Question

An average of 40 cars per hour arrive to be painted at a single-server GM painting facility. 95% of the cars require 1 minute to paint; 5% must be painted twice and require 2.5 minutes to paint. Assume that interarrival times are exponential.

a. On the average, how long does a car wait before being painted?
b. If cars never had to be repainted, how would your answer to part (a) change?

Answer 1

2.719 minutes

Explanation:

Step 1 :

We have to consider using the M/G/I /GD /∞/∞ Queuing system with the rate of arrival λ and the rate of service μ.

Since average of 40 cars arrive every hour at the painting facility, it follows that:

Arrival rate λ = 40cars /hour

= 40/60 cars/hour

=2/3 cars/hour

More, we were told that 95% of the cars require 1 minute to paint, 5% must be painted twice and require 2.5 minutes to paint, therefore, the average time to paint a car is given by

95/100x1 + 5/100 x 2.5 = 19/20 + 1/8 = 43/40min

It follows that:

Service rates μ = 40/43cars/min