modelled as a Discrete-Event Simulation (DES)?

An event is an instantaneous occurrence that may change the state of the system
The number of events is countable
Between events, all the state variables remain constant
Output: snapshots of the state of the system over time

Common examples:

customers arriving at a bank,
products being manipulated in a supply chain,
packets traversing a network,
...

and many more applications from manufacturing systems, construction engineering, project management, logistics, transportation systems, business processes, healthcare, telecommunications networks...

3 / 20

Introduction

Simulation

DES

Programming styles (Banks 2005):

Activity-oriented: fixed time increments; scan and verify conditions
Event-oriented: event routines; event list ordered by time of ocurrence
Process-oriented: life cycle of entities of the real system; triggered by events

4 / 20

Introduction

Simulation

DES

Programming styles (Banks 2005):

Activity-oriented: fixed time increments; scan and verify conditions
Event-oriented: event routines; event list ordered by time of ocurrence
Process-oriented: life cycle of entities of the real system; triggered by events

Spectrum of tools:

High complexity and specialization generally means more accuracy

but

More specialization requires more effort
More complexity requires more effort

4 / 20

Introduction

Simulation

DES

`simmer`

Main characteristics:

General versatile framework for fast prototyping
Rich and user-friendly R API over a fast C++ simulation core
Process-oriented trajectory-based modelling
Automatic monitoring capabilities
Integration with R: repeatability, analysis, visualization

5 / 20

Introduction

Simulation

DES

`simmer`

Main characteristics:

General versatile framework for fast prototyping
Rich and user-friendly R API over a fast C++ simulation core
Process-oriented trajectory-based modelling
Automatic monitoring capabilities
Integration with R: repeatability, analysis, visualization

Resources:

Online documentation (manual + 10 vignettes): https://r-simmer.org
Ucar I, Smeets B, Azcorra A (2019). “simmer: Discrete-Event Simulation for R.” Journal of Statistical Software, 90(2), 1-30. doi: 10.18637/jss.v090.i02.
Ucar I, Hernández JA, Serrano P, Azcorra A (2018). “Design and Analysis of 5G Scenarios with simmer: An R Package for Fast DES Prototyping.” IEEE Communications Magazine, 56(11), 145-151. doi: 10.1109/MCOM.2018.1700960.

5 / 20

Example: Job Shop

From M. Pidd (1988), Section 5.3.1:

Jobs are allocated to the first available machine.
Machines need to be retooled (sometimes) and reset by an operative.
Operatives may be away attending other tasks.

6 / 20

Example: Job Shop

From M. Pidd (1988), Section 5.3.1:

Jobs are allocated to the first available machine.
Machines need to be retooled (sometimes) and reset by an operative.
Operatives may be away attending other tasks.

job <- trajectory() %>%
  seize("machine") %>%
  timeout(RUNNING) %>%
  branch(
    CHECK_WORN, continue = TRUE,
    trajectory() %>%
      seize("operative") %>%
      timeout(RETOOL) %>%
      release("operative")
  ) %>%
  seize("operative") %>%
  timeout(RESET) %>%
  release("operative") %>%
  release("machine")

6 / 20

Example: Job Shop

From M. Pidd (1988), Section 5.3.1:

Jobs are allocated to the first available machine.
Machines need to be retooled (sometimes) and reset by an operative.
Operatives may be away attending other tasks.

job <- trajectory() %>%
  seize("machine") %>%
  timeout(RUNNING) %>%
  branch(
    CHECK_WORN, continue = TRUE,
    trajectory() %>%
      seize("operative") %>%
      timeout(RETOOL) %>%
      release("operative")
  ) %>%
  seize("operative") %>%
  timeout(RESET) %>%
  release("operative") %>%
  release("machine")

task <- trajectory() %>%
  seize("operative") %>%
  timeout(AWAY) %>%
  release("operative")

