Exam 19: Supplement B Waiting Lines

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?

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. -When not directing patrons to their seats, the octogenarian usher in Scenario B.1 sneaks in a little knitting. If she can knit one stitch every two seconds, how many stitches can she knit in an average hour of seating patrons?

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.

The best method for analyzing a waiting-line problem is to relate the five operating characteristics and their alternatives to dollars.

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?

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. -What is the likelihood that two patrons are in the system?

A drive-through system with one lane at a fast food restaurant where the first facility takes the order, the second takes the money, and the third provides the food is an example of a:

In the single-server model, the:

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?

A bank lobby with six teller windows, each with a separate line, is an example of a:

SimQuick is a process simulation software tool that can provide statistics on cycle time for simple processes such as waiting lines, inventory control, and projects.