17.23.
MomandPop’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 P_n
that exactly n spaces currently are being used is P_0 = 0.2, (please
notice that here “_” means the subscript) P_1 = 0.3, P_2 = 0.3, P_3 = 0.2.
(a)
Describe how this parking lot can be interpreted as being a queuing system. In
particular, identify the customers and the severs. What is the service being provided?
What constitutes a service time? What is the queue capacity?
(b)
Determine the basic measures of performance—L, L_q, W, and W_q—for this
queuing system.
(c)
Use the results from part (b) to determine the average length of time that a car
remains in a parking space.
17.24.
For each of the following statements about the queue in a queuing system,
label the statement as true or false and then justify your answer by referring to a
specific statement in the chapter.
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 Spring '08
 SteinW.Wallace
 Poisson Distribution, Probability theory, Exponential distribution, Grocery store, 2 hours, 10minutes

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