Extended Example: Discrete-Event Simulation in R
Discrete-event simulation (DES) is a technique for modeling systems where state changes occur at discrete points in time. In R, you can simulate such systems using functions, loops, and random number generation. Let’s delve into a more detailed example of discrete-event simulation in R.
Scenario: Event Simulation for a Queuing System
Consider a simple queuing system where customers arrive at a service center and wait for service. The goal is to simulate this process over a period to understand metrics like average wait time and queue length.
Define the Parameters
First, define the parameters for the simulation:
- Arrival Rate: The average number of customers arriving per unit time.
- Service Rate: The average number of customers served per unit time.
- Simulation Time: The total time to run the simulation.
arrival_rate <- 5 # customers per unit time service_rate <- 4 # customers per unit time simulation_time <- 100 # total time for simulation
Initialize Variables
Set up variables to keep track of the queue, event times, and statistics.
queue <- numeric() # Queue to store waiting times arrival_times <- numeric() # Record of customer arrival times service_times <- numeric() # Record of service start times current_time <- 0 # Simulation time counter next_arrival <- rexp(1, rate = arrival_rate) # Time of next arrival next_departure <- Inf # Time of next departure
Simulate the System
Use a loop to run the simulation. In each iteration, determine which event (arrival or departure) occurs next.
while (current_time < simulation_time) {
if (next_arrival < next_departure) {
# Process arrival
current_time <- next_arrival
arrival_times <- c(arrival_times, current_time)
queue <- c(queue, current_time) # Add arrival time to the queue
# Schedule the next arrival
next_arrival <- current_time + rexp(1, rate = arrival_rate)
# Start service if queue was not empty
if (length(queue) == 1) {
next_departure <- current_time + rexp(1, rate = service_rate)
}
} else {
# Process departure
current_time <- next_departure
service_times <- c(service_times, current_time)
# Remove the first customer from the queue
queue <- queue[-1]
# Schedule the next departure if queue is not empty
if (length(queue) > 0) {
next_departure <- current_time + rexp(1, rate = service_rate)
} else {
next_departure <- Inf # No departure if queue is empty
}
}
}
Analyze Results
After the simulation, analyze the results to compute metrics like average wait time and queue length.
# Calculate waiting times
waiting_times <- service_times - arrival_times[1:length(service_times)]
# Average waiting time
avg_waiting_time <- mean(waiting_times)
cat("Average Waiting Time:", avg_waiting_time, "\n")
# Queue length over time
queue_length <- sapply(seq(0, simulation_time, by = 1), function(t) sum(arrival_times <= t & service_times > t))
plot(seq(0, simulation_time, by = 1), queue_length, type = "l", xlab = "Time", ylab = "Queue Length", main = "Queue Length Over Time")
Summary
- Parameters: Set arrival rate, service rate, and simulation time.
- Initialization: Create variables to track arrivals, services, and queue status.
- Simulation Loop: Use a loop to process arrivals and departures based on time.
- Analysis: Calculate metrics like average waiting time and plot queue length.