4 A singlebay car wash with a Poisson arrival rate and an ex

4. A single-bay car wash with a Poisson arrival rate and an exponential service time has cars arriving at an average of 10 minutes apart with an average service time of 4 minutes. What is the system utilization?

Solution

Given cars arriving at an average of 10 minutes

so arrival rate = 6 per hour;

average service time is 4 minutes; i.e = 15 cars per hour

system utilization = arrival rate/service rate = 6/15 = 0.4 =40%