Vehicles begin to arrive at a parking lot after the start of a major sporting event. They are arriving at a deterministic but time-varying rate:
λ(t) = 3.3 − 0.1t
[λ(t) is in veh/min and t is in minutes]. A single parking lot attendant processes vehicles (assigns spaces and collects fees) at a deterministic rate at the station. A queue exceeding four vehicles will back up onto a congested street, and is to be avoided.
How many vehicles per minute must the attendant process to ensure that the queue does not exceed four vehicles?