Internal Technical Memorandum ITM-1998-03
Optimizing Scheduling in a Two-Instrument
Environment
Wayne M. Kinzel, Ian Jordan and David Soderblom
October 16, 1998
ABSTRACT
We investigated the sustained scheduling rate of STIS/MAMA orbits when the mix of orbits is
composed predominantly (>90%) of STIS and WFPC observations. Assuming no interaction with
non-MAMA visits, we find that the maximum sustained MAMA orbits scheduled per week can be
no greater than 41. Including interactions between MAMA and non-MAMA visits, and assuming
the structure of non-MAMA visits is changed to make them more schedulable in SAA-intersected
orbits, the maximum sustained number of MAMA orbits per week is 33. In order to decrease
scheduling conflicts between MAMA and non-MAMA observations, we recommend that existing
and future non-MAMA visits be made more flexible in their ability to schedule, and that observers
be encouraged to create small STIS/MAMA visits. These results imply that we must limit the percentage of MAMA orbits accepted in Cycle 8.
1. Introduction
With the removal of NICMOS observations from the scheduling pipeline, we will be left with
observations which are either forced to schedule only in SAA-free orbits (STIS/MAMAs) or
schedule around the largest SAA model (05) (which is most of the remaining non-MAMA visits).
An accurate estimate of the projected MAMA usage is needed because if the accepted number of
MAMA orbits it too large for Cycle 8, we will create a backlog of MAMA and non-MAMA visits.
This is because there are not enough SAA-free orbits to get them all scheduled in the same timeframe as visits that can schedule in SAA-intersected orbits. On the other hand, if the number of
accepted MAMA orbits is too low, then utilization of the STIS/MAMAs will not be maximized.
Given the current state of STIS and WFPC visits, we may require a restriction on the percentage of
MAMA orbits accepted for Cycle 8, modifications to observations, or both.
1.1 Background
The HST orbital period is 96.6 minutes, meaning there are 104.3 physical HST orbits per week.
The largest SAA model (05) provides an average of 5.8 SAA-free orbits per day. The newer (and
smaller) SAA model 27 averages 7.3 SAA-free orbits per day. Historically, we have scheduled 89
orbits per week on flight calendars, thus the scheduling system has consistently filled the physical
orbits at about the 85% level. Throughout this document we will be using the term orbits with two
different definitions: a physical HST orbit, or as a scheduling resource indicating the visit size,
with the distinction between the two depending upon the context of the term’s usage.
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Internal Technical Memorandum ITM-1998-03
The STIS/MAMA scheduling rate is dependent upon the answers to two questions:
1. How densely can STIS/MAMA visits be packed in the SAA-free orbits?
2. How many of the non-STIS/MAMA visits require SAA-free orbits?
The answer to the first question provides the maximum limit imposed upon the STIS/MAMAs by
their own intrinsic restrictions. The second question addresses the effect the non-MAMA visits
will have on the MAMA visits, since they will displace MAMA visits from the SAA-free orbits.
Reasons for this may be their visit structure, time criticality, science requirements, or other scheduling factors.
Section 2, “How Densely Can STIS/MAMA Visits Be Scheduled in the SAA-free Orbits?,” on
page 2 and Section 3, “How Many of the Non-MAMA Visits Require SAA-Free Orbits?,” on
page 4 describe the methods used to collect the scheduling statistics. Readers more interested in
the results may skip directly to Section 4, “What Does it All Mean?,” on page 6.
2. How Densely Can STIS/MAMA Visits Be Scheduled in the SAA-free
Orbits?
To address this question we created test calendars and attempted to schedule as many STIS/
MAMA orbits in them as possible. Before starting, we determined the time frame to use for the
test and the selection of a pool of visits to schedule. These are related because to save work effort
we used available visits from the operational database in their current preparation state and determined a time frame when most of those visits could schedule. Some of the visits initially selected
were removed from the test because they were not in states adequate to allow scheduling in the test
time frame.
In order to collect enough orbits for the test, plan windows were ignored, thereby maximizing the
number of available visits by not imposing additional plan window timing constraints. Visits
which had already executed on past calendars were also considered and included in the pool. A
total of 555 prime STIS/MAMA visits were found in the operational database in states for which
adding them to a candidate list could be attempted.
