Introduction

With the initial simulation complete, we now proceed to finish the simulation by incorporating the remaining features necessary for a complete simulation. We now define what an agent does within the simulation prior to departing.

Reader’s Note

This simulation tutorial is the second part of an earlier tutorial. Please be sure to visit magic_kingdom_dev.html if you have any questions.

Setup

Since we are explaining and documenting our model in a piece-wise-linear fashion, we will introduce code chuncks and visuals throughout this document. The following code is setup code that should be ran to ensure reproducibility.

#set the seed value for the random generator
set.seed(123)

# bring in code scripts
knitr::read_chunk('../../R/modeling_agent_entry.R')
knitr::read_chunk('../../R/simplequeue.R')
knitr::read_chunk('../../R/choose_turnstile.R')
knitr::read_chunk('../../R/event_record.R')
knitr::read_chunk('../../R/theme_park_sim_1.R')
knitr::read_chunk('../../R/modeling_departures.R')
knitr::read_chunk("../../R/line.R")
knitr::read_chunk("../../R/attraction.R")
knitr::read_chunk("../../R/dining.R")
knitr::read_chunk("../../R/theme_park_sim_final.R")
knitr::read_chunk("../../R/extract_data.R")
knitr::read_chunk("../../R/agent_arrivals.R")
knitr::read_chunk("../../R/modeling_arrivals.R")
knitr::read_chunk("../../R/modeling_arrival_dist.R")

Modeling: Agent Departures

We now derive a model governing agent departures. In the previous simulation we used a static departure delay in order to show a working simulation. Of course, a static delay is probably not a reasonable approximation, so we now build a stochastic empirical model for modeling agent departures. Based upon data in [6], we assume the average number of attractions visited is between 8 - 12 (average of 10) with 1 dining experience (this also assumes downtime for sleeping, eating, shopping and recreation at your local hotel). We define a Gaussian \(\mathcal{N}(10,2)\) to represent the number of attractions visited. The process is stochastic because we use a random deviate generated from the Gaussian. The process is also empirical as the model is based upon observation.

In code,

generate_route_length <- function(n, route_length_mean, route_length_std){
  floor(rnorm(n, route_length_mean, route_length_std))
}

Using this process, when an agent arrives, we generate the number of attractions to be visited by that agent. Once the agent has visited the set number of attractions, the agent leaves the park with a constant time of 10 minutes. In addition to meeting the attractions requirement, the agent must also meet the dining experience requirement. We assume that all agents stop once at a dining experience. Therefore, the requirements for departure are:

  1. The required number of attractions have been visited, and

  2. the agent has dined at a dining experience

Once these requirements are met, the agent leaves with a constant time of 10 minutes.

route_length_mean = 10
route_length_std = 2
required_dining = 1
constant_departure = 10 * 60 #10 minutes in seconds format

Obviously, at this point, without attractions and dining experiences to visit, we cannot correctly simulate departures. Therefore, we now turn our attention to modeling the attractions and dining experiences.

Testing: No formal testing performed as the generate_route_length() function is rather trivial.

Modeling: Attractions

Attractions are visited by agents. Each attraction has a name, a duration (time it takes to experience the attraction), a batch size (number of agents serviced at one time) and a unique id. We utilize the TouringPlans (touringplans.com) website to collect the basic data needed to model the attractions. Due to limitations in obtaining accurate attraction durations and batch sizes, these numbers were invented based upon postulated data.

Each attraction also has a line associated with it. We use the Line class to model this.

In code, we define an attraction class as:

Attraction <- R6::R6Class(
  "Attraction",

  public = list(

    initialize = function(name, short_name, duration, batch_size, unique_id){
      private$validate(name, short_name, duration, batch_size, unique_id)

      private$.name <- name
      private$.short_name <- short_name
      private$.duration <- duration
      private$.batch_size <- batch_size
      private$.line <- Line$new(unique_id)
    }
  ),

  active = list(
    name = function(value){
      if(missing(value)){
        private$.name
      } else{
        stop("Cannot set `$name`\n")
      }
    },

    short_name = function(value){
      if(missing(value)){
        private$.short_name
      } else{
        stop("Cannot set `$short_name`\n")
      }
    },

