Congestion and uncertainty on the airport surface are major constraints to the available capacity of the air transport system. This project is to study the problem of planning and scheduling airport surface movement at large airports. Specifically, we focus on the departure time scheduling and taxiway path planning of multiple aircraft under uncertainty. We also developed a simulation tool that is capable of simulating aircraft movement along the taxiway and possible uncertainty during the movement

Gong, Mimi

Koenig, Sven

Li, Jiaoyang

Liang, Zi

Liu, Weizi

Morris, Robert

Pasareanu, Corina

Tong, Zhongyi

Yi, Liangchen

Zhang, Han

NASA Technical Reports Server

Scheduling and Airport Taxiway Path Planning under
Uncertainty
Jiaoyang Li∗ and Han Zhang∗
University of Southern California, Los Angeles, CA, 90089
Mimi Gong†, Zi Liang†, Weizi Liu†, Zhongyi Tong†, and Liangchen Yi†
Carnegie Mellon University Silicon Valley, Moffett Field, CA, 94025
Robert Morris‡ and Corina Pasareanu§
NASA Ames Research Center MS-269-1, Moffett Field, CA, 94025
Sven Koenig¶
University of Southern California, Los Angeles, CA, 90089
Congestion and uncertainty on the airport surface are major constraints to the available
capacity of the air transport system. This project is to study the problem of planning and
scheduling airport surface movement at large airports. Specifically, we focus on the departure
time scheduling and taxiway path planning of multiple aircraft under uncertainty. We also
developed a simulation tool that is capable of simulating aircraft movement along the taxiway
and possible uncertainty during the movement.
I. Introduction
Airport surface operations present a difficult, large-scale logistics problem with a wide range of sub-problems,
including: runway sequencing and scheduling; spot or gate release scheduling; gate allocation and taxi route planning
and scheduling. Surface movement planning and scheduling is dynamic, with aircraft continuously entering and leaving
the operating space. Furthermore, surface movement is unpredictable and prone to unexpected changes in operating
conditions due to external factors such as weather. In general, efficiency and safety are difficult objectives to achieve
in practice, due to the challenges posed by the presence of uncertainties, human factors, and competing stakeholder
interests.
Fast-time simulation of uncertainty in airport surface operations allows for the testing and analysis of modeling
concepts and algorithms for planning and scheduling aircraft movement. This paper extends previous and current
work in this area [1] [2] by evaluating the result of incorporating probabilistic models into the planning and scheduling
process. Our goal is to compare probabilistic approaches to planning and scheduling with standard heuristic approaches
that assume a deterministic world, and as a separate stage address uncertainty through continuous re-planning [3]. The
goal is to determine whether incorporating recent advances in probabilistic reasoning in planning and scheduling yields
more robust schedules through the anticipation of surface delays.
In the remainder of this paper we will provide an overview of a fast-time simulation and scheduling tool for evaluating
approaches to planning surface operations, including the technical approach to modeling the geometry and dynamics of
airport movement, and the approach to scheduling. We conclude with a summary of the current and expected results of
this work for the final draft of the paper.
II. System Overview
The Airport Surface Planner and Simulation System is summarized in Figure 1. The inputs to the main system
component, the Simulator, consists of the following:
∗PhD Student, Computer Science Department.
†Master Students, Information Networking Institute.
‡Senior Researcher, Intelligent Systems Division.
§Researcher, Intelligent Systems Division/Associate Research Professor, Carnegie Mellon University Silicon Valley.
¶Professor, Computer Science Department.
1
https://ntrs.nasa.gov/search.jsp?R=20190028238 2019-09-26T20:11:53+00:00Z
• An airport node-link model automatically generated from a Google Map page;
• An aircraft dynamics model, for specifying speeds along the taxiway for different types of aircraft;
• A set of shortest path routes to and from gates and runways, used by the scheduler to generate itineraries for each
aircraft on the surface;
• A scenario, a problem instance to the scheduler, consisting of a set of arrivals and departure information, including
scheduled arrival or departure times, as well as gate and runway information;
• A set of clock parameters to guide the progression of the simulation;
• A set of parameters that describe the level of uncertainty in the problem. These parameters allow for the testing of
different levels of uncertainty during simulation;
• A scheduler used in the simulation; and
• A set of test parameters that allow for the collection of statistics when the simulator is in batch mode (i.e. when
multiple simulations are run).
Fig. 1 Airport Surface Planner and Simulation Architecture
