12-12 From historical data, Harry’s Car Wash estimates that dirty cars arrive at the rate of 10 per hour all day Saturday. With a crew working the wash line, Harry figures that cars can be cleaned at the rate of one every 5 minutes. One car at a time is cleaned in this example of a single-channel waiting line.     Assuming Poisson arrivals and exponential service times, find the     average number of cars in line.      average time a car waits before it is washed.     average time a car spends in the service system.     utilization rate of the car wash.

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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12-12 From historical data, Harry’s Car Wash estimates that dirty cars arrive at the rate of 10 per hour all day Saturday. With a crew working the wash line, Harry figures that cars can be cleaned at the rate of one every 5 minutes. One car at a time is cleaned in this example of a single-channel waiting line. 

  

Assuming Poisson arrivals and exponential service times, find the 

  

average number of cars in line.

 

  

average time a car waits before it is washed. 

  

average time a car spends in the service system. 

  

utilization rate of the car wash. 

  

probability that no cars are in the system. 

 

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