A low-cost airline currently checks its passengers using two desks and a Maitre d'Hotel queuing system. Passengers arrive according to a Poisson process with a mean rate of 35 per hour, and the check in time at either desk is negatively exponentially distributed with a mean time of 3.2 minutes per passenger. The airline is considering implementing a new system which is expected to halve the mean check-in time whilst also making the process less variable so that the standard deviation of check in times will be only 0.6 minutes. The airline's management is hoping that, with the new system, they will be able to use only one check-in desk. Carry out an investigation to enable you to advise them on whether this is likely to be correct and also on how the average queue length will be affected by this proposed change.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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A low-cost airline currently checks its
passengers using two desks and a Maitre
d'Hotel queuing system. Passengers arrive
according to a Poisson process with a mean
rate of 35 per hour, and the check in time at
either desk is negatively exponentially
distributed with a mean time of 3.2 minutes
per passenger. The airline is considering
implementing a new system which is
expected to halve the mean check-in time
whilst also making the process less variable
so that the standard deviation of check in
times will be only 0.6 minutes. The airline's
management is hoping that, with the new
system, they will be able to use only one
check-in desk. Carry out an investigation to
enable you to advise them on whether this
is likely to be correct and also on how the
average queue length will be affected by
this proposed change.
Transcribed Image Text:A low-cost airline currently checks its passengers using two desks and a Maitre d'Hotel queuing system. Passengers arrive according to a Poisson process with a mean rate of 35 per hour, and the check in time at either desk is negatively exponentially distributed with a mean time of 3.2 minutes per passenger. The airline is considering implementing a new system which is expected to halve the mean check-in time whilst also making the process less variable so that the standard deviation of check in times will be only 0.6 minutes. The airline's management is hoping that, with the new system, they will be able to use only one check-in desk. Carry out an investigation to enable you to advise them on whether this is likely to be correct and also on how the average queue length will be affected by this proposed change.
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