A truck weighing station has a single scale. The time between truck arrivals at the station is exponentially distributed with a mean arrival rate of 1.5 veh/min. the time it takes vehicles to be weighed is exponentially distributed with a mean rate of 2 veh/min. when more than 5 trucks are in the system, the queue backs up onto the highway and interferes with through traffic.

Find:

a. The probability of blocking the highway through traffic.

b. Average time in the queue and in the system.

c. The average number of trucks in the system, and its variance.