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

Answer:

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

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