    duration = function(value){
      if(missing(value)){
        private$.duration
      } else{
        stop("Cannot set `$duration`\n")
      }
    },

    batch_size = function(value){
      if(missing(value)){
        private$.batch_size
      } else{
        stop("Cannot set `$batch_size`\n")
      }
    },

    line = function(value){
      if(missing(value)){
        private$.line
      } else{
        stop("Cannot set `$line` after instantiation\n")
      }
    }
  ),

  private = list(
    .name = NULL,
    .short_name = NULL,
    .duration = NA,
    .batch_size = NA,
    .line = NULL,

    validate = function(name, short_name, duration, batch_size, unique_id){
      stopifnot(is.character(name))
      stopifnot(is.character(short_name))
      stopifnot(is.numeric(duration) || is.na(duration))
      stopifnot(is.numeric(batch_size))
      stopifnot(is.numeric(unique_id))
    }
  )
)

As one can see, the Attraction class makes use of the Line class for handling the flow of agents through the attraction. We define the Line class below.

Testing: No formal testing performed on the Attraction class as it is simply a container for storing information that is accessible through getter/setter methods. Formal unit testing was performed, as noted below, on the Line class which the Attraction class makes use of.

Simulation: Line

Line <- R6::R6Class(
  "Line",

  public = list(

    initialize = function(id){
      private$.id <- id
      private$.queue <- datastructures::queue()
    },

    add_agent = function(agent){
      invisible(datastructures::insert(private$.queue, agent))
      invisible(self)
    },

    remove_agent = function(n = 1){
      removed <- mapply(function(i){
        datastructures::pop(private$.queue)
      }, 1:n)

      #idea for this came from
      #https://stackoverflow.com/questions/33004238/r-removing-null-elements-from-a-list
      return(Filter(Negate(is.null), removed))
    }
  ),

  active = list(
    id = function(value){
      if(missing(value)){
        private$.id
      } else {
        stop("Cannot set `$id` after instantiation\n")
      }
    },

    num_of_agents = function(value){
      if(missing(value)){
        datastructures::size(private$.queue)
      } else{
        stop("Cannot set `$num_of_events`, use add_agent() or remove_agent()\n")
      }
    },

    queue = function(value){
      if(missing(value)){
        private$.queue
      } else {
        stop("Cannot set `$queue`, use add_event() or remove_event()")
      }
    }
  ),

  private = list(
    .id = -1,
    .queue = NULL
  )
)

Testing: Unit testing was performed with results available on the accompanying website (http://projects.jamesonmorgan.com/disneyworldsim/test_line.html).

Modeling: Dining Experiences

We now define a dining experience. A dining experience contains the experience’s name and a category code defining the type of restaurant (either quick-service or table-service). For quick-service restaurants, \(\mu_{qs} \in \{1500, 1800, 2100, 2400, 2700, 3000\}\) where each element of the set is measured in seconds. The mean of the quick-service set is 37.5 minutes (or 2250 seconds). For table-service restaurants, \(\mu_{ts} \in \{2700, 3000, 3300, 3600, 3900, 4200, 4500\}\) where each element of the set is measured in seconds. The mean of the table-service set is 60 minutes (or 3600 seconds).

These values where created as deterministic emperical model based upon postulated average service times for each class of restaurant. The model is deterministic as the output is predetermined. The mode is also emperical as we based it on postulated data. Quick-service restaurants are similar to fast-food and therefore we hypothesize that the average service time will be around 37 minutes. Table-service restaurants are more formal and therefore we believe the average service time for such restaurants will be closer to 60 minutes. Additionally, while quick-service restaurants have no restraint on the number of active users (at least within this simulation) table-service restaurants are limited by capacity. We take this into account by creating a counter that monitors the number of active diners in the restaurant. This counter is a field of the dining experience defined above.

If an agent has remaining dining experiences and remaining attractions that must be visited, we use a binomial distribution (probability = 0.5) to determine whether an agent should choose a dining experience or an attraction next.