6 / 20

Example: Job Shoplibrary(simmer); set.seed(1234)
RUNNING <- function() rexp(1, 1)
CHECK_WORN <- function() runif(1) < 0.2
RETOOL <- function() rexp(1, 2)
RESET <- function() rexp(1, 3)
AWAY <- function() rexp(1, 1)
job <- trajectory() %>%
  seize("machine") %>%
  timeout(RUNNING) %>%
  branch(
    CHECK_WORN, continue = TRUE,
    trajectory() %>%
      seize("operative") %>%
      timeout(RETOOL) %>%
      release("operative")
  ) %>%
  seize("operative") %>%
  timeout(RESET) %>%
  release("operative") %>%
  release("machine")

task <- trajectory() %>%
  seize("operative") %>%
  timeout(AWAY) %>%
  release("operative")

7 / 20

Example: Job Shoplibrary(simmer); set.seed(1234)
RUNNING <- function() rexp(1, 1)
CHECK_WORN <- function() runif(1) < 0.2
RETOOL <- function() rexp(1, 2)
RESET <- function() rexp(1, 3)
AWAY <- function() rexp(1, 1)
job <- trajectory() %>%
  ...
task <- trajectory() %>%
  ...
NEW_JOB <- function() rexp(1, 5)
NEW_TASK <- function() rexp(1, 1)

8 / 20

Example: Job Shoplibrary(simmer); set.seed(1234)
RUNNING <- function() rexp(1, 1)
CHECK_WORN <- function() runif(1) < 0.2
RETOOL <- function() rexp(1, 2)
RESET <- function() rexp(1, 3)
AWAY <- function() rexp(1, 1)
job <- trajectory() %>%
  ...
task <- trajectory() %>%
  ...
NEW_JOB <- function() rexp(1, 5)
NEW_TASK <- function() rexp(1, 1)

env <- simmer("Job Shop") %>%
  add_resource("machine", 10) %>%
  add_resource("operative", 5) %>%
  add_generator("job", job, NEW_JOB) %>%
  add_generator("task", task, NEW_TASK) %>%
  run(until=1000)
env

## simmer environment: Job Shop | now: 1000 | next: 1000.09508921831
## { Monitor: in memory }
## { Resource: machine | monitored: TRUE | server status: 3(10) | queue status: 0(Inf) }
## { Resource: operative | monitored: TRUE | server status: 2(5) | queue status: 0(Inf) }
## { Source: job | monitored: 1 | n_generated: 5177 }
## { Source: task | monitored: 1 | n_generated: 995 }
8 / 20

Example: Job Shop

library(simmer); set.seed(1234)
RUNNING <- function() rexp(1, 1)
CHECK_WORN <- function() runif(1) < 0.2
RETOOL <- function() rexp(1, 2)
RESET <- function() rexp(1, 3)
AWAY <- function() rexp(1, 1)
job <- trajectory() %>%
  ...
task <- trajectory() %>%
  ...
NEW_JOB <- function() rexp(1, 5)
NEW_TASK <- function() rexp(1, 1)

env <- simmer("Job Shop") %>%
  add_resource("machine", 10) %>%
  add_resource("operative", 5) %>%
  add_generator("job", job, NEW_JOB) %>%
  add_generator("task", task, NEW_TASK) %>%
  run(until=1000)
env

## simmer environment: Job Shop | now: 1000 | next: 1000.09508921831
## { Monitor: in memory }
## { Resource: machine | monitored: TRUE | server status: 3(10) | queue status: 0(Inf) }
## { Resource: operative | monitored: TRUE | server status: 2(5) | queue status: 0(Inf) }
## { Source: job | monitored: 1 | n_generated: 5177 }
## { Source: task | monitored: 1 | n_generated: 995 }

aggregate(cbind(server, queue) ~ resource, get_mon_resources(env), mean)

##    resource   server     queue
## 1   machine 7.987438 1.0355590
## 2 operative 3.505732 0.4441298

8 / 20

Simulation core design

Architecture

Overview of the C++ core (white) and R API (blue)

Terminology

9 / 20

Simulation core design

Architecture

Overview of the C++ core (white) and R API (blue)

Terminology

Resource: server (configurable capacity) + priority queue (configurable size), supports preemption
Manager: modifies resources at run time (schedule)

