Mom-and-Pop’s Grocery Store has a small adjacent parking lot with three parking spaces reserved for the store’s customers. During store hours, cars enter the lot and use one of the spaces at a mean rate of 2 per hour. For n = 0, 1, 2, 3, the probability Pn that exactly n spaces currently are being used is P0 = 0.2, P1 = 0.3, P2 = 0.3, P3 = 0.2.
(a) Describe how this parking lot can be interpreted as being a queueing system. In particular, identify the customers and the servers. What is the service being provided? What constitutes a service time? What is the queue capacity?
(b) Determine the basic measures of performance—L, Lq, W, and Wq—for this queueing system.
(c) Use the results from part (b) to determine the average length of time that a car remains in a parking space.