Simulate_Simple_Queue<-function(Customers,n_cust) {
  for (i in c(1:n_cust)) {
    if (i==1) {
      Customers$AT[i]<-0+Customers$IAT[i] #ARRIVAL TIME
      Customers$TSB[i]<-0                 #TIME SERViCE BEGINS
      Customers$TWQ[i]<-0                 #WAITING TIME IN QUEUE
      Customers$TSE[i]<-Customers$TSB[i]+Customers$ST[i] #TIME SERVICE ENDS
      Customers$TIS[i]<-Customers$TSE[i]-Customers$AT[i] #TOTAL TIME IN SYSTEM
      Customers$IDTS[i]<-0 #IDLE TIME OF THE SERVER
    } else {
      Customers$AT[i]<-Customers$AT[i-1]+Customers$IAT[i] #ARRIVAL TIME
      Customers$TSB[i]<-max(Customers$AT[i],Customers$TSE[i-1]) #TIME SERViCE BEGINS
      Customers$TWQ[i]<-Customers$TSB[i]-Customers$AT[i] #WAITING TIME IN QUEUE
      Customers$TSE[i]<-Customers$TSB[i]+Customers$ST[i] #TIME SERVICE ENDS
      Customers$TIS[i]<-Customers$TSE[i]-Customers$AT[i] #TOTAL TIME IN SYSTEM
      Customers$IDTS[i]<-Customers$TSB[i]-Customers$TSE[i-1] #IDLE TIME OF THE SERVER
    }
  }
  return(Customers)
}

Simple_Queue_Stats<-function(Customers) {
  queue_stats<-data.frame(TST=0,AWT=0,Pr_W=0,Pr_I=0,AST=0,ATBA=0,AWT_C=0,ATS=0)
  n<-length(Customers$TSE) # CUSTOMERS
  queue_stats$TST<-Customers$TSE[n] #TOTAL SIMULATION TIME
  queue_stats$AWT<-mean(Customers$TWQ) #AVERAGE WAITING TIME
  queue_stats$Pr_W<-length(which(Customers$TWQ>0))/n #PROB CUSTOMER HAS TO WAIT
  queue_stats$Pr_I<-sum(Customers$IDTS)/queue_stats$TST #PROB SERVER IS IDLE
  queue_stats$AST<-mean(Customers$ST) #AVERAGE SERVICE TIME
  queue_stats$ATBA<-mean(Customers$IAT) #AVERAGE TIME BETWEEN ARRIVALS
  queue_stats$AWT_C<-mean(Customers$TWQ[which(Customers$TWQ>0)]) #AVERAGE WAITING TIME OF THOSE CUSTOMERS THAT WAIT
  queue_stats$ATS<-mean(Customers$TIS) #AVERAGE TIME IN THE SYSTEM
  return(queue_stats)
}

n<-10
The_Customers = data.frame(AT=replicate(n,0),            # Arrival Time
                           IAT=replicate(n,0),           # Inter Arrival Time
                           ST=replicate(n,0),            # Service Time
                           TSB = replicate(n,0),         # Time Service beings
                           TWQ = replicate(n,0),         # Waiting Time in the Queue
                           TSE = replicate(n,0),         # Time Service Ends
                           TIS = replicate(n,0),         # Time in System
                           IDTS = replicate(n,0))        # Idel Time of Server

The_Customers$IAT<-c(0,3,1,3,7,2,3,7,9,3)
The_Customers$ST<-c(2,5,2,3,2,7,3,2,1,7)
The_Customers<-Simulate_Simple_Queue(The_Customers,n)
The_Customers_Stats<-Simple_Queue_Stats(The_Customers)

The_Customers
The_Customers_Stats