Write a computer program to simulate the queue in exercise


1. Write a computer program to simulate the queue in Exercise 20. Have your program keep track of the proportion of the time that the queue length is for = 0, 1, . . . , and the average queue length. Show that the behavior of the queue length is very different depending upon whether the traffic intensity has the property s <>1, = 1, or s > 1.

2. In the queueing problem of Exercise 20, let be the total service time required by a customer and the time between arrivals of the customers.

(a) Show that P (S=j) = (1-r)j-1r and P (T=j)  =  (1-p)j-1p, for 0.

(b) Show that E(S) = 1/r and E() = 1/p.

(c) Interpret the conditions 1, = 1 and s > 1 in terms of these expected values.

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Basic Statistics: Write a computer program to simulate the queue in exercise
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