Simulating trick-or-treaters as a Poisson Process

halloweenPoissonProcess

# Load library
library(ggplot2)

# ToT = Trick-or-Treators
tEnd = 3*60*60 # 3 hours (in seconds)
lambdaMin = 1 # Define the rate as 1 ToT per minute
lambdaSec = lambdaMin/60 # converted rate in ToT per second

# Randomly inter-arrival times between ToT using an exponential distribution
t = 0; k = 0
times = NULL
while(t < tEnd){
	u = runif(1, 0, 1)
	t = t - log(u)/lambda
	k = k + 1
	times = c(times, t)
}
times = round(times)

# Histogram of interarrival times and their frequency
start = ISOdate(2014, 10, 31, 5, 30, 0, tz = "")
qplot(start + times, binwidth = 60*2, xlab = "Halloween Night", 
		ylab = "Number of Trick-or-Treaters", 
		main = "Trick-or-Treaters as a Poisson Process")