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A small appropriate, operated by a single barber, has room for at most two customers.
9. A small appropriate, operated by a single barber, has room for at most two customers. Potential customers arrive at a Poisson rate of three per hour, and the successive service times are independent exponential random variables with mean 1/4 hour. What is (a) the average number of customers in the shop? (b) the proportion of potential customers that enter the shop? (c) If the barber could work twice as fast, how much more business would he do? 10. Consider two machines, both of which have an exponential lifetime with mean 1/. There is a single repairman that can service machines at an exponential rate . Set up the Kolmogorov backward equations; you need not solve them. If you can solve this equation, what questions will you be able to answer?
