# Arrivals from outside the system occur only at the

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Unformatted text preview: tion? (c) They are amorous now. What is the expected amount of time until depression sets in? 4.29. A small company maintains a ﬂeet of four cars to be driven by its workers on business trips. Requests to use cars are a Poisson process with rate 1.5 per day. A car is used for an exponentially distributed time with mean 2 days. Forgetting about weekends, we arrive at the following Markov chain for the number of cars in service. 0 1 2 3 4 0 1.5 0.5 0 0 0 1 1.5 2.0 1.0 0 0 2 0 1.5 2.5 1.5 0 3 0 0 1.5 3 2 4 0 0 0 1.5 2 (a) Find the stationary distribution. (b) At what rate do unfulﬁlled requests come in? How would this change if there were only three cars? (c) Let g (i) = Ei T4 . Write and solve equations to ﬁnd the g (i). (d) Use the stationary distribution to compute E3 T4 . 4.30. A submarine has three navigational devices but can remain at sea if at least two are working. Suppose that the failure times are exponential with means 1 year, 1.5 years, and 3 years. Formulate a Markov chain with states 0 = all parts working, 1,2,3 = one part failed, and 4 = two failures. Compute...
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## This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).

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