Dining <- R6::R6Class(
  "Dining",

  public = list(
    initialize = function(name, short_name, category_code, capacity, unique_id){
      private$validate(name, short_name, category_code, capacity, unique_id)

      private$.name <- name
      private$.short_name <- short_name
      private$.category_code <- category_code
      private$.capacity <- capacity
      private$.id <- unique_id
      private$.currently_dining <- 0
    },

    add_diner = function(){
      private$.currently_dining <- private$.currently_dining + 1
      invisible(self)
    },

    remove_diner = function(){
      private$.currently_dining <- private$.currently_dining - 1

      if (private$.currently_dining <= 0){
        private$.currently_dining <- 0
      }

      invisible(self)
    }
  ),

  active = list(

    name = function(value){
      if(missing(value)){
        private$.name
      } else{
        stop("Cannot set `$value\n`")
      }
    },

    short_name = function(value){
      if(missing(value)){
        private$.short_name
      } else{
        stop("Cannot set `$short_name`\n")
      }
    },

    category_code = function(value){
      if(missing(value)){
        private$.category_code
      } else{
        stop("Cannot set `$category_code\n`")
      }
    },

    capacity = function(value){
      if(missing(value)){
        private$.capacity
      } else{
        stop("Cannot set `$capacity\n`")
      }
    },

    unique_id = function(value){
      if(missing(value)){
        private$.unique_id
      } else {
        stop("Cannot set `$unique_id`\n")
      }
    },

    service_time = function(value){
      if(missing(value)){

        #returns the service time in seconds
        if(private$.category_code == "quick-service"){
          sample(c(25, 30, 35, 40, 45, 50) *60, 1)
        } else if (private$.category_code == "table-service"){
          sample(c(45,50,55,60,65,70,75)*60, 1)
        } else {
          -1
        }
      } else {
        stop("Cannot set `$service_time`; function of `$category_code`\n")
      }
    },

    currently_dining = function(value){
      if(missing(value)){
        private$.currently_dining
      } else {
        stop("Cannot set `$currently_dining`; use add_diner() and remove_diner()\n")
      }
    }
  ),

  private = list(
    .name = NULL,
    .short_name = NULL,
    .category_code = NULL,
    .capacity = NULL,
    .id = -1,
    .currently_dining = NA,

    validate = function(name, short_name, category_code, capacity, unique_id){
      stopifnot(is.character(name))
      stopifnot(is.character(short_name))
      stopifnot(is.character(category_code))
      stopifnot(is.numeric(capacity))
      stopifnot(is.numeric(unique_id))
    }
  )
)

Testing: Unit testing performed with results available on the accompanying website (http://projects.jamesonmorgan.com/disneyworldsim/test_dining.html).

Simulation: Adding in Attractions and Dining Experiences

With a definition of an attraction and a dining experience, we now proceed to build the final simulation which includes attractions, dining experiences and non-static departure times.

Extracting the Required Data

We now must load in the data. We have compiled datasets that define the attractions and the dining experiences at the Magic Kingdom theme park. We use the following scripts to preprocess the data into a usable form.

The datasets are stored at data.world. We set the secure download URLs as follows:

magic_kingdom_attractions_path = "https://query.data.world/s/bjxzwnu7cyom6ymj3x3ker63rvv6ca"
magic_kingdom_dining_path = "https://query.data.world/s/lxpgmylxhduebtvobxe3zol3iat3np"

We now proceed to preprocess this data into a usable form.

library(foreach)

magic_kingdom_attractions_raw <- read.csv(magic_kingdom_attractions_path,
                                          stringsAsFactors = FALSE)

magic_kingdom_attractions <- foreach::foreach(i = 1:nrow(magic_kingdom_attractions_raw)) %do% {

  #create an attraction object
  #name, shortname, duration (comes in seconds) and batch size
  Attraction$new(magic_kingdom_attractions_raw[i, 1],
                 magic_kingdom_attractions_raw[i, 2],
                 magic_kingdom_attractions_raw[i, 3],
                 magic_kingdom_attractions_raw[i, 4],
                 i)
}

#extract dining experiences
magic_kingdom_dining_raw <- read.csv(magic_kingdom_dining_path,
                                     stringsAsFactors = FALSE)
magic_kingdom_dining <- foreach::foreach(i = 1:nrow(magic_kingdom_dining_raw)) %do% {

  #create an attraction object
  #name, shortname, duration (comes in minutes; convert to hours) and batch size
  Dining$new(magic_kingdom_dining_raw[i, 1],
             magic_kingdom_dining_raw[i, 2],
             magic_kingdom_dining_raw[i, 3],
             magic_kingdom_dining_raw[i, 4],
             i)
}

Complete Simulation

We now define the complete simulation of our theme park.

