The airside models discussed so far are descriptive in nature. Their objective is to help users understand and predict the operational characteristics of the various airside facilities under different operating scenarios. A considerable amount of OR work with an optimization focus also exists, much of it concerned with the effective use of runway systems. The capacity of a runway is largely determined by the separation requirements specified by the providers of ATM services (e.g., the FAA in the United States). For any pair of consecutive runway operations these requirements depend on the type of aircraft involved. For example, in the United States, when an arriving “heavy” (H) aircraft—defined as one with a maximum takeoff weight (MTOW) greater than 255,000 lbs—is immediately followed by an arriving “small” (S) aircraft (MTOW < 41,000 lbs), the required separation between them, at the instant when H is about to touch down on the runway, is 6 nautical miles (∼10.9 km). This is because “heavy” aircraft (wide-body jets) may generate severe wake turbulence, which may be hazardous to other aircraft behind it. By contrast, when an aircraft of type S is followed by one of type H, the required separation is 2.5 nautical miles (∼4.5 km). Note that given a number n of aircraft, all waiting to land on a runway, the problem of determining the sequence of landings, such that the time when the last aircraft lands is minimized, is a Hamiltonian path problem with n points. However, this is only a static version of a problem which in truth is a dynamic one: Over time the pool of aircraft available to land changes, as some aircraft reach the runway while new aircraft join the arrivals queue. Moreover, minimizing the “latest landing time” (or maximizing “throughput”) should not necessarily be the objective of optimal sequencing. Many alternative objective functions, such as minimizing the average waiting time per passenger, are just as reasonable. A further complication is that the very idea of “sequencing” runs counter to the traditional adherence of ATM systems to a first-come, first-served (FCFS) discipline. Deviations from FCFS raise concerns among some airside users about thepossibility of systematic discrimination against certain classes of aircraft operators (e.g., general aviation) when it comes to runway access. In a dynamic environment, this may even result in a compromise of safety, if some aircraft are indefinitely relegated to the end of the queue as new aircraft show up to land. These observations have led many investigators to study the runway-sequencing problem with the objective of increasing operating efficiency while ensuring that all airport users are treated equitably. Dear (1976) and Dear and Sherif (1991) developed the concept of constrained position shifting (CPS), i.e., of a limit in the number of positions by which an aircraft can deviate from its FCFS position in a queue. For instance, an aircraft in the 16th position in a FCFS queue would have to land in one of the positions 14–18 if the specified maximum position shift (MPS) is 2. Through many numerical examples and for several reasonable objective functions, Dear (1976) showed that by setting MPS to a small number, such as two or three, one can obtain most of the benefits of an unconstrained optimized system (e.g., 60%–80% of the potential improvements). This finding motivated several researchers (e.g., Psaraftis 1980, Venkatakrishnan et al. 1992, Bianco et al. 2001) to investigate a number of increasingly complex and realistic versions of the sequencing problem. Two advanced terminal airspace automation systems, CTAS and COMPAS, that have been implemented in the United States and in Germany, respectively, incorporate sequencing algorithms based on CPS (Erzberger 1995). However, this feature of CTAS and of COMPAS has not been activated, primarily because of concerns about a potential increase in controller workload. Gilbo (1993) and Hall (1999) have gone beyond the sequencing of arrivals only by considering how available capacity can best be allocated in a dynamic way between landings and takeoffs to account for the distinct peaking patterns in the arrival and departure streams at airports over the course of a day. Pujet et al. (1999) have further examined the issue of optimizing the number of aircraft taxiing out during periods of congestion, based on the empirical observation that departure rates at major airports seem to decrease when the number of active aircraft on the taxiway system exceeds a certain airport-specific threshold.
Although still at the theoretical stage, some of these promising ideas will eventually find their way into practice.
The airside models discussed so far are descriptive in nature. Their objective is to help users understand and predict the operational characteristics of the various airside facilities under different operating scenarios. A considerable amount of OR work with an optimization focus also exists, much of it concerned with the effective use of runway systems. The capacity of a runway is largely determined by the separation requirements specified by the providers of ATM services (e.g., the FAA in the United States). For any pair of consecutive runway operations these requirements depend on the type of aircraft involved. For example, in the United States, when an arriving “heavy” (H) aircraft—defined as one with a maximum takeoff weight (MTOW) greater than 255,000 lbs—is immediately followed by an arriving “small” (S) aircraft (MTOW < 41,000 lbs), the required separation between them, at the instant when H is about to touch down on the runway, is 6 nautical miles (∼10.9 km). This is because “heavy” aircraft (wide-body jets) may generate severe wake turbulence, which may be hazardous to other aircraft behind it. By contrast, when an aircraft of type S is followed by one of type H, the required separation is 2.5 nautical miles (∼4.5 km). Note that given a number n of aircraft, all waiting to land on a runway, the problem of determining the sequence of landings, such that the time when the last aircraft lands is minimized, is a Hamiltonian path problem with n points. However, this is only a static version of a problem which in truth is a dynamic one: Over time the pool of aircraft available to land changes, as some aircraft reach the runway while new aircraft join the arrivals queue. Moreover, minimizing the “latest landing time” (or maximizing “throughput”) should not necessarily be the objective of optimal sequencing. Many alternative objective functions, such as minimizing the average waiting time per passenger, are just as reasonable. A further complication is that the very idea of “sequencing” runs counter to the traditional adherence of ATM systems to a first-come, first-served (FCFS) discipline. Deviations from FCFS raise concerns among some airside users about thepossibility of systematic discrimination against certain classes of aircraft operators (e.g., general aviation) when it comes to runway access. In a dynamic environment, this may even result in a compromise of safety, if some aircraft are indefinitely relegated to the end of the queue as new aircraft show up to land. These observations have led many investigators to study the runway-sequencing problem with the objective of increasing operating efficiency while ensuring that all airport users are treated equitably. Dear (1976) and Dear and Sherif (1991) developed the concept of constrained position shifting (CPS), i.e., of a limit in the number of positions by which an aircraft can deviate from its FCFS position in a queue. For instance, an aircraft in the 16th position in a FCFS queue would have to land in one of the positions 14–18 if the specified maximum position shift (MPS) is 2. Through many numerical examples and for several reasonable objective functions, Dear (1976) showed that by setting MPS to a small number, such as two or three, one can obtain most of the benefits of an unconstrained optimized system (e.g., 60%–80% of the potential improvements). This finding motivated several researchers (e.g., Psaraftis 1980, Venkatakrishnan et al. 1992, Bianco et al. 2001) to investigate a number of increasingly complex and realistic versions of the sequencing problem. Two advanced terminal airspace automation systems, CTAS and COMPAS, that have been implemented in the United States and in Germany, respectively, incorporate sequencing algorithms based on CPS (Erzberger 1995). However, this feature of CTAS and of COMPAS has not been activated, primarily because of concerns about a potential increase in controller workload. Gilbo (1993) and Hall (1999) have gone beyond the sequencing of arrivals only by considering how available capacity can best be allocated in a dynamic way between landings and takeoffs to account for the distinct peaking patterns in the arrival and departure streams at airports over the course of a day. Pujet et al. (1999) have further examined the issue of optimizing the number of aircraft taxiing out during periods of congestion, based on the empirical observation that departure rates at major airports seem to decrease when the number of active aircraft on the taxiway system exceeds a certain airport-specific threshold.Although still at the theoretical stage, some of these promising ideas will eventually find their way into practice.
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