(4) (a) Write a computer program that simulates an M/Ek/1 queue. Here, Ek is an Erlang random variable with k phases. (b) Based on this program, plot...

(4) (a) Write a computer program that simulates an M/Ek/1 queue. Here, Ek is an Erlang

random variable with k phases.

(b) Based on this program, plot Pn against n when k = 4, λ = 5 and μ = 6. Also, find

the expected number in the system. How do these results compare with your M/M/1

results in (3)?

(c) Plot the expected number in the system for different values of the utilization when

k = 40. Also plot the expected number in the system in an M/D/1 queue from the

analysis in class and compare the results with your simulation. What does this tell you

and why?