Loading Required Code from Earlier Attempt

Building off of our initial simulation file, we import the relevant portions of the code originally defined for use within the initial simulation. Namely,

Event codes:

event_arrive_park = 1
event_enter_park = 2
event_leave_park = 30
event_leave_dining = 31
event_leave_ride = 32
event_process_attraction = 40
event_choose_experience = 50
event_choose_attraction = 51
event_choose_dining = 52

choose_turnstile() utility function:

choose_turnstile <- function(turnstiles, rule){
  if (rule == "shortest"){
    shortest <- 1 #index into turnstiles, not necessarily turnstile id
    line_length <- turnstiles[[shortest]]$agents_waiting

    #find the first shortest line
    for (i in 1:length(turnstiles)){
      if (turnstiles[[i]]$agents_waiting < line_length){
        shortest <- i
        line_length <- turnstiles[[i]]$agents_waiting
      }
    }

    return(shortest)
  }
}

layover() utility function:

layover <- function(turnstile, time){
  return(turnstile$calculate_wait_time(time) + turnstile$service_time)
}

turnstile class:

Turnstile <- R6::R6Class(
  "Turnstile",
  inherit = SimpleQueue
)

SimpleQueue class:

SimpleQueue <- R6::R6Class(
  "SimpleQueue",

  public = list(
    initialize = function(id, service_time){

      #initialize with unique turnstile id and zero agents waiting
      private$.id <- id
      private$.service_time <- service_time
      private$.agents_waiting <- 0
    },

    add_agent = function(current_time){
      if(!missing(current_time)){
        private$.agents_waiting <- private$.agents_waiting + 1

        if(is.na(private$.service_complete_at)){
          private$.service_complete_at <- current_time + private$.service_time
        }
      } else {
        stop("Cannot add agent without knowing the current time\n")
      }
      invisible(self)
    },

    remove_agent = function(){

      private$.agents_waiting = private$.agents_waiting - 1
      private$.service_complete_at <- private$.service_complete_at + private$.service_time

      if (private$.agents_waiting <= 0){
        private$.agents_waiting = 0
        private$.service_complete_at <- NA
      }

      invisible(self)
    },

    calculate_wait_time = function(current_time){
      if(missing(current_time)){
        stop("Cannot calculate current wait time without current time\n")
      } else {
        current_wait_time <- (private$.service_time * (private$.agents_waiting - 1)) +
          (private$.service_complete_at - current_time)

        #if we return a negative wait time, that means no one is in line, so
        #replace with zero
        if (is.na(current_wait_time) || current_wait_time < 0){
          current_wait_time <- 0
        }

        return(current_wait_time)
      }
    }
  ),

  active = list(
    id = function(value){
      if(missing(value)){
        private$.id
      } else{
        stop("Cannot set `$turnstile_id` after instantiation\n")
      }
    },

    service_time = function(value){
      if(missing(value)){
        private$.service_time
      } else{
        stop("Cannot change `$service_time` after instantiation\n")
      }
    },

    agents_waiting = function(value){
      if(missing(value)){
        private$.agents_waiting
      } else {
        stop("Cannot set `$agents_waiting`\n")
      }
    },

    service_complete_at = function(value){
      if(missing(value)){
        private$.service_complete_at
      } else{
        stop("cannot set `$service_complete_at`, use `$add_agent\n`")
      }
    }
  ),

  private = list(
    .id = -1,
    .service_time = -1,
    .agents_waiting = -1,
    .service_complete_at = NA
  )
)

Event record class:

Event <- R6::R6Class(
  "Event",

  public = list(
    initialize = function(agent_id = NA, trigger_time, arrive_park = NA, event_type,
                          remaining_attractions=NA, turnstile_chosen = NA,
                          remaining_dining = NA, attractions_visited = NA,
                          dining_visited = NA, attraction_index = NA){
      private$.agent_id <- agent_id
      private$.event_type <- event_type
      private$.trigger_time <- trigger_time
      private$.arrive_park <- arrive_park
      private$.remaining_attractions <- remaining_attractions
      private$.turnstile_chosen <- turnstile_chosen
      private$.remaining_dining <- remaining_dining
      private$.attractions_visited <- attractions_visited
      private$.dining_visited <- dining_visited
      private$.attraction_index <- attraction_index
      private$.data <- list()
    }
  ),

  active = list(
    agent_id = function(value){
      if(missing(value)){
        private$.agent_id
      } else{
        stop("Cannot set `$agent_id`\n")
      }
    },

    event_type = function(value){
      if(missing(value)){
        private$.event_type
      } else {
        private$.event_type <- value
      }
    },

    trigger_time = function(value){
      if(missing(value)){
        private$.trigger_time
      } else {
        private$.trigger_time <- value
      }
    },

    arrive_park = function(value){
      if(missing(value)){
        private$.arrive_park
      } else{
        stop("Cannot change `$arrive_park` after instantiation\n")
      }
    },

    retired = function(value){
      if(missing(value)){
        private$.retired
      } else{
        private$.retired <- value
      }
    },

    remaining_attractions = function(value){
      if(missing(value)){
        private$.remaining_attractions
      } else {
        private$.remaining_attractions <- value
      }
    },

    turnstile_chosen = function(value){
      if(missing(value)){
        private$.turnstile_chosen
      } else {
        private$.turnstile_chosen <- value
      }
    },

    remaining_dining = function(value){
      if(missing(value)){
        private$.remaining_dining
      } else{
        private$.remaining_dining <- value
      }
    },

    attractions_visited = function(value){
      if(missing(value)){
        Filter(Negate(is.na),private$.attractions_visited)
      } else{
        private$.attractions_visited <- c(private$.attractions_visited, value)
      }
    },

    dining_visited = function(value){
      if(missing(value)){
        Filter(Negate(is.na),private$.dining_visited)
      } else{
        private$.dining_visited <- c(private$.dining_visited, value)
      }
    },

    attraction_index = function(value){
      if(missing(value)){
        private$.attraction_index
      } else{
        private$.attraction_index <- value
      }
    },

    data = function(value){
      if(missing(value)){
        private$.data
      } else{
        private$.data <- append(private$.data, value)
      }
    }
  ),

  private = list(
    .agent_id = -1,
    .event_type = -1,
    .trigger_time = NA,
    .arrive_park = NA,
    .remaining_attractions = -1,
    .retired = FALSE,
    .turnstile_chosen = NA,
    .remaining_dining = NA,
    .attractions_visited = NA,
    .dining_visited = NA,
    .attraction_index = NA,
    .data = NULL
  )
)

get_daily_average() function:

get_daily_average <- function(quarter){
  #attendance numbers
  year_disney_total_2017 <- 20450000
  year_tourism_total_2017 <- 118756000
  q1_tourism_2017 <- 31891000
  q2_tourism_2017 <- 30017000
  q3_tourism_2017 <- 27854000
  q4_tourism_2017 <- 28993000

  #days in quarters
  q1 <- 90
  q2 <- 91
  q3 <- 92
  q4 <- 92

  #percentage of Florida tourists visiting mk
  per_visit_mk <- year_disney_total_2017/year_tourism_total_2017

  #quarterly totals
  q1_disney_2017 <- q1_tourism_2017 * per_visit_mk
  q2_disney_2017 <- q2_tourism_2017 * per_visit_mk
  q3_disney_2017 <- q3_tourism_2017 * per_visit_mk
  q4_disney_2017 <- q4_tourism_2017 * per_visit_mk