For test scheduling, an 8-week interval was considered to be a minimum for a valid test, as this
duration is one HST sidereal orbital precession period. A review of the visits indicated we could
probably build reasonably full test calendars with a duration of 8 weeks over the time span of
98.320 to 99.011.
Out of the initial pool of visits, only about a quarter of the linkset visits and a third of the nonlinked visits would add to the calendar candidate list. Of those which added, 8 of the 25 linkset visits and 14 of the 150 non-linked visits would not schedule on an empty calendar and were removed
from the test. In the test, the MAMA visit scheduling was constrained by the SAA model 05 contours, which defines an average of about 5.8 SAA-free orbits per day. During the 8 week test
interval, there were about 325 model-05 SAA-free orbits (physical) and the remaining schedulable
MAMA visits provided a pool with about 34% more orbital resources than the available room. A
summary of the remaining schedulable visits is given in Table 1, “Schedulable STIS/MAMA
Visits”.
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Internal Technical Memorandum ITM-1998-03
Table 1. Schedulable STIS/MAMA Visits
Number of
visits
Number of
orbits
Average
orbits per
visit
Linked
25
76
Non-linked
150
359
Type
Number of visits by orbit size
1
2
3
4
5+
3.0
4
7
1
10
3
2.4
53
42
18
18
20
The test calendars were built as follows: The MAMA linkset visits were first scheduled on the calendar by using the software “schedule linkid” feature for each linkset. Several calendars were
manually created where the order in which the linkset scheduling attempts was changed, so as to
find a combination yielding the most scheduled orbits. The non-linked visits were then scheduled
on the calendar using two different approaches, and the results are shown in Table 2, “Scheduled
STIS/MAMA Visits on Test Calendar ijj21751”. Scenario A shows the result of a blind “calendar/
auto” scheduling run, while Scenario B was a manual, conscious attempt to maximize the number
of orbits scheduled on the calendar.
Table 2. Scheduled STIS/MAMA Visits on Test Calendar ijj21751
Type
Linked
Number of
visits
Number of
orbits
Average
orbits per
visit
16
48
3.0
Number of visits by orbit size
1
2
3
4
5+
3
3
1
9
0
Non-linked (A)
110
234
2.1
42
38
13
8
9
Non-linked (B)
115
251
2.2
50
29
12
13
11
Scenario B produced an 8-week calendar with 299 orbits of STIS/MAMA scheduled. A count of
the SAA-free orbits actually available over this time interval yielded 328, so the efficiency with
which the STIS/MAMAs packed the SAA-free orbits in this calendar was 91%. The scenario B
calendar results will be used for the remainder of this discussion.
In Table 3, “Comparison of Successful Test Schedule and Total Pool”, note that the mean size of
the scheduled visits was smaller than the mean size of the total remaining Cycle 7 visits. Note specifically that there are 64 one-orbit MAMA visits remaining in Cycle 7 and that 53 of those visits
were scheduled during this 8 - week test. Thus, if flight calendars are packed as densely with
MAMAs as in this test case, the pool of small (1- and 2-orbit) visits would quickly run out.
Table 3. Comparison of Successful Test Schedule and Total Pool
Number of
visits
Number of
orbits
Average
orbits per
visit
Scheduled
131
299
Available Pool
175
LRP >98.327
326
Type
Number of visits by orbit size
1
2
3
4
5+
2.3
42
32
13
22
11
435
2.5
57
49
19
28
23
908
2.8
64
105
54
43
60
The test showed that when the STIS/MAMAs were scheduled out of an unrestricted pool, close to
90% of the SAA-free orbits could be filled over a short period of time. However, because of the
current mix of visit sizes and the fact that the SAA-free time will be more difficult to effectively
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Internal Technical Memorandum ITM-1998-03
fill (with MAMA observations) in normal scheduling operations, over the long term, we estimate
would be able to fill only about 80% of the SAA-free orbits with MAMA observations. Using an
80% occupation efficiency would imply 5.8 × 7 × 0.80 = 32 orbits per week of MAMAs which
could schedule on an average empty calendar. If we assume the larger SAA-model 27 (~7.3 SAAfree orbits/day) and the same occupation efficiency, this implies 7.3 × 7 × 0.80 = 41 orbits per
week as an upper limit. This upper limit will be unattainable in operations since other non-MAMA
visits will require SAA-free orbits. To determine this interaction, further tests were conducted as
outlined in the following section.
