MATH 632 Midterm: 2004 Math 632 - Spring Exam 2
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Instructions: show calculations and give concise justi cations for full credit. Points add up 100: (20 pts) eileen is catching sh at the poisson rate of per hour. Sh is a salmon with probability 1/3 and a trout with probability 2/3. In symbols, nd the expectation e[ t2 |n (t) = 2]: (15 pts) consider an m/m/1 queue where customers arrive as a poisson process with rate and services happen at rate . The system starts empty, and then customers start arriving one by one. Suppose that customers are impatient in this sense: each customer in queue but not yet in service leaves the system with rate independently of the other customers. Let again xt be the number of customers in the system, a markov chain with state space {0, 1, 2, 3, . Give the rates of this markov chain: let , and be positive constants. Markov chain xt on the state space s = {1, 2, 3}.
