Each airline passenger and his luggage must be checked for security. Suppose that at Gotham City Airport, 3.6 passengers per minute arrive, on average. Also, assume that interarrival times are exponentially distributed. To check passengers for security, the airport must have a checkpoint consisting of a metal detector and baggage X-ray machine. Whenever a checkpoint is in operation, two employees are required. These two employees work simultaneously to check a single passenger. A checkpoint can check an average of 4.2 passengers per minute, where the time to check a passenger is also exponentially distributed. Under the assumption that the airport has only one checkpoint, answer the following questions. a. Why is an M / M /1, not an M / M /2, model relevant here? b. What is the probability that a passenger will have to wait before being checked for weapons? c. On average, how many passengers are waiting in line to enter the checkpoint? d. On average, how long will a passenger spend at the checkpoint (including waiting time in line)?

BuyFind

Practical Management Science

6th Edition
WINSTON + 1 other
Publisher: Cengage,
ISBN: 9781337406659
BuyFind

Practical Management Science

6th Edition
WINSTON + 1 other
Publisher: Cengage,
ISBN: 9781337406659

Solutions

Chapter
Section
Chapter 12.5, Problem 18P
Textbook Problem

Each airline passenger and his luggage must be checked for security. Suppose that at Gotham City Airport, 3.6 passengers per minute arrive, on average. Also, assume that interarrival times are exponentially distributed. To check passengers for security, the airport must have a checkpoint consisting of a metal detector and baggage X-ray machine. Whenever a checkpoint is in operation, two employees are required. These two employees work simultaneously to check a single passenger. A checkpoint can check an average of 4.2 passengers per minute, where the time to check a passenger is also exponentially distributed. Under the assumption that the airport has only one checkpoint, answer the following questions.

  1. a. Why is an M/M/1, not an M/M/2, model relevant here?
  2. b. What is the probability that a passenger will have to wait before being checked for weapons?
  3. c. On average, how many passengers are waiting in line to enter the checkpoint?
  4. d. On average, how long will a passenger spend at the checkpoint (including waiting time in line)?

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Chapter 12 Solutions

Practical Management Science
Ch. 12.5 - The MM1 Template.xlsx file is now set up so that...Ch. 12.5 - The MM1 Template.xlsx file is now set up so that...Ch. 12.5 - Expand the MM1 Template.xlsx file so that the...Ch. 12.5 - For an M/M/1 queueing system, L = /( ). Suppose...Ch. 12.5 - Suppose that you observe a sequence of...Ch. 12.5 - In the M/M/s model, where is the service rate per...Ch. 12.5 - Expand the MMs Template.xlsm file so that the...Ch. 12.5 - Each airline passenger and his luggage must be...Ch. 12.5 - A supermarket is trying to decide how many cash...Ch. 12.5 - A small bank is trying to determine the number of...Ch. 12.5 - In this problem, assume that all interarrival and...Ch. 12.5 - MacBurgers is attempting to determine how many...Ch. 12.5 - On average, 100 customers arrive per hour at the...Ch. 12.5 - A service facility consists of one server who can...Ch. 12.5 - On average, 40 cars per hour are tempted to use...Ch. 12.5 - A laundromat has five washing machines. A typical...Ch. 12.5 - The limited source model can often be used to...Ch. 12.5 - Consider an airport where taxis and customers...Ch. 12.5 - A bank is trying to determine which of two...Ch. 12.5 - A worker at the State Unemployment Office is...Ch. 12.5 - For the M/M/1 queueing model, why do the following...Ch. 12.5 - Referring to Problem 18, suppose the airline wants...Ch. 12.5 - The manager of a bank wants to use an M/M/s...Ch. 12.5 - On average, 100 customers arrive per hour at...Ch. 12.5 - Consider the following two queueing systems....Ch. 12.5 - Two one-barber shops sit side by side in Dunkirk...Ch. 12.5 - The small mail-order firm Seas Beginning has one...Ch. 12 - On average, 50 customers arrive per hour at a...Ch. 12 - On average, 300 customers arrive per hour at a...Ch. 12 - Ships arrive at a port facility at an average rate...Ch. 12 - A printing shop receives an average of one order...Ch. 12 - On average, 40 jobs arrive per day at a factory....Ch. 12 - At the Franklin Post Office, patrons wait in a...Ch. 12 - The manager of a large group of employees must...Ch. 12 - On average, 90 patrons arrive per hour at a hotel...Ch. 12 - Bloomington Hospital knows that insurance...Ch. 12 - Excessive delays have recently been noted on New...Ch. 12 - Suppose that annually an average of library...Ch. 12 - Based on Quinn et al. (1991). Winter Riggers...Ch. 12 - Zerox has 16 service centers throughout the United...Ch. 12 - Based on Kolesar et al. (1974), Metropolis PD...

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