There are 4 servers in the checkout area. The interarrival time of customers is 2 minutes. The processing time is 5 minutes. The coefficients of variation for the arrival process and the service process are 1 and 0.85 respectively. What is the average time in queue

0.12 minutes

Step-by-step 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

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