Exam 18: Waiting Line

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 combined time a customer waits in line and spends being seated by the ticket taker?

Customers arrive and wait in one line single file as their documents are checked.Then they load their carry-on items on the conveyor belt for inspection.Finally,they walk through a metal detector before retrieving their carry-on items and proceeding to their departure gate.This facility is ________ channel,________ phase.

Your employer is considering a choice between a single-line and a multiple-line arrangement.The operation involves multiple servers and a single-phase service.When would each arrangement be ideal?

With a single-server model,increasing the arrival rate by 10 percent and also increasing the service rate by 10 percent will result in a(n):

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 waiting for service?

In the single-server model the:

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 time a customer spends in line?

Customers are serviced at a rate of four customers per hour according to an exponential distribution.What is the probability that customer service will require fewer than 30 minutes?

With a single-server model,increasing the service rate while holding all other factors constant will:

In a waiting-line problem,assigning additional employees to a service facility will have a direct effect on:

A(n)________ is a single step in providing a service.

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

Customers in a small retail store arrive at the single cashier at the rate of 10 per hour.The average service time for the cashier is five minutes.Arrivals tend to follow a Poisson distribution,and service times follow an exponential distribution. a.What is the average utilization of the cashier? b.What is the average number of customers in the system? c.What is the average number of customers in line? d.What is the average time spent in the system? e.What is the average time spent in line?

The manger of a car wash wants to know how fast his new crew is processing cars through the wash area.He notices that it takes cars an average of about 30 minutes in line to reach the car wash,and his spot checks during the day indicated an average of seven cars in line waiting to be washed.What was the processing rate for his new crew that day?

What is Little's Law? How might it be applied to determine the average length of time it takes an MBA student to complete the program?

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 probability that a traveler will pull up to the attendant's service window without having to wait for another customer?

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 people waiting in line and being seated?

Scenario B.4 Customers arrive at an airline ticket counter at the rate of 50 customers per hour,according to a Poisson distribution.There are three ticket agents.Customers select the first available agent from one line.Each agent can process 20 customers per hour with exponential service times. -Use the information in Scenario B.4.What is the average utilization of the three-agent system?

The four elements common to all waiting-line situations are a customer population,a waiting line of customers,the service facility,and a priority rule.

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.How many minutes per hour is the attendant not serving customers?