The Simulator is comprised of three main components: the initialization, the Tick module, and the Scheduler. The
Initialization component loads the inputs and models, and invokes the main loop, called the Tick module. The Tick
module advances a world state in time, where a world state is comprised of the locations and speeds of all the aircraft.
The state also consists of a set of itineraries (schedules) for each aircraft, generated from previous calls to the Scheduler.
Tick uses the current state as well as the input data, models and parameters to add, delete or advance aircraft along the
airport surface. The output of each run of Tick is a new state. The new state is either fed back directly into the Tick, or,
as designated intervals, into the Scheduler. Finally, the Scheduler updates the itineraries associated with the airport
state. Specifically, an itinerary is a set of aircraft and associated targets, where the targets are nodes on the node-link
graph of the airport. The targets are either generated by the pre-compiled shortest path routes, or incrementally inside
the scheduler itself. The output of the scheduler is an updated set of conflict free itineraries, which are fed back into
the next iteration of the Tick. An itinerary is said to be conflict-free if no pair of aircraft are ever in an unsafe state
(violating separation constraints) as the result of executing their associated itineraries simultaneously.
The entire system was implemented in Python and C++. The remainder of this section will explore the main system
components in more detail.
2
A. Node-Link Model and Scenario Generation
The system allows for a node-link model to be generated for any airport from Google Maps. The steps required
to build an airport model consist of, first, editing a Google map by adding the desired nodes and edges for runways,
taxiways, spots (nodes linking ramp areas with taxiways), and gates; second, downloading the KML file from Google
Maps; and third, build a graphical node-link model by running a Python script using the downloaded KML file. It
should be noted that the system automatically creates a node-link model with two degrees of resolution: a coarse model
that can be used by the Scheduler to generate itineraries; and a fine-grained model that allows for a more realistic
simulation and visualization of airport movement.
For faster processing of large airport models, we performed some optimizations. In particular, the routing and
scheduling requires a model with nodes for every intersection on the surface, in order to test for conflicts, as discussed
below. In addition, for high resolution modeling of movement along a curved link, we split a link into a set of segments
that were approximately joined by a straight line. Adding gates and runway terminal nodes results in a graph with a
potentially large number of nodes. On the other hand, airports tend to be graphically sparse: each node typically has only
one or two nodes coming in or out of it, and relatively few nodes are intersecting nodes. Therefore as a pre-processing
step, for the purpose of fast routing, a set of optimizations was performed to limit the graph used for routing to nodes
that formed intersections between links.
A random scenario can be generated from a node-link model. The scenario generator is not at this point fully
automatic; rather the user must specify a set of arrival and departure flight templates using the nodes of the model (gates,
runways) and a list of aircraft. The generator will randomly assign arrival or departure times to the templates. The user
can set parameters that indicate the ’tightness’ of the scenario, i.e., the spacing of the times.
For this paper, we selected a specific flow pattern or arrivals and departures from San Francisco Airport (SFO).
Figure 2 shows a node-link model extracted from Google Maps, containing 100 gates, all taxiways and 4 runways
that allow for modeling flows on specific pattern called the Southeast Plan. In this flow, aircraft typically arrive on
Runway 19L with Runway 19R used as an alternate arrival runway (red lines running northeast/southwest). Departure
runways are 10L and 10R (red lines running northwest/southeast). Also modeled are exits and entrances to taxiways
from runways, and taxiways (blue lines). Finally, unrestricted areas contain gates and node/links to spot nodes. The
result, although a simplification from the complete model of airport flow, is complex enough to test our concepts of
planning under uncertainty.
Fig. 2 SFO airport model.
3
B. Simulator and Visualizer Models
Airport operations is a distributed logistics problem. Consequently, to simulate operations we explicitly model the
coordination between a ground controller and pilots for ensuring safe surface movement. Specifically, a Controller
module (invokes during a Tick operation) observes the current flow to control the traffic in the intersections. It decides
the order of aircraft to pass through each intersection while keeping safe separation between aircraft. The eventual goal
