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) 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.