Math 538 HW1 Textbook #1.9

Textbook 1.9

hospital.sim <- function(NUMSIM) {
  sim.num.patients <- rep(0, NUMSIM)
  sim.n.waited <- rep(0, NUMSIM)
  sim.average.wait.time <- rep(0, NUMSIM)
  sim.office.close <- rep(0, NUMSIM)
  lambda = 1/10
  minutes.in.workday = 7 * 60 # 7 hours times 60min/hr
  for(k in 1:NUMSIM) {
    inter.times = rexp(n=1000, rate=lambda)
    arrival.times = cumsum(inter.times) #minutes after 4pm
    arrival.times = arrival.times[arrival.times <= minutes.in.workday]
    
    #i.) Number of patients came to office
    number.patients = length(arrival.times)
    
    n.waited <- 0 #number of patients that needed to wait at some point
    wait.patient <- rep(0, number.patients)
    doctor.available.at <- c(0,0,0) #all doctors start with availability at start time of clinic
    
    for(i in 1:number.patients) {
      #select doctor index
      doctor.j = which.min(doctor.available.at)
      if(min(doctor.available.at) - arrival.times[i] > 0) {
        wait.patient[i] = min(doctor.available.at) - arrival.times[i] 
        n.waited = n.waited + 1
      } else {
        wait.patient[i] = 0
      }
      
      appt.start <- max(min(doctor.available.at), arrival.times[i])
      appt.end <- appt.start + runif(1, min=5, max=20)
      
      #update doctors next available time. the one that worked on patient i
      doctor.available.at[doctor.j] <- appt.end
    } #end inner for loop
    
    if(n.waited > 0) {
      average.wait.time = sum(wait.patient)/n.waited
    } else {
      average.wait.time = 0
    }
    
    office.close <- appt.end
    
    sim.num.patients[k] <- number.patients
    sim.n.waited[k] <- n.waited
    sim.average.wait.time[k] <- average.wait.time
    sim.office.close[k] <- office.close - 420
  }
  return.list = list(num.patients = sim.num.patients, n.waited=sim.n.waited, average.wait = sim.average.wait.time, office.closed = sim.office.close)
  return(return.list)
}

set.seed(100)
lambda <- 1/10
NUMSIM <- 100
answer = hospital.sim(NUMSIM)

Our 50% median results can be seen below in the following order:
Number of Patients
Number of Patients that Waited
Average Wait Time
Minutes after 4pm the clinic closed

quantile(answer$num.patients, 0.50)

## 50% 
##  42

quantile(answer$n.waited, 0.50)

## 50% 
##   6

quantile(answer$average.wait, 0.50)

##      50% 
## 3.629005

quantile(answer$office.closed, 0.50)

##      50% 
## 4.838912