Answer:
0.12 minutes
Explanation:
There are 4 servers in the checkout area.
Step 1
We calculate the rate of utilization.
The formula is given as = Average activity time/Average Interarrival time
The processing time is 5 minutes
Average activity time = μ = 1/5 = 0.20 per minute.
The interarrival time of customers is 2 minutes.
λ = Average Interarrival time of customers per minute = 1/2 = 0.5 per minutes.
Rate of Utilization = 0.20/0.50
= 0.4
Step 2
We find the Average time in the queue using the formula.
= Activity time × [ Utilization rate/ 1 - Utilization rate] ×[ Cva² + Cvp²/2]
The coefficients of variation for the arrival process (Cva) = 1
The coefficients for the service process
= 0.85
Average time in the queue =
0.20 × [0.4/ 1 - 0.4] × [1² + 0.85²/2]
0.20 × [0.4/0.6] × [1.7225/2]
0.20 × 0.6666666667 × 0.86125
= 0.1154075
Approximately ≈ 0.12 minutes