These results will be important when we consider

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Unformatted text preview: tates give the number of customers in the system, with a or b indicating there is one customer at a or b respectively. Show that this system is time reversible. Set ⇡ (2) = c and solve to find the limiting probabilities in terms of c. 4.37. At present the Economics department and the Sociology department each have one typist who can type 25 letters a day. Economics requires an average 156 CHAPTER 4. CONTINUOUS TIME MARKOV CHAINS of 20 letters per day, while Sociology requires only average of 15. Assuming Poisson arrival and exponentially distributed typing times find (a) the average queue length and average waiting time in each departments (b) the average overall waiting time if they merge their resources to form a typing pool. 4.38. Consider an M/M/s queue with no waiting room. In words, requests for a phone line occur at a rate . If one of the s lines is free, the customer takes it and talks for an exponential amount of time with rate µ. If no lines are free, the customer goes away never to come back. Find the stationary distribution. You do not have...
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