Quantitative Analysis Problem - Mike Dreskin manages a large Los angeles movie theater complex

Mike Dreskin manages a large Los angeles movie theater complex called Cinema l, ll, lll, lV. Each of the four auditoriums palys a different film; the schedule is set so that starting times are staggered to avoid the large crowd that would occure if all four movies started at the same time. The theater has a single ticket booth and a cashier who can maintain an average serivice rate of 280 movie patrons per hour. Service times are assumed to follow an exponiential 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 busy?

(c) What is the average time that a customer spends in the system?

(d) What is the average time spent wiaing 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?