Mike Dreskin manages a large Los Angeles movie

theater complex called Cinema I, II, III, and IV. Each

of the four auditoriums plays a different film; the

schedule is set so that starting times are staggered to

avoid the large crowds that would occur if all four

movies started at the same 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 busy?

(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?