DELAYS (MIT) (ARO; 7/31/96)
1. Primary Model Category:
Airport delays.2. Summary:
DELAYS is an approximate and easy-to-use analytical model (not simulation) for estimating quickly delays at airports due to runway system congestion. The model solves approximately and very efficiently a set of first- order ordinary differential equations that describe the formation and dissipation of queues for the use of the runway system over time. DELAYS is a dynamic queueing model, i.e., it can be used with airport demand and/or airport capacity that varies over time. Unlike so-called "steady state" queueing models, DELAYS allows demand to exceed capacity for short or long periods of time. For any given dynamic capacity "profile" and demand "profile" on a particular day, DELAYS provides approximate estimates of expected delay and expected queue length at the airport by time of day, as well as of the fraction of aircraft delayed by more than any specified amount of time at any time of the day. In fact, DELAYS computes the entire probability distribution for the number of aircraft waiting to land and/or to take off at any time during a day and thus can be programmed to provide approximate estimates of any aggregate or distributive metric related to airport delay as a function of time.
3. Input Requirements:
The fundamental inputs to DELAYS are the "capacity profile" and the "demand profile" during the day of interest. For example, when the day is subdivided into 24 one-hour time intervals, the capacity profile consists of an array of 24 numbers describing the airport capacity (maximum throughput capacity should be used) in hour 1, hour 2, ...., hour 24. Similarly the demand profile would be described by another array giving the number of operations demanding access to the runway system in hour 1, 2, ...., 24. The only other input of significance is the "order" of the probability distribution for the service time (see Section 5 below); this input describes implicitly the general "shape" of the distribution. The remaining inputs specify the length of the run, the outputs desired, etc.
4. Outputs:
The principal quantity computed by DELAYS is the probability vector P(i, t) that i aircraft (arrivals, departures, or both --depending on the case specified) will be in queue (landing queue only, take-off queue only or both, respectively) at time t. The values of this probability vector 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 being analyzed, which is typically (default value) equal to 24 hours. Using the P(i, t), DELAYS then computes: the expected queue length at time t (for any set of desired time intervals); the expected waiting time for an operation requesting access to the runway system at time t; the total delay suffered by aircraft during the entire period of interest; and the fraction of aircraft delayed by more than X minutes (e.g., 15 minutes) during the period of interest, where X is a user-specified value.
5. Major Assumptions:
The airport is represented as a queueing system with a demand rate and a capacity that can be (and usually are) dynamic (i.e., may vary with time of the day, day of the week, season, weather conditions, etc.). "Demand" and "capacity" can refer to:
- Arrival demand and arrival capacity only, if arrivals are
processed relatively independently of departures at the airport of
interest, as is the case at many European and several major US
airports.
- Departure demand and departure capacity only, under the
same conditions as (i),
- Total operations demand and total airport capacity, for
airports where arrival and departure capacity are strongly
interdependent (for example, share the same runway(s)) as at many
U.S. airports; in this case the entire airport is viewed as a single
queueing system.
6. Computational Characteristics:
DELAYS is written in C and therefore requires a C compiler. It runs on desktop computers, with both PC and Macintosh versions of the software are available. Typical running times on a Power Mac are of the order of 20 seconds for a 24-hour run for a very busy airport, with capacity and demand of the order of 100 operations per hour and long queues forming. A run involving 200 consecutive days of operations at Logan International Airport of Boston took approximately 20 minutes
7. Modularity and Flexibility:
DELAYS can be made part of a package with a capacity model (such as the FAA Airfield Capacity Model or the LMI Capacity Model). In this arrangement, the airfield capacity estimated by the capacity modeland becomes an input to DELAYS, which then computes delay measures. DELAYS can also be incorporated as a module in more complex schemes: for example, it currently serves as the engine of the Approximate Network Delays (AND) model. There is no GUI.
8. Status of Model:
No changes are planned at this time.
9. Extent of Model Validation:
The accuracy of the approximate estimates of queueing statistics provided by DELAYS has been validated extensively by Malone (see Item 12 below) through comparisons with exact solutions of queueing systems with non- homogeneous Poisson demands and Erlang-distributed service times. Comparisons with simulation results and with field data from Logan airport also indicate good agreement with model predictions.
10. Principal applications:
DELAYS has been used extensively in location-specific studies of airport delays (Boston, Milan, New York LaGuardia, Sydney, Stockholm). It has also been used in several cost-benefit analyses, in connection with the estimation of the delay savings that would be obtained from various types of capacity improvements.
11. Model Availability:
DELAYS is available through MIT's Operations Research Center at a cost of $500. Contact Professor Amedeo R. Odoni, Room 33-218, MIT, Cambridge, MA 02139, USA [(617) 253-7439, fax: (617) 253-7397; odoni@mit.edu].
12. Information Base for Model Evaluation:
The following MIT theses cover various aspects of DELAYS:
- Abundo, S. (1990) An approach for estimating delays at a
busy airport, S.M. Thesis, Operations Research Center, Massachusetts
Institute of Technology, Cambridge, MA.
- Kivestu, P. (1976) Alternative methods of investigating
the time-dependent M/G/K queue, S.M. Thesis, Department of Aeronautics
and Astronautics, Massachusetts Institute of Technology, Cambridge,
MA.
- 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.
- 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:
DELAYS is a powerful and easy-to-use tool for computing approximately airport delays under dynamic conditions. It is particularly well-suited for parametric studies, for example in identifying the level of demand at which delay at a particular airport will exceed a specified threshold thus necessitating an increse in airport capacity. Being an analytical model DELAYS does not suffer from the standard difficulties associated with simulation models (multiple runs needed, lack of cause-and-effect relationships, need for identyification of confidence intervals of a simulation's results).On the negative side, DELAYS cannot provide a level of detail and realism comparable to that of a simulation model. The model also cannot capture the effects on airport delays of aircraft sequencing strategies that deviate from first- come, first-served. For example, if arrivals share a runway with departures and receive priority over departures, DELAYS will compute the same average delay for arrivals and for departures, whereas, in truth, arrivals will experience a lower average delay (per operation) and departures a higher average delay than the overall average computed by DELAYS. The lack of a graphical interface is another deficiency of DELAYS.
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