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Queuing Networks

An airline security checkpoint may be modelled as a system of two queueing networks, one for trays and the other for passengers. Let's focus on the queue associated with the passengers. The passengers arrive at a rack of trays to hold items to be X-rayed, load the trays, and then queue to walk through a metal detector while the trays go through an X-ray machine. The network seen by the customers consists of one or more guard stations at which identities and boarding passes are checked, followed by a queue for trays, and then another queue to go through the metal detector.

Identify the type of queueing network traversed by the passengers. Explain the effect on passenger delays of having (i) multiple X-ray machines and tray racks, (ii) too few trays, and (iii) a single agent for checking boarding passes and identity documents.

Propose configurations of X-ray machines, tray pallets, and ID inspection lines when the airport has a policy of giving priority to frequent fliers at the entrance to the security area. Explain what happens if the proportion of frequent fliers at a given hour is high or low.

Full Answer Section

Here are some proposed configurations of X-ray machines, tray pallets, and ID inspection lines when the airport has a policy of giving priority to frequent fliers at the entrance to the security area:

One X-ray machine, one tray pallet, and one ID inspection line: This is the simplest configuration and is likely to be the least efficient. Frequent fliers will have to wait in line with everyone else, and this could lead to long delays.
Multiple X-ray machines, one tray pallet, and one ID inspection line: This configuration is more efficient than the previous one because it allows more passengers to be processed through the security checkpoint at the same time. Frequent fliers will still have to wait in line with everyone else, but the wait time will be shorter.
Multiple X-ray machines, multiple tray pallets, and one ID inspection line: This is the most efficient configuration and is likely to be the best option for airports with a high volume of traffic. Frequent fliers will have their own dedicated line, which will ensure that they do not have to wait as long.

If the proportion of frequent fliers at a given hour is high, then the airport should use the configuration with multiple X-ray machines, multiple tray pallets, and one ID inspection line. This will ensure that the security checkpoint can handle the increased volume of traffic. If the proportion of frequent fliers is low, then the airport could use a less complex configuration, such as the one with one X-ray machine, one tray pallet, and one ID inspection line.

Here are some additional factors that should be considered when designing the configuration of X-ray machines, tray pallets, and ID inspection lines:

The number of passengers expected to pass through the security checkpoint each hour.
The size of the security checkpoint.
The budget available for the project.
The security requirements of the airport.

By carefully considering all of these factors, airports can design a configuration that will minimize passenger delays and ensure the security of the security checkpoint.

Sample Answer

The queueing network traversed by the passengers is a tandem queue. A tandem queue is a queueing network in which customers must go through a series of queues, each of which represents a different stage in the process. In the case of an airline security checkpoint, the first queue is for the trays, the second queue is for the metal detector, and the third queue is for the ID inspection.

The effect on passenger delays of having (i) multiple X-ray machines and tray racks, (ii) too few trays, and (iii) a single agent for checking boarding passes and identity documents is as follows:

Multiple X-ray machines and tray racks: This will reduce passenger delays because it will allow more passengers to be processed through the security checkpoint at the same time.
Too few trays: This will increase passenger delays because it will force passengers to wait longer for a tray.
A single agent for checking boarding passes and identity documents: This will increase passenger delays because it will slow down the process of checking passengers in.

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