2.6.9

Theoretical

MM1 <- function(m_int, m_serv, sd){
  lambda <- 1 / m_int                                                   # Mean rate of arrival (lambda)
  mu <- 1 / m_serv                                                      # Mean service rate (mu)  

  var <- sd^2                                                           # Variance of service time
  
  rho <- lambda / mu                                                    # Utilization of the server
  W_q <- (lambda * (var + 1 / mu^2)) / (2 * (1 - lambda/mu))            # Mean wait in the queue
  W <- W_q + m_serv                                                     # Mean wait in the system
  L_q <- lambda * W_q                                                   # Mean number of customers in the queue
  L <- lambda * W                                                       # Mean number of customers in the system
  
  df <- data.frame(rho, W_q, W, L_q, L)
  knitr::kable(df)
  
}



MD1 <- MM1(1,0.9,0)
MD1
rho W_q W L_q L
0.9 4.05 4.95 4.05 4.95
***

4.10.15

Got the following results afer running simulaton for 24 weeks with 4 days warm_up period and 10 replications:

Simio Model

Simio Model

Theory almost replicates the simulation for this instance.