# Single server queueing simulation
# 0. Save this file into a directory as queue1.r
# 1. Download R from http://www.r-project.org/
# 2. Run R; File -> Change directory to the directory including this file 
# 3. At the R prompt, issue source("queue1.r") to make R read queue1.r
# 4. Try simulating a queue with exponential intearrival and service times 
#    where "a"=average interarrivval time; "p"=average service time
#    for "numarrivals" many arrivals
#    For example, queue1(2,1,100) simulates 100 customers with 
#    average interarrival time of 2 and service time of 1
#    More examples 
# > queue1(5,1,1000000)
#   Utilization TimeInQueue TimeInSystem NumberInQueue NumberInSystem
# 1   0.2001452   0.2501673     1.250167    0.04998645      0.2499865
# > queue1(2,1,1000000)
#   Utilization TimeInQueue TimeInSystem NumberInQueue NumberInSystem
# 1   0.4997648    1.006667     2.006667     0.5033223       1.003322

queue1 <- function(a, p, numarrivals) {

wait_time  <- 0;          # waiting time excluding service time
total_wait_time <- 0;     # total waiting time
total_idle_time <- 0;     # total idle time
total_arrival_time <- 0;  # total arrival time
# Suppose that the queue already has a customer who arrived at time total_arrival_time=0
# Name this customer as customer 0

for (i in 1:numarrivals) {

  service_time <- rexp(1, 1/p);      # service time of customer i-1
  interarival_time <- rexp(1, 1/a);  # interarrival time between customer i-1 and i

  total_arrival_time <- total_arrival_time + interarival_time;  # advancing the clock from total_arrival_time to total_arrival_time+interarival_time
  wait_time  <- wait_time - interarival_time + service_time;    # wait_time-interarival_time+service_time is custoimer i's waiting time given that customer (i-1) waited for wait_time time
  # if wait_time>=0, it is the work found by customer i
  # if wait_time<0, it is the server idle time between finishing customer i-1 and starting customer i

  if (wait_time >= 0)
    total_wait_time <- total_wait_time + wait_time    # total_wait_time includes the waiting time of the (i)th customer 
  else {
    total_idle_time <- total_idle_time - wait_time;   # the (i)th customer does not experince wait but finds service idle
    wait_time  <- 0;                                  # since the queue is idle, customer i waiting time is zero
    }
  }
  
result <- data.frame(Utilization=1-total_idle_time/total_arrival_time,
		     TimeInQueue=total_wait_time/numarrivals,
		     TimeInSystem=total_wait_time/numarrivals+p,
		     NumberInQueue=total_wait_time/total_arrival_time,      
		     NumberInSystem=total_wait_time/total_arrival_time+p/a);
return(result)   
}