Even when the expanded SAA model 27 is used for STIS/MAMAs under ideal conditions with no
plan windows or other scheduling restrictions it will take at least: [60+43+(54/2)] = 130 days to
schedule all of the remaining large Cycle 7 STIS/MAMAs. This assumes that one 4 or 5 orbit visit
or two 3 orbit visits are scheduled each day during the SAA-free orbits and little non-MAMA visit
competition occurred for the SAA-free orbits.
3. How Many of the Non-MAMA Visits Require SAA-Free Orbits?
Three different methods were used to estimate this number:
1. A continuation of test scheduling visits on the previous test calendar.
2. A determination using SPIKE.
3. An examination of the historical scheduling of visits.
3.1 Follow-on scheduling test of the non-MAMA visits
The resultant test calendar that was described in Section 2, “How Densely Can STIS/MAMA Visits Be Scheduled in the SAA-free Orbits?,” on page 2 was used as input to this part of the test.
Since the calendar has 90% of the SAA-free orbits already filled with STIS/MAMA observations,
it can be used to test the ability of non-MAMA observations to schedule in non SAA-intersected
orbits. That is, if a visit cannot schedule on such a calendar, it probably needs SAA-free orbits.
A search of the operational database found 258 non-MAMA visits using 639 orbits whose plan
windows intersected the test time-frame. Once again, visits were dropped from the test if they were
not in a prepared state to attempt scheduling in the test time-frame. Since these non-MAMA visits
were selected and added to the test calendar because they have plan windows overlapping the test
time-frame, it was assumed that the visits could schedule on an empty calendar. The available pool
of non-MAMA visits available for test scheduling is shown in Table 4, “Non STIS/MAMA Visits
Added as Candidates to 98.320 – 99.011”.
Table 4. Non STIS/MAMA Visits Added as Candidates to 98.320 – 99.011
Number of
visits
Number of
orbits
Average
orbits per
visit
Linked
25
36
Non-linked (A)
108
Total
133
Type
Number of visits by orbit size
1
2
3
4
5+
1.4
16
8
0
1
0
286
2.6
44
20
15
12
17
322
2.4
60
28
15
13
17
Since an average of about 89 orbits of prime science and calibrations are scheduled per week, we
can expect the test calendar to schedule 712 orbits in total. Subtracting the 299 orbits previously
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Internal Technical Memorandum ITM-1998-03
scheduled on the Scenario B calendar, we expected about 413 more orbits could be scheduled on
the calendar. Thus the available visit pool is 22% smaller than the available room on the calendar.
A similar approach outlined in Section 2, “How Densely Can STIS/MAMA Visits Be Scheduled in
the SAA-free Orbits?,” on page 2 for scheduling the MAMAs was used, except that unlike the
MAMAs, the non-MAMA visits were chosen and attempted to be scheduled to obey plan windows. The results of attempting to schedule the non-MAMA visits, basically in SAA-free orbits, is
shown in Table 5, “Non STIS/MAMAs on Top of 98.320 – 99.011”.
Table 5. Non STIS/MAMAs on Top of 98.320 – 99.011
Type
Number of
visits
Number of
orbits
Average
orbits per
visit
Number of visits by orbit size
1
2
3
4
5+
Linked
16
21
1.3
11
5
0
0
0
Non-linked (A)
71
152
2.1
36
13
8
8
6
Total
87
173
2.0
47
18
8
8
6
In the test calendar, 173 of the 322 non-MAMA candidate orbits successfully scheduled (54%) in
the SAA-intersected and leftover SAA-free orbits. Since the initial scheduling pool was smaller
than the available space on the calendar and so few of the available non-MAMA visits scheduled,
there were probably few conflicts among the non-MAMA visits on the test calendar implying that
46% of the non-MAMA orbits needed to schedule in SAA-free orbits.
3.2 A SPIKE estimate of the required SAA-free consumption by non-MAMA visits
For a given LRP, SPIKE can produce reports listing the total number of orbits per day and the
number of SAA-free orbits per day used by the planned visits. The 98224A LRP was split such
that the resultant LRP had all MAMA visits removed and the orbits per day report output was then
summed to find the resource allocations between 98.327 and 99.365 for the non-MAMA visits:
SPIKE LRP 98224A Resource Report Summary
----------------------------------------------1057 orbits of non-MAMA SAA-free consumption.
