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Q. Mike Dreskin manages a large Los Angeles movie theatre complex called Cinema I, II, III, also IV. Each of four auditoriums plays a different film; schedule is set so which starting times are staggered to avoid large crowds which would occur if all four movies started at same time. Theatre has a single ticket booth also 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 also average 210 per hour.
To evaluate efficiency of present ticket operation, Mike wishes to examine several queue operating characteristics.
(a) Find average number of moviegoers waiting in line to purchase a ticket.
(b) Illustrate what percentage of time is cashier bus)?
(c) Illustrate what is average time which a consumer spends in system?
(d) Illustrate what is average time spent waiting in line to get to ticket window?
(e) Illustrate what is probability which re are more than two people in system? More than three people or more than four?
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