of the Controller is to simulate common ATC instructions to pilots, such as "Taxi via...", "Cross Runway..." , "Hold
short", etc [4].
An agent model is used to simulate aircraft decision making on the surface (this could be the pilot, or an autonomous
aircraft towing vehicle, as proposed in [5]. Specifically, this model is used to simulate pilot adjustments to ensure safe
distances. In developing the agent model we incorporated recent advances in car-following models for self-driving cars
[6].
The Uncertainty model allows for the simulation of exogenous events (specifically delays) that affect run-time
operations and allows for the testing of more sophisticated scheduling strategies. Delays are injected randomly into
the simulator during a Tick operation based on a set of parameters specifying the frequency with which delays occur.
Currently, delays can be injected at gate nodes and runway nodes. Injecting a delay during a simulation means that with
some probability an aircraft will not advance from its current node (for example, a departure from a gate node) to a
target node specified on its itinerary.
The output of the simulator is a sequence of states that provides a complete run of the scenario. This output can be
either stored and played back, or streamed in ’real time’ by the Visualizer. A window in the display shows the set of
active aircraft and their progress along the surface. Figure 3 shows a snapshot of the visualizer replaying a scenario. We
plan to add a capability to allow uncertainties to be manually injected during Visualization to allow more fine-tuned
testing of scheduling algorithms.
Fig. 3 The Visualizer playing back a scenario.
C. Scheduling
As noted above, the Scheduler is called by the Simulator periodically (a period specified by an input parameter;
to model real operations, we chose 15 minutes in world time). The inputs are the current state of the world and the
scenario. It outputs a set of paths and departure times (the time to leave the gate nodes for departures), called itineraries,
one for each active aircraft on the surface.
The algorithm is motivated by the idea that a model of uncertainty can be employed during scheduling to predict
delays and so generate schedules that are more robust to unexpected events in the world. Specifically, the scheduling
problem becomes a multi-agent path finding problem under uncertainty [7] and use a prioritized planning framework.
4
The travel time of an aircraft along a link is a random variable which is decided by the previous movement of this aircraft,
the travel time of the aircraft that is in front of this aircraft, and the uncertainties of the environment. This is formulated
as a probability propagation Markov Chain model which propagates travel time distribution from the aircraft with the
highest priority to the aircraft with the lowest priority. We propose two prioritized algorithms: First-Come-First-Serve
algorithm (FCFS) where agents with earlier release times have higher priorities and First-Leave-First-Serve algorithm
(FLFS) where agents with earlier desired finish times have higher priorities. Once we have the priorities, we use a
modified Cooperative A* search [8] to plan paths. In particular, the state in the path-planning search space is specified
by a node and a time distribution, and the solution is evaluated by wait times at the gates and the expected travel times.
III. Experimental Results
We need the following experiments:
1) Efficiency/scalability of the scheduler: report the runtime of the scheduler with different numbers of agents
(without rolling horizon);
2) Accuracy of the scheduler: compare the finish time from the scheduler with the finish time from the simulator
under different uncertainties and different agent densities (without rolling horizon). Note the that under each
uncertainty, we need to run the simulator multiple times.
3) Effectiveness and Robustness of the system: compare the solution quality (i.e., wait time and travel time) from
the simulator and the workload of the controller (number of stop commands) by using different schedulers (i.e.,
the baseline algorithm where each aircraft leaves the gate as soon as possible and follows the short path, the two
deterministic algorithms that do not consider uncertainties, and the two proposed algorithms) with different
uncertainties and different agent densities.
Fig. 4 Solution qualities of FCFS and FLFS.
We compared the two algorithms of Planner/Scheduler, FCFS and FLFS, on a simple node-link model which has 10
gate nodes, 3 spot nodes, 3 taxiway intersection nodes and 1 runway node. Currently we only tested departures. The
number of aircraft varies from 10 to 100. For each number of aircraft, we tested 10 random Scenarios and reported the
average results. Our code is written in C++, and our experiments are conducted on a 2.80 GHz Intel core i7-7700 laptop
with 8 GB RAM.
Figure 4 shows the solution qualities of both algorithms. “wait_time” represents the expected wait time at gates