1939 orbits of non-MAMA total in interval.
Thus SPIKE estimates that in the 98224A LRP 55% of the non-MAMA orbits require SAA-free
orbits. This estimate could be a few percent high because SPIKE is conservative in its estimate of
how visits will actually schedule. That is, SPIKE assumes a visit will schedule within the estimated orbits as modeled by TRANS. However, during scheduling on a calendar, a visit’s duration
may increase by as much as one orbit. By scheduling smaller pieces of a visit in more orbits, a
non-MAMA visit could be allowed to partially or fully schedule in SAA intersected orbits not
allowed by SPIKE.
3.3 Historically, what has been the percentage of non-MAMA observations requiring SAA-free orbits?
All non-SMOV, prime observations scheduled between 1997.147 to 1998.257 were examined to
determine if they were scheduled during the SAA-free part of the day. For this analysis, we examined only the start and end times of SAA model 05 crossings since, during this interval, all the
WFPC and STIS configurations were using SAA contours equivalent to model 05. Contributions
from visits that partially scheduled during SAA free orbits were scaled by:
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Internal Technical Memorandum ITM-1998-03
est_orbits × SAA_free_orbit_time / total_scheduled_time
Since the visit sizes from the other tests are based upon the estimated orbits predicted by TRANS,
it was felt this orbit accounting provided a more accurate comparison of how much of each visit
used SAA-free orbits.
Table 6. Scheduled Orbits during 97.147 – 98.257
Instrument
Total orbits
SAA-free
Entire visit in SAA-free orbits
WFPC2
1,571
738
471
STIS/CCD
461
194
127
Total
2,032
932 (46%)
598
NICMOS (comparison)
2,816
1,039 (37%)
695
While the number of scheduled NICMOS orbits is nearly 40% more than the CCD-type observations, only 37% of the NICMOS orbits were scheduled during SAA-free orbits compared to 46%
for the CCDs. This implies that many (up to 46% of the orbits) of the non-MAMA observations
are forced to schedule in the SAA-free orbits.
4. What Does it All Mean?
First, it appears that without regard to competition for SAA-free orbits between MAMA and nonMAMA visits, HST scheduling could achieve about 41 orbits per week of MAMA usage if the
new SAA model 27 is used. Second, it appears that given the current visit structure for WFPC and
STIS/CCD observations, three different methods indicate that 45% to 50% of the non-MAMA
orbits need to schedule in SAA-free orbits.
Even if there were no MAMAs in the system (~100% CCD type observations), without some modification to the non-MAMA observations, we will eventually get into trouble. That is, the tests
show we need about 45% of the orbits contained in current visits to schedule SAA-free. However,
only about 38% of the physical orbits are SAA-free for model 05. Thus as time goes on, we would
slowly build a backlog of visits that need to schedule in SAA-free orbits. Including MAMA observations that consume SAA-free orbits makes the problem worse.
For example, scheduling at 89 orbits per week implies that 49 scheduled orbits a week are in the
model 05 SAA-intersected orbits and 89 – 49 = 40 orbits per week of SAA-free time. Currently
planned in the LRP after NICMOS end of science are 2,037 non-MAMA orbits and 908 MAMA
orbits. If 45% of the non-MAMA orbits need SAA-free time, this implies 1,825 orbits of MAMA
and non-MAMA observations require the SAA-free orbits, and that 1,120 non-MAMA orbits can
schedule in the SAA-intersected orbits. This means we have about 1825/40 = 46 weeks where we
can fill SAA-free orbits but only have enough to fill about 1120/49 = 23 weeks of SAA-intersected
orbits. So somewhere around late April, 1999, we should see a drop in calendar efficiency as we
exhaust visits that will schedule in SAA-intersected orbits. Note that this scenario assumes the
SAA hiding visits that have plan windows at later times have some how been made available to the
calendar building process when needed. Alternatively, HST could see a more prolonged period
where observing efficiency is reduced.
If we can somehow modify the non-MAMA visits to become more schedulable, we can attempt to
answer how much interaction the two type of visits will have on each other by solving the following set of equations:
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Internal Technical Memorandum ITM-1998-03
T=M+W
F = M + pW
Where T is the total number of scheduled orbits per week, M is the number of scheduled MAMA
orbits per week, and W is the number of scheduled non-MAMA orbits per week. F is the usable
number of model 27 SAA-free orbits, and p is the fractional amount of non-MAMA orbits requiring SAA-free time.
