The average waiting time on a Thursday night for a table at a popular Chinese restaurant is 30 minutes.If customers arrive at the rate of four per hour and both the service and arrival rates are Poisson distributed,what is the average service time?
A)greater than 3 but less than 4 per hour
B)greater than 4 but less than 5 per hour
C)greater than 5 but less than 6 per hour
D)Cannot be determined from the information provided.

Question

Quizplus · Accepted Answer

The average waiting time is 30 minutes, which implies the system is stable. The arrival rate is 4 customers per hour. For stability, the service rate must be greater than the arrival rate. Therefore, the service rate must be greater than 4 but less than 6 per hour.

The Average Waiting Time on a Thursday Night for a Table