Week 5: Homework
8. 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.)
What is the average customer time in the system?
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?
Would system waiting time be less than you found in (b) if a second window was opened with each server doing all three tasks.
9.To support National Heart Week, the Heart Association plans to install a free blood pressure testing booth in El Con Mall for the week. Previous experience indicates that, on average, 10 persons per hour request a test. Assume arrivals are Poisson distributed from an infinite population. Blood pressure measurements can be made at a constant time of five minutes each. Assume the queue length can be infinite with FCFS discipline.
What average number in line can be expected?
What average number of persons can be expected to be in the system?
What is the average amount of time a person can expect to spend in line?
On average, how much time will it take to measure a person’s blood pressure, including waiting time?
On weekends, the arrival rate can be expected to increase to over 12 per hour. What effect will this have on the number in the waiting line?
11.An engineering firm retains a technical specialist to assist four design engineers working on a project. The help that the specialist gives engineers ranges widely in time consumption. The specialist has some answers available in memory, others require computation, and still others require significant search time. On average, each request for assistance takes the specialist one hour.
The engineers require help from the specialist on the average of once each day. Because each assistance takes about an hour, each engineer can work for seven hours, on average, without assistance. One further point: Engineers needing help do not interrupt if the specialist is already involved with another problem.
Treat this as a finite queuing problem and answer the following questions:
How many engineers, on average, are waiting for the technical specialist for help?
What is the average time an engineer has to wait for the specialist?
What is the probability an engineer will have to wait in line for the specialist?
