Question

Assume a warehouse operates 24 hours a day Truck arrivals follow Poisson distribution with a mean rate of 40 per day and service (unloading using a single bay) operations follow exponential distribution with a rate of 48 trucks per day. What is the average waiting time in the system (in hours) for a typical truck?

a. 0.25 hours
b. 3 hours
c. 1 hour
d. 2 hours
e. 0.5 hours

Answer 1

The average waiting time in the system for a typical truck is approximately 29 hours.

Step-by-step explanation:

The average waiting time in the system can be calculated using Little's Law, which states that the average number of customers in the system is equal to the average arrival rate multiplied by the average waiting time in the system.

Given that the arrival rate is 40 trucks per day and the service rate is 48 trucks per day, we can calculate the average waiting time in the system as follows:

Average waiting time = Average number of trucks in the system / Arrival rate = 48 trucks per day / 40 trucks per day = 1.2 days.

Since there are 24 hours in a day, the average waiting time in the system is 1.2 days * 24 hours/day = 28.8 hours.

Therefore, the average waiting time in the system for a typical truck is approximately 29 hours.