Problem 1 (Questions 11-15) An airport has a single runway for landings. The tim

Question

Problem 1 (Questions 11-15) An airport has a single runway for landings. The time between airplane arrivals (inter-arrival time of landings) is 12 minutes and each landing requires about 9 minutes (service time). Select the option closest to your result. 1.How busy is the runway? 2 What is the average number of airplanes waiting to land? . What is the average waiting time per plane (in minutes)? .What is the probability there are no planes waiting to land? What is the probability there are 2 or more planes w a) 6796; b) 50%; c) 7596; d) 58% a) 0.81; b) 2.19; c) 0.50; d) 1.33 a) 16.0; b) 26.3; c) 9.7; d) 6.0 a) 5096; b) 2596; c) 33%; d) 42%

Explanation / Answer

: mean rate of arrival = 1/12 = 0.0833
µ: mean service rate = 1/8 = 0.125

1. Utilization = 8/12 = 0.6667 = 67% (option A)

2.
Lq: mean number of customers in the queue

Lq = (1/12)^2 / ((0.125*(0.125 - 1/12))) = 1.3333

Option (D)

3.
Wq: mean wait in the queue

Wq = 1.33/(1/12) = 15.96 mins

Option (A) is correct

4.
P0 = 1 - 0.6667 = 0.3333

P1 = (0.6667)^1*0.3333 = 0.2222

Required probability = 1 - P0 - P1 = 1 - 0.3333 - 0.2222 = 0.4445

Option A is correct

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