MIT AATT Model Review Project under AATT Program

AND (MIT + MITRE)

(ARO; 7/15/96)

1. Primary Model Category:

System-wide model of airport delays

2. Summary:

AND (Approximate Network Delays) is a network queueing model developed at the MIT Operations Research Center, with software development support and database provided by the MITRE Corporation. Its objective is to analyze the impact of changes in airline schedules, traffic volume and airport capacity on flight delays on a national or regional basis. AND is an analytical tool and uses the DELAYS model as its engine for solving the differential equations that describe the distribution of delays over a network of airports, given flight schedules, aircraft itineraries and airport capacities. AND currently includes a database that encompasses the 58 busiest airports in the United States and can thus be used to estimate, on a national scale, the benefits and costs of local or regional changes in airport infrastructure and in terminal area ATM technologies and procedures.

3. Input Requirements:

The inputs required by AND are:

  1. The capacity profile of each of the airports of interest for the period of interest. (The typical period of interest in AND is one full day of network operations.) This capacity profile can be dynamic, i.e., the capacity may change at specified intervals of time. For example, if the period of interest is one day (midnight to midnight) and if the time interval specified is one hour, the capacity profile of each of the airports in thenetwork is specified by an array of 24 numbers, the first number giving the airports capacity from midnight to 1 a.m., the second from 1 a.m. to 2 a.m., etc.

  2. The demand profile for arrivals and for departures at each of the airports of interest for the period of interest. The demand profiles are specified in exactly the same way as the capacity profiles (see above) and thus can be dynamic.

  3. A complete schedule of flights that must be performed duringf the period of interest in the airport network of interest and the itineraries of each of the aircraft which will perform this schedule. For example, if Flight 123 by airline XYZ will begin from Airport A and then visit successively Airports B and C, before it terminates at D, the scheduled times of departure from A, arrival and departure at B and C and arrival at D must be provided. If, moreover, the aircraft that performed flight 123 will, after its arrival at D, be assigned to perform Flight 456, scheduled to depart from D at a later time, this also has to be indicated in the set of inputs to AND. (In the absence of data on aircraft itineraries, the AND model can be preceded by a pre-processor, prepared by the MITRE Corporation, which processes airline schedules to infer such itineraries.)

4. Outputs:

The principal quantity computed by AND is the probability vectors P(i, t, k) that i aircraft will be in queue (waiting to land or to take-off) at time t at airport k. The values of these probability vectors are computed for all values of i (i = 0, 1, 2, .....) at time t, for t = 0, Dt, 2 Dt, 3 Dt, ... up to the end of the time period of interest for all the airports in the network. Using the P(i, t, k), AND then computes derivative measures of performance such as:

  • the expected queue length at each airport as a function of time;
  • the expected waiting time for operations at each airport as a function of time;
  • the total delay suffered by aircraft during the entire period of interest at each airport;
  • the fraction of aircraft delayed at each airport by more than X minutes (e.g., 15 minutes) during the period of interest, where X is a user-specified value;
  • the part of the expected delay at each airport that can be attributed to local congestion and the part which is attributed to "upstream" delays, i.e., to congestion at airports visited earlier in the day.

5. Major Assumptions:

The AND model makes two fundamental assumptions: First, it does not deal at all with delay due to en route airspace congestion, assuming implicitly that the great majority of delays in the ATM system is due to airport and terminal area congestion. This assumption is true in certain ATM environments (such as the United States) but false in others (e.g., in Western Europe, where a substantial amount of air traffic delay is caused by lack of en route sector capacity).

Second, AND assumes that airports in the network under study are "weakly connected" meaning that no airport receives more than approximately 25% of its flights from any other single airport. This condition is necessary if the methodology used by AND is to be valid (see Reference (2) under item 12 below) and is indeed true for practically all major commercial airports in the world.

AND makes no distinction between arrivals and departures and treats all airport operations as demands that are served according to a first-come, first- served queue discipline. However, the effects of variations in the traffic mix (e.g., a high percent of arrivals during any particular hour) can be captured by adjusting accordingly the capacity of airports to reflect these variations.