9 / 20

Simulation core design

Architecture

Overview of the C++ core (white) and R API (blue)

Terminology

Resource: server (configurable capacity) + priority queue (configurable size), supports preemption
Manager: modifies resources at run time (schedule)

Source: creates new arrivals following some distribution of inter-arrival times
Arrival: interacting processes, with attributes and prioritization values

9 / 20

Simulation core design

Architecture

Overview of the C++ core (white) and R API (blue)

Terminology

Resource: server (configurable capacity) + priority queue (configurable size), supports preemption
Manager: modifies resources at run time (schedule)

Source: creates new arrivals following some distribution of inter-arrival times
Arrival: interacting processes, with attributes and prioritization values

Trajectory: interlinkage of activities, a common path for arrivals of the same type
Activity: unit of action, main building block

9 / 20

The simmer API

Trajectory

Similar to dplyr for data manipulation. In the words of H. Wickham,

by constraining your options, it simplifies how you can think about [something]

Trajectories are recipes, lists of activities defining the life time of arrivals
Activities are common functional DES blocks

10 / 20

The simmer API

Trajectory

Similar to dplyr for data manipulation. In the words of H. Wickham,

by constraining your options, it simplifies how you can think about [something]

Trajectories are recipes, lists of activities defining the life time of arrivals
Activities are common functional DES blocks

Fixed vs. dynamic parameters:

traj0 <- trajectory() %>%
  log_("Entering the trajectory") %>%
  timeout(10) %>%
  log_("Leaving the trajectory")

traj1 <- trajectory() %>%
  log_(function() "Entering the trajectory") %>%
  timeout(function() 10) %>%
  log_(function() "Leaving the trajectory")

10 / 20

The simmer APITrajectory
Activities
Spend time in the systemtimeout, timeout_from_attribute, timeout_from_global

Modify arrival propertiesset_attribute, set_global
set_prioritization

Interaction with resourcesseize, release
set_capacity, set_queue_size
select, seize_selected...

Interaction with sourcesactivate, deactivate
set_trajectory, set_source

Loopsrollback


Branchingbranch
clone, synchronize

Batchingbatch, separate

Inter-arrival communicationsend, trap, untrap, wait

Renegingleave
renege_in, renege_if, renege_abort
handle_unfinished

Debugginglog_
stop_if


11 / 20

The simmer API

Trajectory

Activities

Spend time in the system
- timeout, timeout_from_attribute, timeout_from_global
Modify arrival properties
- set_attribute, set_global
- set_prioritization
Interaction with resources
- seize, release
- set_capacity, set_queue_size
- select, seize_selected...
Interaction with sources
- activate, deactivate
- set_trajectory, set_source
Loops
- rollback

Branching
- branch
- clone, synchronize
Batching
- batch, separate
Inter-arrival communication
- send, trap, untrap, wait
Reneging
- leave
- renege_in, renege_if, renege_abort
- handle_unfinished
Debugging
- log_
- stop_if

(Plus many getters to retrieve parameters at run time)

11 / 20

The simmer APITrajectory
Activities
Simulation environment
Create a simulator and attach a monitorsimmer
monitor_mem (default), monitor_csv... (extensible, see simmer.mon on GitHub)


12 / 20

The simmer APITrajectory
Activities
Simulation environment
Create a simulator and attach a monitorsimmer
monitor_mem (default), monitor_csv... (extensible, see simmer.mon on GitHub)


Add sources of arrivalsadd_generator: based on a distribution function
add_dataframe: based on a data frame (additional columns as attributes)


12 / 20

The simmer APITrajectory
Activities
Simulation environment
Create a simulator and attach a monitorsimmer
monitor_mem (default), monitor_csv... (extensible, see simmer.mon on GitHub)


Add sources of arrivalsadd_generator: based on a distribution function
add_dataframe: based on a data frame (additional columns as attributes)


Add resourcesadd_resource: priority resource, with capacity and queue size; optional preemption


