The milk plant in a city distributes its products by trucks, loaded at a single loading dock. It has its own fleet plus trucks of a private company. The private company has complained that sometimes its trucks have to wait in line and thus the company loses money paid for a truck and driver that is only waiting. The company has asked the milk plant management to either go in for a second loading dock or discount prices equivalent to the waiting time. The following data are available:

Average arrival rate (all trucks) = 3/hr

Average service rate = 4/hr

The transport company has provided 40% of the total number of trucks. Assuming that these rates are random according to passion distribution. 

Determine: 

a) The probability that a truck has to wait?

 

 

b)  The waiting time of a truck that waits  ?

 

 

c)  The expected waiting time of` company trucks per day ?