Problem #4 Mike Dreskin manages alarge Los Angeles movie theater complex called Cinema I, II, III,and IV. Each of the four auditoriums plays a different film; theschedule is set so that starting times are staggered to avoid thelarge crowds that would occur if all four movies started at thesame time. The theater has a single ticket booth and a cashier whocan 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 andaverage 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 topurchase a ticket.
(b) What percentage of the time is the cashier busy?
(c) What is the average time that a customer spends in thesystem?
(d) What is the average time spent waiting in line to get to theticket window?
(e) What is the probability that there are more than two peoplein the system?
