Exam 19: Supplement B Waiting Lines

Scenario B.1 A single volunteer octogenarian usher can scan tickets with a handheld device and direct theater patrons to their seats at a rate of 30 per hour with an accuracy rate approaching 23%. On average, about twenty-five customers arrive every hour for assistance and always wait, regardless of how long the line gets. Arrivals are governed by the Poisson distribution and service is governed by the exponential distribution. -How many theater patrons from Scenario B.1 are either waiting in line to be seated or being seated by the volunteer octogenarian usher?

Customers are serviced at a rate of six customers per hour according to an exponential distribution. What is the probability that customer service will require fewer than 20 minutes?

A ________ is a single step in the service process.

Instead of having one worker perform all eight steps to process a customer, an operations manager assigns each step to a different worker. In doing so, the operations manager has increased the:

If you were using SimQuick to determine how opening an additional airport security inspection station would affect passenger wait times, a ________ would be used to model each of the waiting lines.

The exponential distribution is based on the assumption that each service time is ________ of those that preceded it.

The standard assumption in the single-server model is that customers are served according to the earliest due date, i.e., which customer needs to be finished first.

Ed Deadbeat races to the Bursar's Office on the first day of class and notes that the line is four students long. Ed figures that the wait will be at least ten minutes and, having better uses of his time, he decides to proceed to the next item on his to-do list. Ed's behavior is best described as:

The distinction between an infinite customer population and a finite customer population is whether the:

A super computer-accessory discount store often has customers who leave the checkout line before being served because of excessive waiting times. The store has a(n):

Scenario B.1 A single volunteer octogenarian usher can scan tickets with a handheld device and direct theater patrons to their seats at a rate of 30 per hour with an accuracy rate approaching 23%. On average, about twenty-five customers arrive every hour for assistance and always wait, regardless of how long the line gets. Arrivals are governed by the Poisson distribution and service is governed by the exponential distribution. -The curtain goes up at 8 pm for the play "The Life and Times of A.K. Erlang." If the parameters in Scenario B.1 are at work, what's the latest a patron of the theater would want to arrive in order to be seated before the light dims, the curtain rises, and the actor playing A.K. Erlang takes his rightful place at center stage?

Scenario B.2 Weary travelers arrive at Will Rogers International Airport, pick up their luggage, stumble to their cars, and proceed to the parking lot attendant to pay for their parking. Traveler interarrival times are exponentially distributed, as are the service times of the attendant. On average, travelers arrive every 25 seconds. The attendant can process three travelers per minute, and processing rates follow a Poisson distribution. -Use the information in Scenario B.2. What is the average amount of time a customer spends waiting in line and being served?

The delivery wagon that the hominy man had used for the last three decades was beyond repair, so he decided to open a hominy stand at a busy intersection in downtown Luther. Customers arrive at the rate of 8 per hour and it takes 5 minutes on average to fill their buckets with hominy. a. What is the likelihood that the line is longer than three people? b. What is the average waiting time in line? c. What is the average number of customers in line?

Students arrive at a university business library during peak evening hours at a rate of 40 students every half hour. Each student stays an average of two hours. On average, how many students are in the library at any one time?

If the nature of the customer population, constraints on the line, the priority rule, and the service time distribution renders waiting line theory no longer useful, then an operations manager should rely on:

A professor's teaching assistants sit in their communal office and answer questions from students the afternoon before the final exam. The class is a mass lecture of 350 students, and the teaching assistants have final exams of their own, so they concentrate on providing explanations as quickly as possible. On average, the three teaching assistants can answer 30 questions an hour and students arrive at their office every five minutes. Student arrivals are Poisson distributed, each student has only one question and answer times are exponentially distributed. a. What fraction of their time do the teaching assistants spend answering questions? b. What is the average number of students waiting outside their office? c. What is the average time a student spends in line outside the teaching assistants' office and having their question answered?

________ is a fundamental law that relates the number of customers in a waiting-line system to the waiting time of customers.

You drive your car into the parking lot of your favorite fast food establishment and get in the line for drive through service. After placing your order into the speaker, you proceed to the first window to pay, and then to the second window to pick up your meal. Since you just studied waiting lines that day in your Operations Management class, you quickly realize as you drive away that this was an example of a ________ channel ________ phase queuing system.

With a finite-source model, increasing the arrival rate by 10 percent and also increasing the service rate by 10 percent will result in:

With a single-server model, increasing the promotions for a service through advertising will most likely: