Question

in a waiting line system, there is only one server. Customer arrivals follow Poisson distribution with mean inter-arrival time 5 minutes. Service time follow exponential distribution and a server can serve 15 customers per hour on average. What is the average waiting time?a. 2 minb. none of the answerc. 20 mind. 30 mine.16 min

Answer 1

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.