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A small company maintains a fleet of four cars to be driven by its workers on business trips….


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:

A small company maintains a fleet of four cars to be driven by its workers on business trips....

(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) = EiT4. Write and solve equations to find the g(i). (d) Use the stationary distribution to compute E3T4.