LMI Runway Capacity Model
(5/6/96 ARO)
1. Primary Model Category:
Runway system capacity.
2. Summary:
The LMI Capacity Model is a generalized analytical and stochastic model for computing the capacity of a runway system. Its fundamental building block is a model that computes the capacity of a single runway, when the runway is used for arrivals only or for departures only or for mixed operations (arrivals and departures).A key feature of the LMI model is that it attempts to take into account explicitly probabilistic aspects of airport operations. So, for example, the approach speeds, the runway occupancy times and the delay in communication time between airport controllers and pilots are all incorporated into the model as random variables. Another important feature is that the model takes a "controller-based view" of operations. In this respect, it calculates the spacing between aircraft as they enter the common approach path such that, with reasonable confidence, no violations will occur later.
The LMI Capacity Model is designed to compute the so-called "runway capacity curve", i.e., the set of points that define the envelope of the maximum throughput capacities that can be achieved at a single runway, under the entire range of possible arrival and departure mixes. Specifically, the model determines four points on the runway capacity curve. By interpolating between pairs of points with straight-line segments, one can then obtain (approximately) the full runway capacity curve. The four points are the following:
- Point 1: The "all arrivals" point, i.e., the capacity of the runway when
it is used for arrivals only.
- Point 2: The "freely inserted departures" point which has the same
arrival capacity as Point 1 and a capacity for departures equal to the number of
departures that can be inserted into the arrival stream "for free", i.e., by
exploiting large interarrival gaps without increasing the separations between
successive arrivals (and, thus, without reducing the number of arrivals from
what can be achieved in the all-arrivals case).
- Point 3: The "alternating arrivals and departures" point, i.e., the point
at which an equal number of departures and arrivals is performed. This is
achieved through an arrival-departure-arrival-departure-... sequencing,
implemented by "stretching", when necessary, the interarrival gaps, so that a
departure can always be inserted between two successive arrivals.
- Point 4: The "all departures" point, i.e., the capacity of the runway
when it is used for departures only.
3. Input Requirements:
Input parameters to the model include: the mix and number of aircraft types at the runway (pi); the length of the common approach path (D); the mean and standard deviation of the approach speed of each aircraft type [Vi, sd(Vi)]; the mean and standard deviation of the arrival and departure runway occupancy times [RAi, sd(RAi), RDi, sd(RDi)]; the miles-in-trail separation minima for all pairs (i,j) of aircraft types (Sij); the standard deviation of wind speed encountered by aircraft i on final approach [sd(Wi)]; the uncertainty in the position of aircraft i, quantified by the standard deviation, sd(Xi) of its location, Xi, along the final approach; and the mean and standard deviation of the communication time delay [c, sd(c)]. For departures, the model also uses the mean and standard deviation of the departure speed for each aircraft class and the minimum distance that departing aircraft must fly before turning. All the input random variables are approximated as normally distributed to facilitate the derivation of approximate expressions for the expected values and standard deviations of parameters of interest.
4. Outputs:
Capacity of a single runway for the four operating conditions (Points 1, 2, 3 and 4) described in Section 2 above. Capacity is defined here as the number of operations that can be carried out on a runway with 95% confidence in the presence of continuous demand. (Note that, although related, this definition is different from the usual definition of "maximum throughput capacity"; the latter is simply the expected number of operations that can be carried out in the presence of continuous demand.)
5 Major Assumptions:
As noted, the LMI capacity model assumes, for computational purposes that all its input variables are normally distributed with known expected values and standard deviations. The model also uses a new definition of capacity ("the number of operations that can be carried out in one hour with 95% confidence"). The model assumes that the "double occupancy rule" (two landing aircraft should not be on the same runway at the same time) should be maintained 98.7% of the time.
6. Computational Characteristics:
The LMI Capacity Model runs on a PC and requires no significant computational features. Versions of the single runway model have been prepared in both Pascal and C. The Pascal code is given in Appendix A of the document referenced in Section 12 below. The model uses a GUI, in the form of a Lotus spreadsheet, which allows the user to enter the model's input parameters and displays the capacity curve implied by the current parameters, as well as the curve implied by a set of reference parameters.
7. Modularity and Flexibility:
The LMI Capacity Model is very easy to use and can potentially be incorporated as a module into models of more extensive scope, such as a model that would compute not only airport capacity, but also airport delays.
8. Status of Model:
The LMI Model has been developed only recently. A generalized model exists only for single-runway operations. Applications that extend the model in an ad hoc way to multiple runway operations have been carried out for the Detroit and Boston Logan airports.
9. Extent of Model Validation:
The single runway model has been partially validated through comparison of its results with those of the FAA Airfield Capacity Model. The ad hoc extensions to multiple runway operations (see Section 8 above) have been validated through comparisons with the capacities actually achieved at the Detroit and Boston Logan airports.
10. Principal applications:
The LMI Capacity Model is currently being used in connection with the evaluation of the potential benefits of the NASA Terminal Area Productivity (TAP) Program.
11. Model Availability:
Arrangements for obtaining the code for the LMI Capacity Model can be made by contacting Dr. David A. Lee [dlee@mail2.lmi.org, (703)-917-7557] or Dr. Peter F. Kostiuk [pkostiuk@lmi.org, (703) 917-7427].
12. Information Base for Model Evaluation:
Brief discussions with Dr. Peter F. Kostiuk and Dr. David A. Lee.Report: Earl W. Wingrove, David A. Lee, Peter F. Kostiuk, Robert V. Hemm, Estimating the Effects of the Terminal Area Productivity Program, Logistics Management Institute, McLean, VA.
13. Summary Evaluation:
The LMI Capacity Model is still not fully developed; it currently consists of a single runway model only with some ad hoc extensions to configurations with multiple runways. A more definitive evaluation of the model must therefore wait until completion of model development. However, the work done to date is very promising. The exposition of the single runway model is rigorous and the model's assumptions are clearly stated and explained. The model constitutes the first attempt after many years to develop another analytical model of a probabilistic nature that would approximate well airport capacity under a wide variety of conditions. Its results, for the cases to which it has been applied to date are close to those observed in the field.A technical aspect that may require improvement in the future is the logic for inserting departures between arrivals on the same runway: for example, the model does not currently include a minimum distance separation between a departure and the following arrival at the time when the departure is set to begin its take-off roll; the model may also be inserting too many "free" departures between arrivals under certain conditions. The definition of capacity as "the number of operations that can be carried out in one hour with 95% confidence" is also unconventional and may result in lower estimates of capacity than those obtained under "the maximum throughput rate" definition of capacity. However, the LMI Capacity Model can be easily adjusted to provide estimates consistent with the "maximum throughput rate” definition.
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