Question

Vehicles leaving North Portal, Saskatchewan arrive at US customs in Portal, North
Dakota in accordance with a Poisson process. On average, 3 vehicles per hour arrive at
the border crossing. There to greet them is Bullwinkle the Moose on behalf of the United
States of America. Inspector Bullwinkle processes vehicles with exponential service
times averaging 15 minutes. For some reason, people don't mind waiting in queue, or
being inspected by a moose. However, once Bullwinkle starts an inspection, passengers
get increasingly impatient. If an inspection takes longer than 15 minutes, the driver of the
vehicle involved sends a complaint to the United States Government! Assume that this
process is in steady state.
(a) (15 points) What is the expected number of complaints to the United States
Government generated during a 24 hour period?
HINT: What is the probability that the driver of the next vehicle to arrive at the customs
stop will complaint to the United States Government?
(b) (15 points) Once the customs stop empty, Bullwinkle takes a coffee break. The coffee
break ends the instant the next vehicle arrives. In a 24 hour period, what is the expected
number of coffee breaks taken by Inspector Bullwinkle?
HINT: What is the average length of a coffee break?

Answer 1