Exam 18: Waiting Line

In a waiting-line problem,increasing advertising expenditures,increasing the number of promotions,or changing the price of a service is most likely to affect:

The standard assumption in the single-server model is that there is an infinite number of customers and that customers will wait in line as long as it takes to get served.

Customers arrive every three minutes governed by a Poisson distribution.A single server is capable of handling twenty-five customers per hour and this service time is exponentially distributed.What is the likelihood that the server is not busy at any given time?

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?

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

Customers arrive at the local grocery store at a steady rate of 40 an hour.Thirty percent of these customers purchase 10 items or less and go to the express line where they enjoy an average checkout time of 5 minutes.Customers that don't meet the express line criterion go to the other checkout line where they spend an average of 10 minutes checking out.How many people are checking out in the express line on average?

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 number of customers in the system?

Short queue lengths typically mean not enough capacity.

Scenario B.5 A trucking firm has five trucks that each requires service at an average rate of once every 50 hours,according to an exponential distribution.The firm has a mechanic who needs five hours to complete the average job with exponential service times. -Use the information in Scenario B.5.What is the average number of trucks in line waiting and being serviced?

A professor sits in his office and answers questions from his students the afternoon before the final exam.His class is a mass lecture of 350 students,so he concentrates on providing explanations as quickly as possible.On average,he can answer 60 questions an hour and students arrive at his 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 his time does the professor spend answering questions? b.What is the average number of students waiting outside his office? c.What is the average time a student spends in line outside the professor's office?

Scenario B.1 A single ticket taker can tear tickets and direct movie patrons to their seats at a rate of 90 per hour.Customers arrive every minute 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. -Use the information in Scenario B.1.What is the average number of customers in line?

Waiting lines cannot develop if the time to process a customer is constant.

A movie complex experiences its peak ticket sales in the early evening when several movies have about the same start times.The ticket booth can process customers buying tickets at a maximum rate of 45 seconds each (or 80 tickets sold per hour).You arrive to buy your ticket and count 16 people in line ahead of you.How long can you expect to wait in line before getting to the booth to buy your ticket?

The average lead time of a unit of product through a manufacturing station is 10 minutes.The production rate has been steady at five units per hour.The average work-in-process inventory at this station is:

A(n)________ is a rule that allows a customer of higher priority to interrupt the service of another customer.

Customers arrive according to a Poisson distribution.The average number of customer arrivals per hour is four.The probability that three customers will arrive in the next two hours is:

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

Customers arrive every three minutes governed by a Poisson distribution.A single server is capable of handling twenty-five customers per hour and this service time is exponentially distributed.About how many minutes per hour is the server not helping customers?

Customers arrive every three minutes governed by a Poisson distribution.A single server is capable of handling twenty-five customers per hour and this service time is exponentially distributed.How many customers are either receiving service or waiting in line on average?

Customers are serviced at a rate of three customers per hour according to an exponential distribution.What is the probability that customer service will require fewer than 10 minutes?