Question

During regular operating hours, passengers of Fly-Hi airlines arrival at the airport at the average rate of 190 per hour (Poisson distributed). Fly-Hi can hire staff for $18 per person per hour, each of whom can check in a passenger in an average time of 1 minute (negative exponential distribution). Fly-Hi has determined that the cost of waiting is $45 per passenger per hour. [Select] What is the minimum number of staff for this system? Select] What is the optimal number of staff for this system? What is the total cost of this system per hour at the optimal number of staff? [Select

Answer 1

The minimum number of staffs that could be hired is 4

The optimal number of stuff is 6 and The total cost per hour is $114.14

Step-by-step explanation:

Average arrival rate, λ = 190 per hour

Average service rate, μ = 1 in 1 minute = 60 per hour

The minimum number of servers required for a stable queuing system

= λ/μ

= 190/60

= 3.167

Therefore, The minimum number of staffs that could be hired is 4.

s P0 Lq Server cost per hour = s*18

4 0.029 2.210 72

5 0.039 0.483 90

6 0.041 0.137 108

Waiting cost per hour = Lq*45 Total cost per hour

99.44 171.44

21.72 111.72

6.14 114.14

The total cost is optimal for s = 6.

Therefore, The optimal number of stuff is 6 and The total cost per hour is $114.14