Question

Customers enter the waiting line at a cafeteria on a first-come, first served basis. The arrival rate follows a Poisson distribution, and service times follow an exponential distribution. If the average number of arrivals is 6 per minute and the average service rate of a single server is 10 per minute. What is the average number of customers in the system?

Answer 1

the average no of customers in the system is 0.9

Explanation:

Given that

The average number of arrivals is 6 per minute

And, the average service rate of a single server is 10 minutes

We need to find out the average no of customers in the system

So,

Lq = rho^2 / 1 ÷ rho

= (6 ÷ 10)^2 ÷ (1 - 6 ÷ 10)

= 36 ÷ 100 × 10 ÷ 4

= 0.9

Hence, the average no of customers in the system is 0.9