Operating characteristics of the Queueing model.
Mike manages a theater complex known as Cinema I, II, III and IV. Each of the 4 auditoriums plays a different film; the starting times are staggered to keep away from the large crowds. The Cinema has one ticket booth and a cashier who can maintain an average service rate of 280 patrons per hour. Service times are assumed to follow an exponential distribution. Arrivals on a typical activity day are Poisson distributed and average 210 per hour.
To resolve the efficiency of the current ticket operation, Mike wishes to examine several queue operating characteristics.
a. Find out the average number of moviegoers waiting in line to purchase a ticket.
b. What percentage of time is the cashier busy?
c. What is the average time the customer spends in the system?
d. What is an average time waiting in line to get to ticket booth?