These can be re-written to solve for M:
M(%) = (F/T – p) × 100/(1 – p)
Where M(%) = 100 × M/T. There is also a fourth equation that constrains p to values less than
~0.40: that is f ≥ pW, where f is the usable number of model 05 SAA-free orbits per week (~32.5
orbits per week). We need this last constraint because the MAMA and non-MAMA observations
will be using different SAA models and most of the non-MAMA visits will be constrained by
SAA model 05. So if we assume T = 89 orbits/week and F = 41 orbits per week, then substituting
different values for p generates Table 7, “Orbits per week”:
Table 7. Orbits per week
Orbits per week
p
M(%)
M
W
pW
0.45
2
<2
87
39
0.40
10
9
80
32
0.30
23
21
68
20
0.15
37
33
56
8
0.10
40
36
53
5
0.05
43
38
51
<3
Table 7, “Orbits per week” implies that the current value of 45% non-MAMA orbits requiring
SAA-free will not have a solution, that is, we can not have a mix of visits with that value and sustain scheduling 89 orbits a week. Note that even if our measurement of p is too high by 15
percentage points – implying a true value of p = 0.30 – this would still allow only 21 MAMA
orbits a week. So something would still need to be done to increase the non-MAMA schedulability
to allow more MAMA orbits to schedule.
Note that any time a non-MAMA observation is forced to schedule in model 05 SAA-free orbits, it
can split the model 27 SAA-free orbits into two sections, thus preventing large MAMA visits from
scheduling during that SAA-free passage. The test described in Section 2, “How Densely Can
STIS/MAMA Visits Be Scheduled in the SAA-free Orbits?,” on page 2 showed that the smaller
visits were used at a much faster rate, because they were used to fill the leftover holes and because
two 3-orbit MAMA visits could not always be scheduled back to back in the same SAA-free passage. This problem will only be exacerbated when a non-MAMA visit is forced to schedule in
SAA-free orbits. Even by restructuring non-MAMA visits to more easily schedule in the SAAintersected orbits, there will still be some, currently undetermined, number of non-MAMA orbits
(an estimate is 15%) that will be forced to schedule in SAA-free orbits because of timing restrictions, link restrictions, CVZ usage etc.
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Internal Technical Memorandum ITM-1998-03
If we assume a value of 15% for p and 89 orbits per week of scheduled observations, over the
course of a year we would expect to schedule about 4630 orbits, 1710 orbits containing MAMA
observations. Note that this number includes repeats (4%) so the number of MAMA orbits that
would be completed is about 1640 (Total scheduled × (1 - repeat rate)).
5. Recommendations
Given that we do not know at this time how schedulable we can make the non-MAMA visits we
should be conservative and accept no more than 33 orbits per week of MAMA observations. In
order to even achieve this recommended number of MAMA orbits per week, we must investigate
and implement ways to make a substantial fraction of the non-MAMA observations more schedulable during SAA-intersected orbits. One way to make them more schedulable would be to reTRANS the visits such that TRANS does not (unless required) create alignments larger than a certain size. This would then allow the visit to more easily schedule around SAA passages. The down
side for this process, besides the re-processing effort, is that for each new alignment created,
approximately 2 minutes of overhead time will be added to the visit. However, a reduction in p of
~30 percentage points should be achievable. For example, there are 75 WFPC visits currently in
the system that are 6 orbits or larger which contain about 25% of the non-MAMA orbits remaining
in the Long Range Plan. If each of these visits currently require about one half of its time to schedule in SAA-free orbits (a reasonable assumption), and we make them totally schedulable in SAAintersected orbits, it would reduce p by ~12 percentage points by just modifying these visits.
In addition, we should investigate ways to make the MAMA observations more schedulable, for
example, by creating smaller visits. Even if the larger SAA model allows more 3 orbit MAMA visits to schedule back to back, competition for SAA-free orbits from non-MAMA visits would still
indicate a need for a larger percentage of smaller MAMA visits than we currently have.
Once the above recommendations are in place, to maximize the number of MAMA orbits scheduled, we may also need to create a scheduling pool containing the small (1 or 2 orbit) MAMA
visits to be available for calendar building and possibly change the calendar building procedure to
accommodate attempts at maximizing MAMA orbits scheduled on calendars.
8