1 suppose that when both machines are down in exercise 20 a, Ask an Expert

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1. Suppose that when both machines are down in Exercise 20 a second repairperson is called in to work on the newly failed one. Suppose all repair times remain exponential with rate μ. Now ?nd the proportion of time at least one machine is working, and compare your answer with the one obtained in Exercise 20.

2. Customers arrive at a single-server queue in accordance with a Poisson process having rate λ. However, an arrival that ?nds n customers already in the system will only join the system with probability 1/(n + 1). That is, with probability n/(n + 1) such an arrival will not join the system. Show that the limiting distribution of the number of customers in the system is Poisson with mean λ/μ.

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