There are two car rental shops next to each other, A and B. A has only 1 car to rent, while B has an infinite number of cars to rent.

Car rental times at A and B are iid with an exponential distribution rate mu (mean 1/mu) (e'g' a person rents a car for that length of time and then returns it). People arrive to the rental shops to rent cars accordign to a poisson process with rate per hour. Assume that at time t=0 there are no cars out rented.

a) suppose that independently, with proabbilityp= 0.5,e ach arrival to the rental shops goes to A or B. If they go to A and the 1 car is already out rented, then they go away and never come back (no waiting allowed). If they go to B, then they immediately rent a car. Compute the long run average number of cars out rented at A, and out rented at B.

b) Suppose instead, that the arrival to the rental shops first goes to company A hoping to get the 1 car , but if the car is already out rented, then they immediately go to company B. (Why? necause A is much cheaper to rent from than B) So in this case every arrival rents a car (nobody goes away). Compute the long run average number of cars out rented at A and out rented at B.

c) Under the same conditions as in b) suppose that the company A car retnal times are iid with a general distribution (non exponential) G(x) but with the same mean 1/mu, while the company B remains having iid exponential rate mu car rental times. Compute the long run average number of cars out rented at A and out rented at B.