12 / 20

The simmer APITrajectory
Activities
Simulation environment
Create a simulator and attach a monitorsimmer
monitor_mem (default), monitor_csv... (extensible, see simmer.mon on GitHub)

Add sources of arrivalsadd_generator: based on a distribution function
add_dataframe: based on a data frame (additional columns as attributes)

Add resourcesadd_resource: priority resource, with capacity and queue size; optional preemption

Add global variablesadd_global

12 / 20

The simmer APITrajectory
Activities
Simulation environment
Create a simulator and attach a monitorsimmer
monitor_mem (default), monitor_csv... (extensible, see simmer.mon on GitHub)

Add sources of arrivalsadd_generator: based on a distribution function
add_dataframe: based on a data frame (additional columns as attributes)

Add resourcesadd_resource: priority resource, with capacity and queue size; optional preemption

Add global variablesadd_global

Run the simulationrun, stepn

12 / 20

The simmer API

Trajectory

Activities

Simulation environment

Monitoring

simmer automatically records every change in the state of the system. All these statistics can be retrieved after the simulation:

names( get_mon_arrivals(simmer(), per_resource=FALSE) )

## [1] "name"          "start_time"    "end_time"      "activity_time"
## [5] "finished"

names( get_mon_arrivals(simmer(), per_resource=TRUE) )

## [1] "name"          "start_time"    "end_time"      "activity_time"
## [5] "resource"

names( get_mon_attributes(simmer()) )

## [1] "time"  "name"  "key"   "value"

names( get_mon_resources(simmer()) )

## [1] "resource"   "time"       "server"     "queue"      "capacity"  
## [6] "queue_size" "system"     "limit"

13 / 20

Modelling

Queueing systems

Natural way to simulate CTMC and birth-death processes:

set.seed(1234)
lambda <- 2
mu <- 4
rho <- lambda/mu

mm1.traj <- trajectory() %>%
  seize("mm1.resource", 1) %>%
  timeout(function() rexp(1, mu)) %>%
  release("mm1.resource", 1)

mm1.env <- simmer() %>%
  add_resource("mm1.resource", 1, Inf) %>%
  add_generator("arrival", mm1.traj, 
                function() rexp(1, lambda)) %>%
  run(2000)

14 / 20

Modelling

Queueing systems

Natural way to simulate CTMC and birth-death processes:

set.seed(1234)
lambda <- 2
mu <- 4
rho <- lambda/mu

mm1.traj <- trajectory() %>%
  seize("mm1.resource", 1) %>%
  timeout(function() rexp(1, mu)) %>%
  release("mm1.resource", 1)

mm1.env <- simmer() %>%
  add_resource("mm1.resource", 1, Inf) %>%
  add_generator("arrival", mm1.traj, 
                function() rexp(1, lambda)) %>%
  run(2000)

14 / 20

Modelling

Replication

Easy replication with standard R functions:

mm1.envs <- lapply(1:20, function(i) {
  simmer() %>%
    add_resource("mm1.resource", 1, Inf) %>%
    add_generator("arrival", mm1.traj, 
                  function() rexp(100, lambda)) %>%
    run(1000/lambda)
})

15 / 20

Modelling

Replication

Easy replication with standard R functions:

mm1.envs <- lapply(1:20, function(i) {
  simmer() %>%
    add_resource("mm1.resource", 1, Inf) %>%
    add_generator("arrival", mm1.traj, 
                  function() rexp(100, lambda)) %>%
    run(1000/lambda)
})

Parallelization

Even easier parallelization of replicas:

mm1.envs <- parallel::mclapply(1:20, function(i) {
  simmer() %>%
    add_resource("mm1.resource", 1, Inf) %>%
    add_generator("arrival", mm1.traj, 
                  function() rexp(100, lambda)) %>%
    run(1000/lambda) %>%
    wrap()
}, mc.cores=4)

15 / 20

Modelling

Replication

Easy replication with standard R functions:

mm1.envs <- lapply(1:20, function(i) {
  simmer() %>%
    add_resource("mm1.resource", 1, Inf) %>%
    add_generator("arrival", mm1.traj, 
                  function() rexp(100, lambda)) %>%
    run(1000/lambda)
})

