Mathematics

Giovanni Hansen

14 May, 09:55

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) 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) = E_i T_4. Write and solve equations to find the g (i). (d) Use the stationary distribution to compute E_3 T_4.