Exam 19: Supplement B Waiting Lines

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?

A drive thru car wash can process cars at a rate of one every five minutes. When you arrive with your car, you see one car just leaving the washer and eight cars in line ahead of you. How long can you expect to wait before you will reach the car wash?

The number of customers in line and being served also relates to service efficiency and capacity.

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 are waiting for their favorite octogenarian usher in Scenario B.1?

Explain how waiting lines can develop even when the service time is a constant.

An operations manager decides that customers should be processed based on the anticipated duration of their request instead of their arrival time. The system has been changed in what fashion?

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?

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 checkout line #2 where they spend an average of 10 minutes checking out. How many people are checking out in line #2 on average?

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 checkout line #2 where they spend an average of 10 minutes checking out. How many people are checking out in both lines on average?

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.

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.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 waiting time in line?

Create a table that lists any three performance measures for a service system in the left column. In the center column, indicate what steps management can take to improve system performance on those metrics. In the rightmost column indicate what steps management can take to improve customers' perceptions of performance on those metrics.

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?

What is a finite-source model? Give an example of its appropriate use.

Scenario B.6 The Jackson Machine Company has four cutting tools that need to be refurbished after an average of 30 hours, according to an exponential distribution. The single machine that refurbishes the tools needs 15 hours for each tool on the average, with exponential service times. -Use the information in Scenario B.6. What is the average utilization of the refurbishing machine?

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

The mean of the Poisson distribution is equal to its standard deviation.

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?

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?