Parallelization

Even easier parallelization of replicas:

mm1.envs <- parallel::mclapply(1:20, function(i) {
  simmer() %>%
    add_resource("mm1.resource", 1, Inf) %>%
    add_generator("arrival", mm1.traj, 
                  function() rexp(100, lambda)) %>%
    run(1000/lambda) %>%
    wrap()
}, mc.cores=4)

head(get_mon_arrivals(mm1.envs), 3)

##       name start_time  end_time activity_time finished replication
## 1 arrival0 0.04471412 0.2337613   0.189047164     TRUE           1
## 2 arrival1 0.17734846 0.2384445   0.004683229     TRUE           1
## 3 arrival2 0.52254010 0.9208069   0.398266801     TRUE           1

15 / 20

Modelling

Best practices

There are usually multiple valid ways of mapping the identified resources and processes into the simmer API

16 / 20

Modelling

Best practices

There are usually multiple valid ways of mapping the identified resources and processes into the simmer API

Design pattern 1

beep <- trajectory() %>%
  log_("beeeep!")

env <- simmer() %>%
  add_generator("beep", beep, function() 1) %>%
  run(2.5)

## 1: beep0: beeeep!
## 2: beep1: beeeep!

16 / 20

Modelling

Best practices

There are usually multiple valid ways of mapping the identified resources and processes into the simmer API

Design pattern 1

beep <- trajectory() %>%
  log_("beeeep!")

env <- simmer() %>%
  add_generator("beep", beep, function() 1) %>%
  run(2.5)

## 1: beep0: beeeep!
## 2: beep1: beeeep!

Design pattern 2

alarm <- trajectory() %>%
  timeout(1) %>%
  log_("beeeep!") %>%
  rollback(2)

env <- simmer() %>%
  add_generator("alarm", alarm, at(0)) %>%
  run(2.5)

## 1: alarm0: beeeep!
## 2: alarm0: beeeep!

16 / 20

Performance

Comparison with similar frameworks (out-of-date!):

SimPy 3.0.9, Python 2.7
SimJulia 0.3.14, Julia 0.5.1

Heavy M/M/1, $ρ \approx 0.9$ :

test_mm1_simmer <- function(n, m, mon=FALSE) {
  mm1 <- trajectory() %>%
    seize("server", 1) %>%
    timeout(function() rexp(1, 1.1)) %>%
    release("server", 1)
  env <- simmer() %>%
    add_resource("server", 1, mon=mon) %>%
    add_generator("customer", mm1,
                  function() rexp(m, 1), mon=mon) %>%
    run(until=n)
}

17 / 20

Performance

Comparison with similar frameworks (out-of-date!):

SimPy 3.0.9, Python 2.7
SimJulia 0.3.14, Julia 0.5.1

Heavy M/M/1, $ρ \approx 0.9$ :

test_mm1_simmer <- function(n, m, mon=FALSE) {
  mm1 <- trajectory() %>%
    seize("server", 1) %>%
    timeout(function() rexp(1, 1.1)) %>%
    release("server", 1)
  env <- simmer() %>%
    add_resource("server", 1, mon=mon) %>%
    add_generator("customer", mm1,
                  function() rexp(m, 1), mon=mon) %>%
    run(until=n)
}

17 / 20

Performance

The cost of calling R from C++ revisited

Very simple deterministic test to study the impact:

test_simmer <- function(n, delay) {
  test <- trajectory() %>%
    timeout(delay)
  simmer() %>%
    add_generator("test", test, at(1:n)) %>%
    run() %>%
    get_mon_arrivals()
}
test_simmer(5, 1)[,1:5]

##    name start_time end_time activity_time finished
## 1 test0          1        2             1     TRUE
## 2 test1          2        3             1     TRUE
## 3 test2          3        4             1     TRUE
## 4 test3          4        5             1     TRUE
## 5 test4          5        6             1     TRUE

