Operations Management
Queueing Problems – INDIVIDUAL
- Sharp Discounts Wholesale Club has two service desks, one at each entrance of the store. Customers arrive at each service desk at an average of one every six minutes. The service time at each service desk is four minutes per customer.
- How often (what percentage of time) is each service desk idle?
- What is the probability that both service clerks are busy?
- What is the probability that both service clerks are idle?
- How many customers, on average, are waiting in line in front of each service desk?
- How much time does a customer spend at the service desk (waiting plus service time)?
- Burrito King (a new fast food franchise opening up nationwide) has successfully automated burrito production for its drive-up fast food establishments. The Burro-Master 9000 requires an average service time of 45 seconds, exponentially distributed, to produce a batch of burritos. It has been estimated that customers will arrive at the drive-up window according to a Poisson distribution at an average of one every 50 seconds. To help determine the amount of space needed for the line at the drive-up window, Burrito King would like to know the expected average time in the system, the average line length (in cars), and the average number of cars in the system (both in line and at the window).
- The Bijou Theater in Hermosa Beach, California, 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?