  #quarterly daily totals
  q1_day_avg_disney_2017 <- as.integer(q1_disney_2017 / q1)
  q2_day_avg_disney_2017 <- as.integer(q2_disney_2017 / q2)
  q3_day_avg_disney_2017 <- as.integer(q3_disney_2017 / q3)
  q4_day_avg_disney_2017 <- as.integer(q4_disney_2017 / q4)

  switch(quarter,
         "q1" = return(q1_day_avg_disney_2017),
         "q2" = return(q2_day_avg_disney_2017),
         "q3" = return(q3_day_avg_disney_2017),
         "q4" = return(q4_day_avg_disney_2017))
}

get_attendance() function:

get_attendance <- function(num_to_sample, quarter){
  sd = 10000
  attendance <- get_daily_average(quarter)
  return(as.integer(rnorm(num_to_sample, attendance, sd)))
}

generate_arrivals() function:

generate_arrivals <- function(num_of_arrivals, begin, end, probs){

  #for each time interval, generate the arrival times of the agents
  results <- mapply(function(i){
    sample(begin[i]:end[i], num_of_arrivals*probs[i], replace = TRUE)
  }, 1:length(begin), SIMPLIFY = TRUE)

  #unlist the results to turn it into a vector
  results <- sort(unlist(results))
}

Generate Agent Arrivals

Next, we setup the agent arrivals.

#set the operating quarter and grab the attendance
quarter <- "q2"
num_of_arrivals <- get_attendance(1, quarter) #1 indicates we want a single value returned

Then we generate the arrivals in accordance with the arrival distribution.

#set the begin and ending times along with the percentage of agents expected during that interval
begin = c(0, 3, 6, 12) * 60 * 60 #time in seconds
end = c(3, 6, 12, 13) * 60 * 60 #time in seconds
probs = c(0.15, 0.7, 0.14, 0.01)

#generate agent arrivals
agent_arrivals <- generate_arrivals(num_of_arrivals, begin, end, probs)

Simulation Setup

Lastly, we setup the simulation. Notice that we load the attraction processing events into the master event queue with their first processing occurring at their duration. Thereafter, each attraction processes itself when triggered and sets it’s future processing event by adding its duration to the current time. This is done so that the simulation of an agent attending an attraction can be handled with a single event queue. If attractions did not have processing events, the handling of agents would have to occur in separate queues for each attraction, complicating the design of the simulation.

#parameters for the generate_route_length() function
route_length_mean = 10 #average number of attractions to visit
route_length_std = 2
required_dining = 1
constant_departure = 10*60 #10 minutes

#set the simulation end time
simulation_end_time = 0.5*60*60 #1/2 hour

#set the turnstile service time
turnstile_service_time = 10 #10 seconds

#define the number of turnstiles to keep open
num_of_turnstiles <- 10
turnstile_rule <- "shortest"

#log info
logging = TRUE
filepath = file.path("..","..","logs","sim_log.txt")

#instantiate turnstiles
turnstiles <- mapply(function(i){
    Turnstile$new(i, turnstile_service_time)
  }, 1:num_of_turnstiles)

#setup master event queue
master_event_queue <- datastructures::fibonacci_heap("integer")

#initialize attractions by scheduling the first event
#instantiate a progress bar
pb <- progress::progress_bar$new(total = length(magic_kingdom_attractions))

#load master event queue with the attraction's next pickup of agents (i.e. the duration)
invisible(
  mapply(function(i){
    event <- Event$new(trigger_time = magic_kingdom_attractions[[i]]$duration,
                       event_type = event_process_attraction,
                       attraction_index = i)
    datastructures::insert(master_event_queue, event$trigger_time, event)
    pb$tick()
  }, 1:length(magic_kingdom_attractions))
)

#instantiate a progress bar
pb <- progress::progress_bar$new(total = length(agent_arrivals))

#load master event queue with arrivals
invisible(
  mapply(function(i){
  datastructures::insert(master_event_queue, as.integer(agent_arrivals[i]), 
                         Event$new(agent_id = i, 
                                   trigger_time = agent_arrivals[i], 
                                   arrive_park = agent_arrivals[i],
                                   event_type = event_arrive_park,
                                   remaining_attractions = 
                                     generate_route_length(1, route_length_mean,
                                                           route_length_std),
                                   remaining_dining = required_dining
                                   ))
  pb$tick()
  }, 1:length(agent_arrivals))
)
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Running the Simulation

We can now run the simulation.

