INFSCI0610 Project 1

Part 1: Simulation

Part 1-1

simulation = function(N, p, rounds){
  for (x in 1:rounds){
    num_active = rbinom(N, 1, p)
  }
  return(mean(num_active)/N)
}
N = c(4, 8)
p = c(0.25, 0.5, 0.75)
rounds = 1000

table = matrix(nrow = length(N), ncol = length(p))
for (x in 1:length(N)){
  for (y in 1:length(p)){
    table[x, y] = simulation(N[x], p[y], rounds)
  }
}
print("Avg Fraction of active users in a time period")

## [1] "Avg Fraction of active users in a time period"

colnames(table) = c("p=0.25", "p=0.5", "p=0.75")
rownames(table) = c("N=4", "N=8")
print(table)

##       p=0.25   p=0.5  p=0.75
## N=4 0.062500 0.12500 0.25000
## N=8 0.046875 0.09375 0.09375

print("Avg Number of active users in a time period")

## [1] "Avg Number of active users in a time period"

simulation = function(N, p, rounds){
  sum_active <- numeric(rounds)
  for (x in 1:rounds){
    active = rbinom(N, 1, p)
    sum_active[x] <- sum(active)
  }
  return(sum(sum_active)/N)
}

N = c(4, 8)
p = c(0.25, 0.5, 0.75)
rounds = 1000

table = matrix(nrow = length(N), ncol = length(p))
for (x in 1:length(N)){
  for (y in 1:length(p)){
    table[x, y] = simulation(N[x], p[y], rounds)
  }
}
colnames(table) = c("p=0.25", "p=0.5", "p=0.75")
rownames(table) = c("N=4", "N=8")
print(table)

##     p=0.25 p=0.5 p=0.75
## N=4 250.25 488.5 740.25
## N=8 248.50 502.5 738.00

Part 2-2

simulation = function(N, p, rounds){
  num_blocked = numeric(rounds)

  for (x in 1:rounds){
    num_active = rbinom(N, 1, p)

    if (sum(num_active)>2){
      rand_num = sample(1:10, N, replace = TRUE)
      sorted_rand_num = sort(rand_num)
      lowest = sorted_rand_num[1:2]
    }  
    else{
      lowest = numeric(0)
    }
    
    num_blocked[x] = sum(num_active[-lowest])
    
  }
  return(mean(num_blocked)/N)
}

N = c(4, 8)
p = c(0.25, 0.5, 0.75)
rounds = 1000

table = matrix(nrow = length(N), ncol = length(p))
for (x in 1:length(N)){
  for (y in 1:length(p)){
    table[x, y] = simulation(N[x], p[y], rounds)
  }
}

print("Avg Fraction of Blocked Users")

## [1] "Avg Fraction of Blocked Users"

colnames(table) = c("p=0.25", "p=0.5", "p=0.75")
rownames(table) = c("N=4", "N=8")
print(table)

##      p=0.25    p=0.5 p=0.75
## N=4 0.02825 0.168250  0.425
## N=8 0.10900 0.372125  0.604

#######################
simulation = function(N, p, rounds){
  num_blocked = numeric(rounds)

  for (x in 1:rounds){
    num_active = rbinom(N, 1, p)

    if (sum(num_active)>2){
      rand_num = sample(1:10, N, replace = TRUE)
      sorted_rand_num = sort(rand_num)
      lowest = sorted_rand_num[1:2]
    }  
    else{
      lowest = numeric(0)
    }
    
    num_blocked[x] = sum(num_active[-lowest])
    
  }
  return(sum(num_blocked)/N)
}

table = matrix(nrow = length(N), ncol = length(p))
for (x in 1:length(N)){
  for (y in 1:length(p)){
    table[x, y] = simulation(N[x], p[y], rounds)
  }
}

print("Avg Number of Blocked Users")

## [1] "Avg Number of Blocked Users"

colnames(table) = c("p=0.25", "p=0.5", "p=0.75")
rownames(table) = c("N=4", "N=8")
print(table)

##     p=0.25 p=0.5  p=0.75
## N=4   30.5 176.0 427.500
## N=8  106.0 376.5 594.875

The numbers I got from part 2 are generally smaller than the numbers from part 1.