Consider a single-server queuing system for which the inter arrival times are exponentially

distributed. A customer who arrives and finds the server busy joins the

end of a single queue. Service times of customers at the server are also exponentially

distributed random variables. Upon completing service for a customer, the server

chooses a customer from the queue (if any) in a FIFO manner:

a. Simulate customer arrivals assuming that the mean inter arrival time equals the

mean service time (e.g., consider that both of these mean values are equal to 1 min).

Create a plot of number of customers in the queue (y-axis) versus simulation time

(x-axis). Is the system stable? (Hint: Run the simulation long enough [e.g., 10,000 min]

to be able to determine whether or not the process is stable.)

b. Consider now that the mean inter arrival time is 1 min and the mean service time

is 0.7 min. Simulate customer arrivals for 5000 min and calculate (i) the average

waiting time in the queue, (ii) the maximum waiting time in the queue, (iii) the

maximum queue length, (iv) the proportion of customers having a delay time in

excess of 1 min, and (v) the expected utilization of the server.