A petroleum company is considering expansion of its one unloading facility at its
Australian refinery. Due to random variations in weather, loading delays, and other
factors, ships arriving at the refinery to unload crude oil arrive according to a Poisson
distribution with a rate of 15 ships per week. Service time is exponential with an
average service rate of 22 ships per week.
a) What are λ and μ?
b) What is the utilisation of the facility?
c) What is the average number of ships waiting to gain access to the single
unloading facility?
d) What is the average time a ship must wait before beginning to deliver its cargo
to the refinery?
e) What is the average total time (waiting plus delivery in the system) that a ship
spends at the refinery?
