Consider a single-server queuing system for which the interarrival 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 interarrival 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 interarrival 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.