A movie theatre complex has a single ticket booth and cashier who can maintain an average service rate of 280 patrons per hour. Service times are assumed to follow a negative exponential distribution (in short exponential distribution). Arrivals on a typical day are Poisson distributed with mean 210 per hour.
1. What are the assumptions of a single-channel single-phase queuing model (M/M/1 model)?
2.To determine the efficiency of the current ticket operation, you are asked to compute the following operating characteristics assuming that M/M/1 situation applies:
(a) average number of movie goers waiting in line to purchase a ticket;
(b) percentage of time the system is busy;
(c) average time that a customer spends in the system;
(d) average time that a customer spends waiting in line to get a ticket;
(e) probability that there are more than two people in the system;
3. Suppose a second cashier who works at the same pace is added. Determine the operating characteristics (i), (iii) and (iv) of part (b) for this new situation.
4 Suppose the cost of a cashier is $27.50 per hour.
(a) When a single server is operating, what should the cost of waiting of one customer be to satisfy the condition that total cost of waiting is equal to the total cost of providing the service?
(b) When a two servers are operating, what should the cost of waiting of one customer be to satisfy the condition that total cost of waiting is equal to the total cost of providing the service?