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(1) (a) Write a computer program to generate random numbers between [0,1]. Such a random
number generator simulates the values generated by a uniform random variable U[0,1].
(b) Write another progam (using the program in (a)) to estimate P(U > x). Plot P(U > x)
for values of x ∈ (0.5,1).
(2) (a) Write a computer program to simulate the values generated by Exponential (X) and
Poisson random (Y) variables using the program you developed in (1).
(b) Provide plots for P(X > x) and P(Y > x), for E(Y) = E(X) = 2. It may be necessary
to show your result on a plot where the vertical axis is logarithmic.
(3) (a) Write a computer program that simulates an M/M/1 queue.
(b) Based on this program plot Pn against n when λ = 5 and μ = 6.
(c) Again, from your program, find the expected number and expected delay in your
M/M/1 queueing system when ρ= 5/6.
(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
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