Speedy Oil provides a single-channel automobile oil change and lubrication service. Customers provide an arrival rate of 4 cars per hour. The service rate is 5 cars per hour. Assume that arrivals follow a Poisson probability distribution and that service times follow an exponential probability distribution.  What is the average number of cars in the system?  What is the average time that a car waits for the oil and lubrication service to begin?  What is the probability that an arrival has to wait for service?

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
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Chapter7: Uncertainty
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Problem 7.3P
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Speedy Oil provides a single-channel automobile oil change and lubrication service. Customers provide an arrival rate of 4 cars per hour. The service rate is 5 cars per hour. Assume that arrivals follow a Poisson probability distribution and that service times follow an exponential probability distribution. 

  1. What is the average number of cars in the system? 
  2. What is the average time that a car waits for the oil and lubrication service to begin? 
  3. What is the probability that an arrival has to wait for service?
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