Answer:
The problem can be represented by single queue model.
Inter-arrival time = 5 min
Arrival rate = 60 min / 5 min
Arrival rate =12 customers per hour
Service rate = µ =15 customers per hour
Utilization of server
P = λ/µ
P = 12 / 15
P = 0.80
Number of customers in queue
L = (12^2)/15(15 - 12)
L = 3.2 customers per hour
Waiting time in queue
W = 3.2 / 12
W = 0.266 hour
Convert hours into minutes as follows:
Waiting time in queue = 0.2667 x 60
Waiting time in queue = 16 minutes
Waiting time in system
Ws = 02667 + 1/15
Ws = 0.333 hour
Waiting time in system = 0.333 x 60
Waiting time in system = 20 mins
Average waiting time in queue = 16 mins
Average waiting time in system = 20 mins
Therefore, average waiting time in the system is 20mins.
