1. In Exercise 20 the service time S has a geometric distribution with E(S) = 1/r. Assume that the service time is, instead, a constant time of t seconds. Modify your computer program of Exercise 21 so that it simulates a constant time service distribution. Compare the average queue length for the two types of distributions when they have the same expected service time (i.e., take t = 1/r). Which distribution leads to the longer queues on the average?
2. A certain experiment is believed to be described by a two-state Markov chain with the transition matrixP, where .5 .5 P = p 1 - p and the parameter p is not known. When the experiment is performed many times, the chain ends in state one approximately 20 percent of the time and in state two approximately 80 percent of the time. Compute a sensible estimate for the unknown parameter p and explain how you found it.