Validating Resources in Least Commitment Scheduling Nazma Ferdous & Mark Giuliano Space Telescope...

Validating Resources in Least Commitment Scheduling

Nazma Ferdous&

Mark GiulianoSpace Telescope Science Institute

October 24, 2006

Outline

• HST Observation Scheduling Process

• Resource Model

• Resource Model Limitations

• Plan Validation Tool

• Operational Results

• Summary & Future Directions

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Outline


• Resource Model






HST Observation Scheduling

Two Phased Approach

• Uncertainty in HST orbit.

• Big problem size (~ 2400 observations per year).

• Better long term HST usage. Year-based

Long Range Planning (Assigns 8 week long

window for start time)

Week-basedShort Term Scheduling

(Assigns start time)


1. Calculating Constraint Window

Observation constraint windows are calculated from all physical and other constraints, which denotes the timeline of when the observation can be scheduled.

2. Generating Plan Window (PW) Using least commitment scheduler SPIKE, observations are assigned plan

windows, which are the preferred window for scheduling.

3. Computing Resource Consumption

Long Range Planning (LRP)

Feb Mar Apr Jun Jul Aug Sep Nov0

1

Feb Mar Apr Jun Jul Aug Sep Nov0

1

Plan Window


Outline


• Resource Model






SPIKE Resources• Total orbits per day (15 per day)

• South Atlantic Anomaly (SAA) related resources– SAA free orbits per day (6-7 per day)

– SAA impacted orbits per day (8-9 per day)

Sun

Target


SPIKE Resource Model • Equally distributes the total resource required by an observation over

the range of the PW.

• Depicts general probability of resource contention/under usage.

O1

O2

O3

Day 1 2 3 4 5 6 7

Plan Windows

2Total Orbits

Consumed 0 2 3 2 2 0 0Available 2 0 -1 0 0 2 2

10

O1

O2

O3

Duration

2 34

State Day Over-subscribed 3 Leveled-subscribed 2,4,5 Under-subscribed 1,6,7


Outline


• Resource Model

• Resource Model LimitationsResource Model Limitations





Resource Model Limitations• Creates false positives.

• No oversubscribed days. • Yet, no feasible schedule exists !

O1

O2

O3

Day 1 2 3 4 5 6 7

Plan Windows

O4

Duration3 364

O1

O2

O3

O4

2Total Orbits

Consumed 0 4 4 4 4 0 0 Available 4 0 0 0 0 4 4

10

43


Resource Model Limitation (cont.)

• Create false negatives.

• Day 3 and 4 are oversubscribed. • Yet, a schedule can be generated !

O1

O2

O3

Day 1 2 3 4 5 6 7

Plan Windows O1

O2

O3

Duration

3 22

1Total Orbits

Consumed 0 1 2.5 2.5 1 0 0 Available 2 1 -0.5 -0.5 1 2 2

0.50

21.5

2.5


Initial Resource Profile

Data from 2006 observation cycleTotal Observations: 2389

Total Orbits Required: 3776 Total Orbits Oversubscription: 1029

Plan Window Generation ++

Short Term Scheduling

LRP

Plan WindowGeneration


Outline


• Resource Model








PlanValidation

Tool

LRP


LRP


Plan Validation ToolGiven a Long Range Plan,

• Treat the plan windows for as the constraint windows.

• Assign 1 day-long scheduling window to the observations, essentially committing all resources required for the observation to that day.

• Analyze the resulting resource profile.


Validation Tool Implementation

• Initial Guess- Scheduling windows are assigned w/o violating the

resource limit if possible. If not, window with least resource contention is chosen.

• Repair- A systematic repair (e.g. utilizes iterative deepening

concept) is used to flatten the resource profile, minimizing false alarm as much as possible.


Iterative Deepening (ID) Repair

• Start at iteration 1 and progressively increase the iteration by 1.• At iteration i, for each conflicted observation, perform a depth-first

search, looking for chain of moves of length i, to resolve the conflict. • The algorithm stops when max iteration (user specified) is reached or

no resource contention exists.

