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Car owners fill up when their tanks are exactly half full. At the present time, an average of 8.5 cars/hr arrive at a single-pump gas station. It takes an average of 3.68 minutes to service a car. Suppose that a gas shortage occurs and panic buying takes place. All car owners now purchase gas when their tanks are exactly 3/4 full. Since each car is putting less gas into the tank for each visit, the average service time has been reduced to 2.54 minutes. Assume that arrival and departure rates are both exponential. What is the difference in length of queue before and after the shortage scenario, in terms of vehicles? answer an absolute value, and in four decimal places.

Practical Management Science

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 9P

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Car owners fill up when their tanks are exactly half full. At the present time, an average of 8.5 cars/hr arrive at a single-pump gas station. It takes an average of 3.68 minutes to service a car. Suppose that a gas shortage occurs and panic buying takes place. All car owners now purchase gas when their tanks are exactly 3/4 full. Since each car is putting less gas into the tank for each visit, the average service time has been reduced to 2.54 minutes. Assume that arrival and departure rates are both exponential. What is the difference in length of queue before and after the shortage scenario, in terms of vehicles? answer an absolute value, and in four decimal places.

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