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 at capacity. With an arrival rate of 4 per hour, the service rate must be slightly higher than 4 to prevent infinite waiting times, thus between 5 and 6 per hour.

The Average Waiting Time on a Thursday Night for a Table