There is only one copying machine in the student lounge of the business school. Students arrive at the rate of λ=50 per hour​ (according to a Poisson​ distribution). Copying takes an average of 50 ​seconds, or μ=72 per hour​ (according to a negative exponential​ distribution). ​a) The percentage of time the machine is used​ =   percent​ (round your response to the nearest whole​ number). ​b) The average length of the queue​ =   students​ (round your response to two decimal​ places). ​c) The average number of students in the system​ =

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 27P
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There is only one copying machine in the student lounge of the business school. Students arrive at the rate of
λ=50
per hour​ (according to a Poisson​ distribution). Copying takes an average of
50
​seconds, or
μ=72
per hour​ (according to a negative exponential​ distribution).
​a) The percentage of time the machine is used​ =
 
percent​ (round your response to the nearest whole​ number).
​b) The average length of the queue​ =
 
students​ (round your response to two decimal​ places).
​c) The average number of students in the system​ =
 
students​ (round your response to two decimal​ places).
​d) The average time spent waiting in the queue​ =
 
minutes​ (round your response to two decimal​ places).
​e) The average time in the system​ =
 
minutes​ (round your response to two decimal​ places)
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