#instantiate current time by setting it equal to the very first item in the master event queue
cur_time = datastructures::peek(master_event_queue)[[1]]$trigger_time

write(paste("cur_time", "agent_id", "attr_index","trig_event_type", "next_trigger_time",
            "next_event_type", "turnstile_chosen", "rem_attractions", "rem_dining",
            "attr_visited", "dining_visited", "arrive_park","retired",
            sep = ","), file = filepath)

#perform the simulation until we go past the simulation end time or we run out of simulation events
while (!is.null(cur_time) && (cur_time < simulation_end_time)){

  #grab the next event record
  event <- datastructures::pop(master_event_queue)[[1]]

  #output the current time so you can know where in the simulation you are
  if (logging){
    cat(paste("\r\014Current Time:", cur_time))
    triggering_event_type <- event$event_type
  }

  if (event$event_type == event_arrive_park){
    #agent has arrived at park so,

    #pick the shortest line and add it to the event record
    shortest_line <- choose_turnstile(turnstiles, turnstile_rule)
    event$turnstile_chosen <- shortest_line

    #schedule next event
    event$event_type <- event_enter_park
    event$trigger_time <- event$trigger_time + layover(turnstiles[[shortest_line]], cur_time)

    #place the agent into the line
    turnstiles[[shortest_line]]$add_agent(cur_time)

  }

  else if (event$event_type == event_enter_park){
    #agent has entered park so,

    #remove agent from turnstile line
    turnstiles[[event$turnstile_chosen]]$remove_agent()

    #schedule next event (immediately upon entry)
    event$event_type <- event_choose_experience

  }

  else if (event$event_type == event_choose_experience){

    # if we still have to dine, determine if that time is now
    #experience_chosen = 0: choose attraction experience
    #experience_chosen = 1: choose dining experience
    #experience_chosen = -1: terminate
    if(event$remaining_dining > 0){
      #if we still have attractions remaining to visit, make the dining choice
      #based on a bionomial
      if (event$remaining_attractions > 0){
        #determine whether to visit an attraction or dining experience
        #based on bionomial distribution
        experience_chosen = rbinom(1, 1, 0.5)
      } else {
        #otherwise, all attractions have been visited so the only remaining
        #thing is to eat
        experience_chosen = 1
      }
    } else if (event$remaining_attractions > 0) {
      experience_chosen = 0
    } else {
      experience_chosen = -1
    }

    #determine where to send the event
    if (experience_chosen == 0){
      event$event_type <- event_choose_attraction
    } else if (experience_chosen == 1){
      event$event_type <- event_choose_dining
    } else {
      #change the event type as we are now ready to terminate after the constant
      #departure time
      event$event_type <- event_leave_park
      event$trigger_time <- event$trigger_time + constant_departure
    }
  }

  else if (event$event_type == event_choose_attraction){

      #randomly pick an attraction
      attraction_index <- sample.int(length(magic_kingdom_attractions), 1)

      #log which attraction we visited
      event$attractions_visited <- attraction_index

      #reduce the number of attraction
      event$remaining_attractions <- event$remaining_attractions - 1

      #retire the event
      event$retired <- TRUE
      event$trigger_time <- NA
      event$event_type <- event_leave_ride

      #add agent to attraction queue
      #note: if the `agent_id` field of the event is defined, the event record
      #doubles as an agent
      magic_kingdom_attractions[[attraction_index]]$line$add_agent(event)

  }

  else if (event$event_type == event_choose_dining){

    #randomly pick a dining experience
    dining_index <- sample.int(length(magic_kingdom_dining), 1)

    #determine the dining category
    cat_code <- magic_kingdom_dining[[dining_index]]$category_code

    #determine whether we have to check capacity
    if (cat_code == "table-service"){
      capacity <- magic_kingdom_dining[[dining_index]]$capacity
      cur_dining <- magic_kingdom_dining[[dining_index]]$currently_dining
      if(cur_dining < capacity){
        #log which dining experience was visited
        event$dining_visited <- dining_index

        #reduce the number of dining experiences
        event$remaining_dining <- event$remaining_dining - 1

        #add diner
        magic_kingdom_dining[[dining_index]]$add_diner()

        #draw service time
        service_time <- magic_kingdom_dining[[dining_index]]$service_time

