Question

The Bijou Theater shows vintage movies. Customers arrive at the theater line at the rate of 100 per hour. The ticket seller averages 30 seconds per customer, which includes placing validation stamps on customers' parking lot receipts and punching their frequent watcher cards. (Because of these added services, many customers don't get in until after the feature has started.)

a. What is the average customer time in the system?

b. What would be the effect on customer time in the system of having a second ticket taker doing nothing but validations and card punching, thereby cutting the average service time to 20 seconds?

c. Would system waiting time be less than you found in(b) if a second window was opened with each server doing all three tasks.

Part C. is the one I need help with the most. Please explain in depth. Thank you!

Answer 1

a)

	Operating Characteristics	Each desk represents single queue and single server model
	Arrival rate (Customers/hour)	? = 100 customers per hour
	Service (minutes/customer)	30 seconds/customer
	Service Rate (customer/hour)	µ= (3600 sec/hour)/(30 sec/customer) µ= 120 customers per hour
	System Utilization ? = ?/µ	? = ?/µ = 100/120 = 0.833 ? = 0.833
	Average waiting time in the system Ws = 1/(µ - ?)	Ws = 1/(120 – 100) Ws = 0.05 hour = 0.05*60 minutes Wq = 3 minutes Average waiting time in the system is 3 minutes per customer

b.

Option: Adding second ticket taker

	Operating Characteristics	Each desk represents single queue and single server model
	Arrival rate (Customers/hour)	? = 100 customers per hour
	Service (minutes/customer)	20 seconds/customer
	Service Rate (customer/hour)	µ= (3600 sec/hour)/(20 sec/customer) µ= 180 customers per hour
	System Utilization ? = ?/µ	? = ?/µ = 100/120 = 0.833 ? = 0.833
	Average waiting time in the system Ws = 1/(µ - ?)	Ws = 1/(180 – 100) Ws = 0.0125 hour = 0.0125*60 minutes Wq = 0.75 minutes or 45 seconds Average waiting time in the system is 0.75 minutes or 45 seconds per customer

c)

Lets assume that the both the counters observes equal arrival rate, that is 50 customers per hour each. Determine waiting time of customer at either of the counter

	Operating Characteristics	Each counter represents single queue and single server model
	Arrival rate (Customers/hour)	? = 50 customers per hour
	Service (minutes/customer)	30 seconds/customer
	Service Rate (customer/hour)	µ= (3600 sec/hour)/(30 sec/customer) µ= 120 customers per hour
	Average waiting time in the system Ws = 1/(µ - ?)	Ws = 1/(120 – 50) Ws = 0.0143 hour = 0.0143*60 minutes Wq = 0.8571 minutes or 51.42 seconds Average waiting time in the system is 0.8471 minutes or 51.42 seconds per customer

Thus, option of adding second ticket taker have lesser waiting time than adding new window.