before pushback, and ”travel_time” represents the expected travel time from the gate to the runway after pushback.
The travel times of both algorithms are similar and stable, which indicates that both algorithms control the taxiway
congestion very well. The wait times of both algorithms increase as the number of agents increases, and FLFS has much
smaller wait times than FCFS. This is because FLFS first predicts desired finish times of aircraft and assign priorities
accordingly. Therefore, FLFS is more effective than FCFS.
Table 1 shows the efficiency of both algorithms. Both algorithms take less than 0.1 s to solve the problem. Although
FLFS plans paths twice and FCFS plans paths only once, FLFS still runs faster than FCFS. This is because FCFS
usually generates longer paths than FLFS and longer paths needs much more search efforts than shorter paths. Therefore,
5
Table 1 Efficiency of FCFS and FLFS.
runtime (ms) expanded search nodes generated search nodes
Aircraft FCFS FLFS FCFS FLFS FCFS FLFS
10 2 1 385 217 595 323
20 6 2 1,058 505 1,697 753
30 10 4 1,741 1,050 2,837 1,600
40 14 8 2,653 1,796 4,413 2,813
50 21 13 3,624 2,679 6,143 4,280
60 28 19 4,899 3,691 8,437 6,040
70 34 24 6,051 4,545 10,487 7,493
80 42 29 7,433 5,947 13,007 9,977
90 53 39 9,325 7,486 16,529 12,786
100 67 48 11,222 9,103 20,074 15,710
FLFS is more efficient than FCFS.
IV. Related Work
This work intersects previous efforts in at least three areas. First, the problem to be solved requires the coordinated
planning and scheduling for multiple agents [9]. Second, this work expands upon work on so-called ’rolling horizon’
approaches to solve complex scheduling problems under uncertainty [10]. Finally, this work contributes to recent work
at building models of uncertainty to improve the robustness of solutions to planning and scheduling problems (for
example [7]).
V. Summary
The full paper will describe in more detail a simulation framework that allows for the quantification of the effects of
uncertainty on the robustness of solutions generated by surface movement planners and schedulers. We are currently
completing the implementation of the agent model and controller, and the full integration of the Simulator with the
Probabilistic planning framework. The full paper will consist of experiments using the full system on the complete SFO
model. The overall goal of this effort is to investigate and quantify the effects of using recent advances in probabilistic
approaches to planning and scheduling to anticipate delays in order to produce more robust plans.
Acknowledgments
References
[1] Montoya, J. V., Windhorst, R. D., Stroiney, S., Griffin, K., Saraf, A., Zhu, Z., and Gridnev, S., “Analysis of Airport Surface
Schedulers Using Fast-time Simulation,” AIAA Aviation Technology, Integration, and Operations (ATIO) Conference, AIAA,
Los Angeles, CA, 2013, p. 4275.
[2] Yang, H., Morris, R., and Păsăreanu, C. S., “Analysing the Effect of Uncertainty in Airport Surface Operations,” ISSTA/ECOOP
Workshop on International Symposium on Software Testing and Analysis, ACM, New York, NY, 2018, pp. 132–137.
[3] Malik, W., Gupta, G., and Jung, Y., “Spot release planner: Efficient solution for detailed airport surface traffic optimization,”
AIAA Aviation Technology, Integration, and Operations (ATIO) Conference and AIAA/ISSMO Multidisciplinary Analysis and
Optimization Conference, AIAA, Indianapolis, IN, 2012, p. 5498.
[4] “Operations at Towered Airports,” AOPA Air Safety Foundation, 2008. https://www.aopa.org/-/media/files/aopa/
home/pilot-resources/asi/safety-advisors/sa07.pdf.
[5] Morris, R., Chang, M. L., Archer, R., II, E. V. C., Thompson, S., Franke, J. L., Garrett, R. C., Malik, W., McGuire, K., and
6
Hemann, G., “Self-Driving Aircraft Towing Vehicles: A Preliminary Report,” AAAI Workshop on Artificial Intelligence for
Transportation: Advice, Interactivity, and Actor Modeling, AAAI Press, Austin, TX, 2015.
[6] Saifuzzaman, M., and Zheng, Z., “Incorporating human-factors in car-following models: A review of recent developments and
research needs,” Transportation Research Part C: Emerging Technologies, Vol. 48, 2014, pp. 379–403.
[7] Wagner, G., and Choset, H., “Path Planning for Multiple Agents under Uncertainty,” International Conference on Automated
Planning and Scheduling (ICAPS), AAAI Press, Pittsburgh, PA, 2017, pp. 577–585.
[8] Silver, D., “Cooperative Pathfinding,” Artificial Intelligence and Interactive Digital Entertainment Conference (AIIDE), AAAI
Press, Marina del Rey, CA, 2005, pp. 117–122.
[9] Ma, H., and Koenig, S., “Optimal Target Assignment and Path Finding for Teams of Agents,” International Conference on
Autonomous Agents & Multiagent Systems (AAMAS), ACM, Singapore, 2016, pp. 1144–1152.
[10] Clare, G., and Richards, A. G., “Optimization of taxiway routing and runway scheduling,” IEEE Transactions on Intelligent
Transportation Systems, Vol. 12, No. 4, 2011, pp. 1000–1013.
7


Scheduling and Airport Taxiway Path Planning Under Uncertainty

Scheduling and Airport Taxiway Path Planning Under Uncertainty

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server