Mike Dreskin manages a large LA movie theater complex called Cinema I, II, III, and IV. Each of 4-auditoriums plays a different movie; the schedule is set so that beginning times are staggered to avoid the large crowds that would occur if all four films started at the similar time. The theater has a single ticket booth and a cashier who can maintain an average service rate of 280 movie patrons per hour. Service times are assumed to follow an exponential distribution. Arrivals on a typically active day are Poisson distributed and average 210 per hour.

To determine the efficiency of the current ticket operation, Mike wishes to examine several queue operating characteristics.
(a) Find the average number of moviegoers waiting in line to purchase a ticket.
(b) What percentage of the time is the cashier bus)?
(c) What is the average time that a customer spends in the system?
(d) What is the average time spent waiting in line to get to the ticket window?
(e) What is the probability that there are more than two people in the system? More than three people? More than four?