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lec8_example

lec8_example - = − = min 8 27 − µ 27 − 25 27 2 25 2...

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An Example of M/M/1 Queue An Example of M/M/1 Queue ± An airport runway for arrivals only ± Arriving aircraft join a single queue for the runway ± Exponentially distributed service time with a rate µ= 27 arrivals / hour (As you computed in PS1.) ± Poisson arrivals with a rate λ= 20 arrivals / hour 1 1 1 ± W = = = hour min 6 . 8 λµ 27 20 7 20 ± L = λ W = λ = 9 . 2 aircrafts 27 20 1 1 1 1 ± W = W 1 = = min 4 . 6 q µ 27 20 27 2 20 2 ± L = λ W = = 27 27 20 ) 1 . 2 aircrafts q q ) ( ( 1.225, 11/20/02 Lecture 8, Page 1
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An Example of M/M/1 Queue (cont.) An Example of M/M/1 Queue (cont.) ± Now suppose we are in holidays and the arrival rate increases λ= 25 arrivals / hour ± How will the quantities of the queueing system change? 1 1 ± W = 1 = = hour = min 30 λµ 27 25 2 λ 25 ± L = λ W = = = 5 . 12 aircrafts 27 25 1 1 1 1 1 ± W q = W =
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Unformatted text preview: = − = min 8 . 27 − µ 27 − 25 27 2 25 2 ± L = λ W = = 27 27 − 25 ) ≈ 6 . 11 aircrafts q q ) ( ( − 1.225, 11/20/02 Lecture 8, Page 2 An Example of M/M/1 Queue (cont.) An Example of M/M/1 Queue (cont.) ± Now suppose we have a bad weather and the service rate decreases µ= 22 arrivals / hour ± How will the quantities of the queueing system change? 1 1 ± W = 1 = = hour = min 30 λµ 22 − 20 2 − λ 20 ± L = λ W = = = 10 aircrafts 22 − 20 − 1 1 1 1 1 ± W q = W − = − = − ≈ min 3 . 27 − µ 22 − 20 22 2 20 2 ± L = λ W = = 22 22 − 20 ) ≈ 1 . 9 aircrafts q q ) ( ( − 1.225, 11/20/02 Lecture 8, Page 3...
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lec8_example - = − = min 8 27 − µ 27 − 25 27 2 25 2...

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