Question

Consider a bank counter that is modeled as a M/M/1 queue with incoming flow rate as 0.1 customer per minute, and service rate as 0.3 customer per minute. What is the probability that only one customer waits in the line. Also find the average number of customers in line waiting for service.

Answer 1

= 0.1 customer per minute

= 0.3 customer per minute

Utilization = 0.1 / 0.3 = 1/3

Probability that only one customer waits in the line = Probability that there are only 2 customers in the system (one waiting and one getting serviced) = (1 - )

= (1 - 1/3) (1/3)²

= (2/3) * (1/9)

= 2/27

= 0.07407

Average number of customers in line waiting for service = / ( - )

= (1/3) 0.1 / (0.3 - 0.1) = 1/6

= 0.1666667