Question

Arrival rate is 6 per minute, service rate is 7.5 per minute the waiting time of a
customer in the system is​

Answer 1

W = 0.67 minutes (waiting time including service)

Wq = 0.54 minutes (waiting in line)

Explanation:

Average arrival rate λ = 6 per min

Average service rate μ = 7.5 per min

p = average utilization of the system = 6/7.5 = 4/5 = 0.8

L = average number of customers in the service system = λ / μ-λ = 6 / 1.5 = 4

Average number of customers waiting in queue = pL = 0.8 * 4 = 3.2

W = 1/ μ-λ = 1/1.5 = 2/3 = 0.67 is the average time spent waiting in the system including service.

Wq = pW is the average time spent waiting in line = 0.8 * 0.67 = 0.536

The waiting time of a customer in the system W = 0.67 minutes (including service)

The waiting time of a customer in line Wq = 0.54 minutes