Question

Customer arrive at a sales counter manned by a single person according to a poisson process with a mean rate of 20 per hour. the time required to serve a customer has an exponential distribution with a mean of 100 seconds. find the average waiting time of a customer.

Answer 1

Arrival rate = λ = 20 customers per hourService rate = μ =3600/100 = 36 customers per hourThe average waiting time of a customer in the queue===hours =The average waiting time of a customer in the system===hours == 225 seconds

Answer 2

Answer:

The average waiting time of a customer is 225 seconds.

Step-by-step explanation:

Given: Arrival rate = $\lambda$ = 20 per hour.

The Service rate can be calculated as $\mu$ = 3600/100 = 36 per hour

The average waiting time of a customer  $=\frac{\lambda}{\mu(\mu-\lambda)}=\frac{20}{36(36-20)}$

Thus, The average waiting time of a customer in the system is 225 seconds.

We have made use of the formula $\bold{\frac{\lambda}{\mu(\mu-\lambda)}}$ here, to compute the average waiting time of a customer when the service rate is 36 customers per hour.