Assuming a 24 hour operation in a warehouse, and an arrival following Poisson distribution with mean rate of 36 per day and service (unloading using a single bay) following exponential distribution with a rate of 48 trucks per day, answer the following question. What is the expected waiting time in the system (in hours) for a typical truck?
A) 2 hours
B) 1 hour
C) 1.5 hour
D) 0.25 hour
E) 0.5 hour

Question

Quizplus · Accepted Answer

The expected waiting time in the system is given by Little's Law: W = L/λ, where W is the expected waiting time, L is the average number of trucks in the system, and λ is the arrival rate. In this case, the arrival rate is 36 trucks per day, and the service rate is 48 trucks per day. The average number of trucks in the system is given by L = λ/(μ-λ), where μ is the service rate. In this case, the average number of trucks in the system is L = 36/(48-36) = 1.5. Therefore, the expected waiting time is W = L/λ = 1.5/36 = 0.042 hours, or approximately 2.5 minutes.

Assuming a 24 Hour Operation in a Warehouse, and an Arrival