Consider a one- pump gas station that satisfies the assumptions for the M / M / 1 model. It is estimated that, on average, customers arrive to buy gas when their tanks are one- eighth full. The mean time to service a customer is 4 minutes, and the arrival rate is 6 customers per hour. a. Determine the expected length of the queue and the expected time in the system. b. Suppose that customers perceive a gas shortage ( when there is none) and respond by changing the fill- up criterion to more than one- eighth full on aver-age. Assuming that changes in l are inversely proportional to changes in the fill- up criterion, compare results when the fill- up criterion is one- quarter full with the results in part a. c. Making the same assumption as in part b, compare the results obtained if the fill- up criterion is one- half full. Do we have the makings of a behaviorally induced gasoline panic? d. It is reasonable to assume that the time to service a customer will decrease as the fill- up criterion increases. Under “ normal” conditions, it takes, on average, 2 minutes to pump the gasoline and 2 minutes to clean the windshield, check the oil, and collect the money. Rework parts b and c if the time to pump the gasoline changes proportionally to changes in the fill- up criterion.
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