Compare two approaches to managing Q&A queues

q-and-a.R

library(tidyverse)

## Parameters ----
## How many people have questions? 
n_questions = 30
## How many questions will actually get answered? 
max_questions = 15
## How many times to run the simulation? 
N = 500

set.seed(2023-10-13)

#' Draw a random set of "questions"
#' 
#' "Questions" are represented by their quality, drawn from a distribution of interest
#' @param n Number of questions to draw
#' @param distf Distribution of question quality, as a random deviate function such as `runif` or `rnorm`
#' @param ... Arguments passed to the distribution function
#' @returns Vector of quality values
rquestions = function(n, distf = runif, ...) {
    distf(n, ...)
}
rquestions(n_questions)

## Simulate Q&A: Default approach ----
qa_default = function(n_questions, max_questions, N) {
    one_sim = function(n_questions, max_questions) {
        dataf = tibble(quality = rquestions(n_questions)) |> 
            slice_head(n = max_questions)
        mean(dataf$quality)
    }
    map_dbl(1:N, one_sim)
}

default = qa_default(n_questions, max_questions, N)
summary(default)
##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
## 0.001636 0.224704 0.459936 0.480693 0.729205 0.999136 

## Simulate Q&A: Randomize approach ----
qa_random = function(n_questions, max_questions, N) {
    one_sim = function(n_questions, max_questions) {
        dataf = tibble(quality = rquestions(n_questions)) |> 
            slice_sample(n = max_questions)
        mean(dataf$quality)
    }
    map_dbl(1:N, one_sim)
}

random = qa_random(n_questions, max_questions, N)
summary(random)
##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
## 0.005136 0.253719 0.493340 0.492655 0.726744 0.998494