Systems Engineering代写 Systems Analysis代写

Systems Analysis, Behavior and Optimization Project

Systems Engineering代写 During peak air travel times in the United States, there are about 5,000 airplanes in the sky every hour.

This project focuses on different aspects of air transportation. The first part is on building a discrete- event simulation model to assess the implications of different air traffic control policies. The second part is on carrying out a reliability analysis for the aircraft landing process. The third part is on building an optimization model for cargo transportation.

1. Air traffic control  Systems Engineering代写

During peak air travel times in the United States, there are about 5,000 airplanes in the sky every hour. This translates to approximately 50,000 airplanes operating in our skies each day. The task of ensuring safe operations of commercial and private aircraft falls mainly on air traffic controllers. They must coordinate the movements of thousands of aircraft, keep them at safe distances from each other, direct them during takeoff and landing from airports, help them around bad weather and ensure that traffic flows smoothly with minimal delays.

The Federal Aviation Administration (FAA) has established strict standards dictating the minimum distance between two aircraft approaching for landing. There are two main motivations to keep a minimum distance during the landing stage: When an aircraft is coming in for landing with flaps deployed and landing gear down, vortices, or air currents, are generated as the aircraft goes through the air. The vortices combine to form a turbulent wake in the aircraft’s path. The wake slowly descends out of the flight path and eventually dissipates.

If one aircraft flies too close behind another, it will encounter the preceding aircraft’s wake.

Flying through the turbulence of another aircraft’s wake can result in severe buffeting and, potentially, loss of control. Apart from the increased risk of wake vortex encounter, the landing aircraft have to keep a minimum separation to give the leading aircraft enough time to evacuate the runway before the trailing aircraft starts landing.  Systems Engineering代写

The distance required for a landing aircraft to come to a complete stop can vary widely. If two aircraft occupy a runway simultaneously, the trailing aircraft may need a longer distance to come to a complete stop than the leading aircraft. This increases the collision risk. Many researchers and experts in the airline industry believe the FAA’s separation standards are too conservative. Even the FAA believes that “$5 billion could be saved annually by the airlines if one could safely reduce the current separations by 15%.”

1.1. Description of the system 

We are concerned with analyzing the queueing of aircraft in the airspace of a single runway under normal operating circumstances. Bad weather and emergency situations are not considered in this analysis. The airspace for a single runway is conceptually divided into four parts: Initial contact point, landing queue, threshold point and landing zone; see Figure 1.  Systems Engineering代写

The aircraft approaching for landing first contact the air traffic controller at the initial contact point. Following this, they proceed to the landing queue to wait for their turn. The role of the landing queue is to provide aircraft with some space to circle around whenever the landing zone is not free and they cannot proceed to the final phase of landing. Each aircraft that reaches the threshold point and finds the landing zone occupied has to give up its turn and circle back to the end of the landing queue. If there are more than one aircraft in the landing queue, then they need to leave a certain amount of space between them. The final phase of landing is completed in the landing zone and there can be at most one aircraft in the landing zone.

1.2. Data

Inter-arrival times of the aircraft arriving at the initial contact point are normally distributed with mean 180 and standard deviation 60 seconds. A normally distributed random variable can take negative values. (If this happens in the simulation, then you should just keep generating normal random variables until you get one that is positive.) Following this, the aircraft proceed to the

landing queue, and the travel time from the initial contact point to the landing queue is normally distributed with mean 600 and standard deviation 150 seconds. (Again, avoid negative times in case they arise.)

If the aircraft arriving at the landing queue finds the queue empty, then it takes about 40 seconds to proceed to the threshold point. Otherwise, the aircraft may potentially spend more time in the landing queue. As far as the separation of the aircraft in the landing queue is concerned, aircraft can be classified into three types: Heavy, large and small.  Systems Engineering代写

Approximately 33%, 46% and 21% of the aircraft are respectively heavy, large and small. Depending on the size of the aircraft, there is a certain distance that should be kept between two successive aircraft in the landing queue.

These distances are not always kept precisely and it is appropriate to assume they are normally distributed. Table 1 shows the means and standard deviations of the distances in seconds.

(Mean)

(Standard deviation)

Table 1: Means and standard deviations of the separation distances in seconds. (If a sample from normal distribution turns out negative, then use the usual re-sampling trick as above.)

Aircraft may circle in the landing queue. Aircraft arriving at the threshold point check if the landing zone is clear. If the landing zone is clear, then it proceeds to the final phase of landing. The final phase of landing takes a normally distributed amount of time with mean 120 and standard deviation 30 seconds. If the landing zone is not clear, then the aircraft circles back to the end of the landing queue. The go-around time is normally distributed with mean 750 and standard deviation 150 seconds. (Same deal on negative values for these normal random variables.)

1.3. Objectives  Systems Engineering代写

Two important performance measures we are interested in are the average number of aircraft in the landing queue and the proportion of time that there are five or more aircraft in the landing queue. These performances measures do not include the aircraft that are in the process of going around. The goal is not only to estimate these performance measures accurately, but also to investigate how they are affected by different problem parameters. An important policy change that is being considered is to reduce the required separation between the aircraft in the landing queue. The pilots are now also required to adhere to the separation standards more strictly and this is expected to reduce the standard deviation of the separation distances. You need to explore other options that you can think of so as to reduce the congestion in the landing queue.

2. Reliability analysis  Systems Engineering代写

This portion of the project focuses on accident risk during final approach and landing due to insufficient in-trail separation between two landing aircraft. Insufficient in-trail separation increases the accident risk due to two main reasons. First, it may cause a wake vortex encounter. Second, it may cause simultaneous runway occupancy.

2.1. Wake vortex encounter

We start by examining the causes of wake vortex encounter. Any aircraft causes a certain amount of wake vortex but whether a wake vortex presents a significant danger to a trailing aircraft depends on the size of the leading aircraft creating the wake vortex and the size of the trailing aircraft subjected to the vortex. Depending on the size of the leading and the trailing aircraft, there is a certain probability that the wake vortex of the leading aircraft creates significant danger to the trailing aircraft.  Systems Engineering代写

These probabilities are given in Table 2. For example, if a heavy aircraft is followed by a small aircraft, then there is a 0.82 probability that the trailing aircraft will be dangerously affected by the wake vortex of the leading aircraft. Recall from Section 1.2 that the proportion of arriving aircraft by size is approximately 33% heavy, 46% large, and 21% small. These should provide enough information to estimate the probability that there is a dangerous wake vortex.

Table 2: Probabilities of wake vortex creating dangerous situation

As the data in Table 2 indicate, there is a high probability that the wake vortex created by a leading aircraft will create a dangerous situation to the trailing aircraft. This is why the FAA established the minimum in-trail separation standards. As long as the in-trail separation distance is maintained, the wake vortex of the leading aircraft will not put the trailing aircraft in any risk. However, in-trail

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