Writing recursion function for probability - r

Question

I am trying to find where the probability reaches a certain point; then, the function will return the value responsible for this probability.
The function I wrote takes two arguments
p represents the number of CPUs
q the number of jobs processed by each CPU
The function wants to optimise the number of CPUs in a server that will guarantee a 0.9 probability that each CPU will handle only one job simultaneously. Therefore, the number of processors (p) needs to be > the number of jobs (q).
opcpu <- function(p,q){
if (p < q){
paste("The number of processors should be",q," or more")
} else {
prob = prod(p:(p-(q-1)))/p^q
while (prob < 0.9){
p = p + 1
opcpu(p,q)
}
return(p)
}
}
I wrote the function as a recursion function. But it seems there is something wrong.
I tried to run the function, but it is not working. Solving the problem by trial and error gives that p = 631 when q = 12.

Answer 1

You’re on the right track. Try using if instead of while, and returning either p or a recursive call:
opcpu <- function(p,q) {
if (p < q) {
stop("The number of processors should be", q, " or more")
}
prob <- prod(p:(p-(q-1)))/p^q
if (prob < 0.9) {
opcpu(p+1,q)
} else {
p
}
}
opcpu(12,12)
# 631
Or you could use while instead of recursion:
opcpu <- function(p,q) {
if (p < q) {
stop("The number of processors should be", q, " or more")
}
prob <- prod(p:(p-(q-1)))/p^q
while (prob < 0.9){
p <- p + 1
prob <- prod(p:(p-(q-1)))/p^q
}
p
}
opcpu(12,12)
# 631
Note, I changed your paste() to stop(), since it seems you’re trying to indicate that p < q isn’t valid input. Another option would be to just start testing at p = q if the input is missing or less than q:
opcpu <- function(p,q) {
if (missing(p) || p < q) p <- q
prob <- prod(p:(p-(q-1)))/p^q
if (prob < 0.9) {
opcpu(p+1,q)
} else {
p
}
}
opcpu(q = 12)
# 631