18 / 20

Performance

The cost of calling R from C++ revisited

Very simple deterministic test to study the impact:

test_simmer <- function(n, delay) {
  test <- trajectory() %>%
    timeout(delay)
  simmer() %>%
    add_generator("test", test, at(1:n)) %>%
    run() %>%
    get_mon_arrivals()
}
test_simmer(5, 1)[,1:5]

##    name start_time end_time activity_time finished
## 1 test0          1        2             1     TRUE
## 2 test1          2        3             1     TRUE
## 3 test2          3        4             1     TRUE
## 4 test3          4        5             1     TRUE
## 5 test4          5        6             1     TRUE

Original benchmark in the JSS paper:

Expr	Min	Mean	Median	Max
test_simmer(n, 1)	429.8663	492.365	480.5408	599.3547
test_simmer(n, function() 1)	3067.9957	3176.963	3165.6859	3434.7979
test_R_for(n)	2053.0840	2176.164	2102.5848	2438.6836

18 / 20

Performance

The cost of calling R from C++ revisited

Very simple deterministic test to study the impact:

test_simmer <- function(n, delay) {
  test <- trajectory() %>%
    timeout(delay)
  simmer() %>%
    add_generator("test", test, at(1:n)) %>%
    run() %>%
    get_mon_arrivals()
}
test_simmer(5, 1)[,1:5]

##    name start_time end_time activity_time finished
## 1 test0          1        2             1     TRUE
## 2 test1          2        3             1     TRUE
## 3 test2          3        4             1     TRUE
## 4 test3          4        5             1     TRUE
## 5 test4          5        6             1     TRUE

Original benchmark in the JSS paper:

Expr	Min	Mean	Median	Max
test_simmer(n, 1)	429.8663	492.365	480.5408	599.3547
test_simmer(n, function() 1)	3067.9957	3176.963	3165.6859	3434.7979
test_R_for(n)	2053.0840	2176.164	2102.5848	2438.6836

Update with -DRCPP_USE_UNWIND_PROTECT:

Expr	Min	Mean	Median	Max
test_simmer(n, 1)	467.8971	481.213	476.1667	521.4916
test_simmer(n, function() 1)	498.2631	583.777	561.6798	816.1343
test_R_for(n)	1158.9348	1201.460	1196.7223	1244.4041

18 / 20

Summary

Generic yet powerful process-oriented Discrete-Event Simulation framework for R [1, 2]
Combines a robust and fast C++ simulation core with a rich and flexible R API

[1] Ucar I, Smeets B, Azcorra A (2019). “simmer: Discrete-Event Simulation for R.” Journal of Statistical Software, 90(2), 1-30. doi: 10.18637/jss.v090.i02.
[2] Ucar I, Hernández JA, Serrano P, Azcorra A (2018). “Design and Analysis of 5G Scenarios with simmer: An R Package for Fast DES Prototyping.” IEEE Communications Magazine, 56(11), 145-151. doi: 10.1109/MCOM.2018.1700960.

19 / 20

Summary

Generic yet powerful process-oriented Discrete-Event Simulation framework for R [1, 2]
Combines a robust and fast C++ simulation core with a rich and flexible R API

Broad set of activities, the basic building block; extensible via custom routines
Activities are chained into a trajectory, a common path for processes of the same type

19 / 20

Summary

Generic yet powerful process-oriented Discrete-Event Simulation framework for R [1, 2]
Combines a robust and fast C++ simulation core with a rich and flexible R API

Broad set of activities, the basic building block; extensible via custom routines
Activities are chained into a trajectory, a common path for processes of the same type

Automatic monitoring: focus on modelling

19 / 20

Summary

Generic yet powerful process-oriented Discrete-Event Simulation framework for R [1, 2]
Combines a robust and fast C++ simulation core with a rich and flexible R API

Broad set of activities, the basic building block; extensible via custom routines
Activities are chained into a trajectory, a common path for processes of the same type

Automatic monitoring: focus on modelling

Integration: easy replication, parallelization, analysis...

19 / 20

Thanks, and happy ing!

https://r-simmer.org

20 / 20

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