A toll booth on a turnpike is open from 8:00AM to 12 Midnight. Vehicles start arriving at 7:45AM at a uniform deterministic rate of six per minute until 8:15AM and from then on at two per minute. If vehicles are processed at a uniform deterministic rate of six per minute, determine when the queue will dissipate, the total delay, the maximum queue length (in vehicles), the longest vehicle delay under FIFO, and the longest vehicle delay under LIFO.
For lifesaver please show equations or diagrams used.