Iteration Operation 1 Oversubscribed Undersubscribed 2 Oversubscribed Leveled subscribed Undersubscribed 3 Oversubscribed Leveled subscribed Leveled subscribed Undersubscribed n Oversubscribed Leveled subscribed Leveled subscribed … (n-2 moves) … Undersubscribed


ID : An example Resource Limit: 2 observations are allowed per day

1 2 3 4 5 6 7 8 9 10 11

U L O L U O L U O L L

AF

BC

DE

O : Over Subscribed Days

L: Level Subscribed Days

U: Under Subscribed Days

Observations PW Conflicted?

A 3 - 5 *

B 5 - 7 *

C 7 - 9

D 9 - 11 *

E 4 - 10

F 1 - 4

A C

B D

FE


1 2 3 4 5 6 7 8 9 10 11

U L O L U O L U O L L

ID : Iteration 1 Oversubscribed Undersubscribed• Observation Chain:

• Actions Performed:

1 2 3 4 5 6 7 8 9 10 11

U L L L L O L U O L L

AF

BC

DEA

Move A from day 3 to day 5

A C

B D

FE

ABD

√XX


ID: Iteration 2Oversubscribed Leveled subscribed Undersubscribed• Observation Chain:

• Actions Performed:

1 2 3 4 5 6 7 8 9 10 11

U L L L L O U L O L L

B

1 2 3 4 5 6 7 8 9 10 11

U L L L L O L U O L L

FB

CD

EA

1 2 3 4 5 6 7 8 9 10 11

U L L L L L L L O L L

C

Move C from day 7 to day 8 to create room for B

Move B from day 6 to day 7.

A C

B D

FE

B,

D, E

A X

XC √


1 2 3 4 5 6 7 8 9 10 11

L L L L L L L L O U L

D

1 2 3 4 5 6 7 8 9 10 11

L L L L L L L L L L L

1 2 3 4 5 6 7 8 9 10 11

L L L U L L L L O L L

1 2 3 4 5 6 7 8 9 10 11

U L L L L L L L O L L

BFD

EA CF E

ID : Iteration 3Oversubscribed Leveled subscribed Leveled subscribed Undersubscribed• Observation Chain:

• Action Performed:

Move F from day 4 to day 1 to create room for E

Move E from day 10 to day 4 to create room for D

Move D from day 9 to day 10.

A C

B D

FE

D, E, A XBCF

XX√


Outline


• Resource Model






Validation Tool Resource Profile

For Total Orbits per day ResourceFalse positives identified: 5

False negatives identified : 90Total oversubscription : 495 (compared to 1029)

Extending Algorithms for

PW Generation • New initial guess and iterative deepening repair algorithms were

extended for plan window generation.

• Resulting long range plan is more resource balanced.

• Validation tool identified fewer false positive/negatives and oversubscription.



PlanValidation

Tool

LRP


New Resource Profile

Data from 2006 observation cycleTotal Observations: 2389

Total Orbits Required: 3776 Total Orbits Oversubscription: 558 (compared to 1029)

Validation Tool Resource Profile

For Total Orbits per day ResourceFalse positives identified: 2 (compared to 5)

False negatives identified : 179 (compared to 90)Total oversubscription : 142 (compared to 558)

Outline


• Resource Model






Summary

• An automated resource verification system is implemented for the long range planning.

• Streamlined the long range planning process.• Significantly reduced human cost and saved

time.• Long range plan is more resource balanced.


Future Directions

• While repairing resource conflicts, knowledge gained in one iteration can be used in subsequent iterations.

• Couple “PW Generation” and “Validation Tool” more tightly so that resources are validated as the plan windows are laid out.


Thanks


Limitations• Swapping observations is not allowed.

• Demonstrates diminishing return as the iteration increases.

• Using appropriate heuristics and utilizing domain knowledge is important.

O1

O2

O3

Day 1 2 3 4

Plan Windows O1

O2

O3

Duration 2 11

10

Total Orbits

32

Consumed 0 3 1 0 Available 2 -1 1 2


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Validating Resources in Least Commitment Scheduling Nazma Ferdous & Mark Giuliano Space Telescope...

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