Cars arrive to a parking lot that has an infifinite number of parking spots (labeled 1, 2, 3, . . .) one at a time according to a Poisson process at rate . Each car remains parked for an exponential amount of time at rate (and then departs leaving the spot free). The fifirst 2 spots are special since they are closest to a main entrance of a Mall. All arriving cars fifirst attempt to obtain one of the 2 special spots; but if none are free they choose one of the others (non-special spots.) The parking lot is initially empty.

Questions:

(a) What is the long-run average number of parked cars?

(b) What is the long-run proportion of arriving cars that are able to park in one of the 2 special spots?

(c) What is the long-run average number of cars parked in the non-special area?