Two additional assumptions of a more technical nature are due to the use of the DELAYS model (see review of DELAYS) as the "engine" of AND. Specifically, it is assumed that: demand at each airport can be approximated by a non-homogeneous Poisson process (i.e., demands occur at random instants with a demand rate that varies over time); and the service time per operation can be approximated by a k-th order Erlang random variable, with expected value (which may change over time) and standard deviation equal, respectively, to the corresponding (observed or estimated) expected service time and standard deviation of service time at the airport. (The appropriate order, k, of the Erlang random variable is determined by the relative magnitude of the expected service time and standard deviation of service time.)

Finally, in propagating delays through the network of airports, AND assumes that the delay suffered by each airport operation is equal to the expected value of the delay at the time when that operation is scheduled to take place. (For further discussion, see References (1) and (2) under item 12 below.)

6. Computational Characteristics:

AND is currently implemented in two versions, a serial model and a parallel model, both of which run on SUN SPARCstation 10 workstations. The parallel version exploits networks of workstations to speed up model execution by a factor of approximately 2. A typical execution time for a run involving a complete day of operations (about 50,000 landings and take-offs) at the 58 principal commercial airports in the United States takes approximately 20 minutes on the serial version (and approximately 10 on the parallel).

AND runs with a mouse-driven GUI, through which the user can select different scenarios for execution, create new scenarios or modify existing ones. An Editor is included with the GUI to facilitate the modification of the capacity profiles of the airports in the network, if desired. A map display facilitates the selection of airports to be included in the network being studied.

7. Modularity and Flexibility:

The AND model is modularly designed in the sense that the DELAYS model which serves as AND's "engine" can be easily replaced, if desired, by another model that computes delays at any given airport. The number of airports in the network can be easily adjusted and can range from 2 to 58, at this point.

8. Status of Model:

The current version of AND is a fully-developed working prototype that, while containing all the fundamental eventual capabilities of the model, can still be significantly improved through the addition of several significant features that would enhance its applicability. A plan for such improvements exists.

9. Extent of Model Validation:

A comparison has been conducted at MITRE between the results of the AND model and those of NASPAC. A set of tests involving a network containing many of the busiest airports in the United States, indicates that when NASPAC is used with all its features, NASPAC and AND give very similar results.

10. Principal applications:

The AND model is still an experimental tool and has not been used to date in specific applications.

11. Model Availability:

The model is not transportable at this point. Arrangements for its use can be made either through MIT (Professor Amedeo R. Odoni, Room 33-404, MIT, Cambridge, MA 02139, USA [(617) 253-7439, fax: (617) 253-7397; odoni@mit.edu]) or through MITRE (Dr. Andrew Haines, CAASD, The MITRE Corporation, 7525 Colshire Drive, McLean VA 22102, USA [(703) 883-6714; haines@mitre.org]).

12. Information Base for Model Evaluation:

The following documents describe the logic of the AND model:

  1. Malone, Kerry (1993) Modeling a network of queues under nonstationary and stochastic conditions, S.M. Thesis, Operations Research Center, Massachusetts Institute of Technology, Cambridge, MA.

  2. Malone, Kerry (1995) Dynamic queueing systems: behavior and approximations for individual queues and networks, Ph.D. thesis, Operations Research Center, Massachusetts Institute of Technology, Cambridge, MA.

13. Summary Evaluation:

The AND model is the first analytically-based (not simulation) model that provides a fast, and flexible tool for delay analysis in a network of airports. It is designed for supporting policy analyses that require approximate estimates of system performance under a broad range of alternative assumptions. Because it is an analytical model (and thus requires but a single run to compute the probability distribution of flight delays for any given set of capacity and demand conditions) AND can outperform considerably, in terms of computational efficiency, existing national-scale simulation models in addressing issues related to the propagation of delays in the system of airports and to the national or regional delay impacts of changes in airline schedules, in airport demand levels and in airport capacities. The model is macroscopic and reflects the dynamic and stochastic nature of ATM/airport operations.

The model disregards completely delays which are due to congestion of en route airspace and it is thus more appropriate for ATM environments (such as the United States) where the great majority of air traffic delays is associated with airport congestion. AND also cannot capture the impact on the distribution of delays among airport users of air traffic control strategies that would assign priorities to certain types of operations (e.g., arrivals) over others (e.g., departures). It can, however, estimate the aggregate effects of such strategies.

The model is still an experimental tool, as it is not transportable and lacks a number of desirable features that would facilitate its use and the preparation of certain of its inputs. If these features were added, AND would constitute a very competitive alternative to system-wide simulation models, such as NASPAC and FLOWSIM, for many types of policy-level studies.

Back to completed models page