        #set trigger time and next event type
        event$event_type <- event_leave_dining
        event$trigger_time <- event$trigger_time + service_time
      } else {
        #cannot dine at dining experience because of capacity, go back and choose
        #another experience
        event$event_type <- event_choose_experience
      }
    } else if (cat_code == "quick-service"){
      #log which dining experience was visited
      event$dining_visited <- dining_index

      #reduce the number of dining experiences
      event$remaining_dining <- event$remaining_dining - 1

      #draw service time
      service_time <- magic_kingdom_dining[[dining_index]]$service_time

      #set trigger time and next event type
      event$event_type <- event_choose_experience
      event$trigger_time <- event$trigger_time + service_time
    } else {
      stop("Invalid category code!")
    }

  }

  else if (event$event_type == event_leave_dining){
    #remove the diner
    magic_kingdom_dining[[event$dining_visited]]$remove_diner()
    event$event_type <- event_choose_experience
  }

  else if (event$event_type == event_leave_park){
    #agent is leaving park so,

    event$event_type <- -1
    event$trigger_time <- NA
    event$retired <- TRUE

  }

  else if (event$event_type == event_process_attraction){
    #an attraction needs to be processed so,

    #grab the attraction index, attraction batch size and the previous line size
    #(those waiting prior to the attraction departure)
    attraction_index <- event$attraction_index
    batch_size <- magic_kingdom_attractions[[attraction_index]]$batch_size
    previous_line_size <- magic_kingdom_attractions[[attraction_index]]$line$num_of_agents

    #simulate the attraction running by removing the waiting agents
    finished_agents <- magic_kingdom_attractions[[attraction_index]]$line$remove_agent(batch_size)

    #now, we have to reschedule all the popped off events
    if (length(finished_agents) > 0){
      invisible(mapply(function(i){

        #grab the ith event and,
        finished_event <- finished_agents[[i]]

        #update the next event type,
        finished_event$event_type <- event_leave_ride

        #come out of retirement (for the event gets added to the master event queue),
        finished_event$retired <- FALSE

        #set the trigger time for the above event
        #remember, we still have to simulate the ride by incorporating the duration
        #of the ride into the next trigger time
        finished_event$trigger_time <- cur_time +
          (magic_kingdom_attractions[[attraction_index]]$duration)

        #insert into master event queue
        datastructures::insert(master_event_queue,
                               finished_event$trigger_time,
                               finished_event)
      }, 1:length(finished_agents)))
    }

    #schedule the next attraction event
    #this is equal to the current time plus the duration of the ride
    event$trigger_time <- cur_time +
      (magic_kingdom_attractions[[attraction_index]]$duration)

  }

  else if (event$event_type == event_leave_ride){
    #agent has riden the ride, choose another experience

    event$event_type <- event_choose_experience
  }

  else{
    stop("Unknown event type\n")
  }

  #print(paste(cur_time, event$attractions_visited))

  #outputs the contents of the event record if logging is enabled
  if (logging){
    write(paste(cur_time, event$agent_id, event$attraction_index,
                triggering_event_type, event$trigger_time,
                event$event_type, event$turnstile_chosen, event$remaining_attractions,
                event$remaining_dining,
                stringi::stri_c(event$attractions_visited, collapse = " "),
                stringi::stri_c(event$dining_visited, collapse = " "),
                event$arrive_park, event$retired,
                sep = ","),
          file=filepath, append = TRUE)
  }

  #add the event record back to the priority queue if the event has not been
  #retired (i.e. the agent has left)
  if(!event$retired){
    datastructures::insert(master_event_queue, as.integer(event$trigger_time), event)
  }

  #advance time to the next event epoch
  cur_time <- datastructures::peek(master_event_queue)[[1]]$trigger_time
}
## 
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Results for a Single Agent

For the above, we ran the simulation for an hour with 10 open turnstiles. Obviously, the size of the log file is very large. For this reason, we only include the first 6000 rows of the data table.

results <- read.csv("../../logs/sim_log.txt")
only_agents <- results[results$next_event_type != 40,]
DT::datatable(results[1:6000,])

Next Steps

Next, we propose two “what-if” questions and run the above simulations in order to answer the questions proposed earlier.