Telescope Network Scheduling

Rationale and Formalisms

Sotiria Lampoudi

and Eric Saunders

Computer Science Department, University of California, Santa Barbara, CA 93106, U.S.A.

Las Cumbres Observatory Global Telescope Network, 6740 Cortona Dr., Suite 102, Goleta, CA 93117, U.S.A.

Keywords:

Scheduling, Astronomy.

Abstract:

Scheduling of university and institutional telescopes is typically performed manually, and astronomers are

used to interacting with a human to explain their requirements for resources and time. Las Cumbres Observa-

tory Global Telescope (LCOGT) is deploying a worldwide network of robotic telescopes. At LCOGT manual

scheduling is infeasible due to: 1) the number of resources and observations that must be scheduled, 2) the

scheduling-time dependencies that arise when concurrent or consecutive access to telescopes is required, and

3) the need to rapidly re-calculate the schedule to accommodate near-real-time requests from high priority ob-

serving programmes (e.g. transient followup programmes), and changing resource availability due to weather

and other reasons. In this paper we develop a formalism capable of expressing the complex requirements and

preferences of astronomers concerning resource and time allocation on a telescope network, and formulate

the ofﬂine telescope network scheduling problem as the problem of choosing and scheduling (i.e. assigning

concrete start and end times to) a maximum priority, non-overlapping subset of an input list of requests.

1 INTRODUCTION

Robotic telescope networks are gaining traction (Hes-

sman, 2006), due to the novel astronomical obser-

vation modes they enable, and their lower opera-

tional and administrative costs. These resource pools

can be homogeneous (Vestrand et al., 2002; Akerlof

et al., 2003) or heterogeneous (Nather et al., 1990),

and designed from the ground up or federated, much

like computational clusters and grids. However, be-

cause astronomical observations must be performed

at speciﬁc times, rather than at the ﬁrst opportunity,

scheduling telescope networks is a form of advance

reservation scheduling that is more challenging than

the batch scheduling usually found on computational

clusters and grids.

Las Cumbres Observatory Global Telescope

(LCOGT) has acquired two 2m robotic telescopes

(Faulkes North and South), and is additionally de-

ploying a worldwide network of 0.4m and 1m optical

telescopes and attached imagers and spectrographs,

dedicated to time-domain astronomy (Martinez et al.,

2010).

Scheduling of individual, non-robotic university

and institutional telescopes is typically performed

manually. But manual scheduling is infeasible on

the LCOGT network for a number of reasons. Pri-

mary among them is the sheer number of resources

and observations that must be scheduled. Secondary

is the desire to encourage requests that take ad-

vantage of features unique to a spatially distributed

telescope network. Such requests are for concur-

rent or consecutive use of resources, and they in-

troduce scheduling-time dependencies, making man-

ual scheduling more difﬁcult. Finally, it is desirable

that schedule (re)calculation be fast, to accommodate

near-real-time observing requests (e.g. for transient

followup (Brown et al., 2007)) with minimal disrup-

tion to long-standing requests, and rapid changes in

resource availability due to weather or technical is-

sues.

In this paper we survey the literature on tele-

scope scheduling, deﬁne a formalism that allows as-

tronomers to express their complex requirements and

preferences regarding resource and time allocation on

a telescope network, formulate the multiple telescope

scheduling problem, and brieﬂy discuss its attributes.

2 RELATED WORK AND

MOTIVATION

The ﬁeld of telescope scheduling has not evolved sys-

165

Lampoudi S. and Saunders E..

Telescope Network Scheduling - Rationale and Formalisms.

DOI: 10.5220/0004274203130317

In Proceedings of the 2nd International Conference on Operations Research and Enterprise Systems (ICORES-2013), pages 313-317

ISBN: 978-989-8565-40-2

 2013 SCITEPRESS (Science and Technology Publications, Lda.)

tematically; the majority of publications report on at-

tempts to engineer real-world scheduling systems for

production use, and therefore contain little theoret-

ical justiﬁcation of their design choices, almost no

theoretical classiﬁcation of their problems and solu-

tion, and few attempts to generalize them into forms

amenable to theoretical exploration. These are omis-

sions we seek to remedy in this paper.

It is helpful to categorize the literature on tele-

scope scheduling according to whether it concerns

scheduling requests from single or multiple “users”.

In this context the term “user” really refers to a scien-

tiﬁc objective, rather than an individual. A single user

can be an astronomer, a group of astronomers sharing

a single science goal, or a computational agent with a

single science goal.

In the case of a single user, although the astro-

nomical literature refers to a “scheduling” problem,

what is being studied bears no similarity to, for ex-

ample, computational resource scheduling. In single-

user “scheduling” the objective is the optimal choice

of targets to observe (Colome et al., 2010; Bakos

et al., 2011, for example) and/or times during which

to observe them (Saunders et al., 2006, for example),

in order to maximize scientiﬁc return, under the as-

sumption of perfect resource availability and with no

concern for contention. This optimisation goal can

only be achieved with very detailed domain-speciﬁc,

astrophysical information. For the purposes of this

paper we will refer to this as an observation selection

problem, not a scheduling problem.

In multi-user telescope scheduling we have a

problem that bears a closer resemblance to compu-

tational resource scheduling. The resource pool is

time- and/or space- shared, and the contention be-

tween user requests must be resolved in a way that

optimises objectives and/or satisﬁes constraints. Each

individual user’s input to the multi-user scheduler

may be the output of a single-user observation selec-

tion step. Multi-user scheduling can concern a single

resource (Kinzel, 2010, for example), or many, as in

the LCOGT network described in this paper.

In telescope scheduling practice the observation

selection problem and the multi-user scheduling prob-

lem have historically been entangled. This situation

is likely due to the fact that traditionally astronomers

will sit down with a human scheduler and manually

produce schedules that take into account both scien-

tiﬁc value and contention at once. The Robonet I

(Fraser, 2006) and II (Tsapras et al., 2009) sched-

ulers are cases in point: they attempt to optimise tar-

get selection (for a single user, whose science goal is

transient followup) using complex scoring functions

(Snodgrass et al., 2008), but are tightly integrated

with the RCS scheduler, which is responsible for all

scheduling of the Faulkes telescopes, and which is

also used by all the other users of those telescopes.

This system was acquired by LCOGT along with the

Faulkes telescopes, and its management requires hu-

man intervention to resolve conﬂicts between auto-

mated (Robonet), professional astronomer and edu-

cational user groups.

A step in the direction of disentangling single-

(observation selection) and multi- user scheduling

was the eStar meta-scheduler (Allan et al., 2006), an

agent-based scheduler acting on behalf of a user (after

the observation selection step) to submit requests for

resources to any telescopes and telescope networks

that were compatible with it. However, as eStar de-

pended on the resources to simply accept or reject

its requests according to their internal criteria, and

prioritised among those accepting its requests using

its own unrelated criteria, little theoretical argument

could be made regarding its tendency to achieve ob-

jectives, satisfy constraints, or otherwise optimise the

scheduling process. No empirical studies addressing

these questions were published.

Our approach conceptually disentangles the

single-user (observation selection) and multi-user

parts of the telescope scheduling problem by factor-

ing them respectively into a formalism that hides the

astronomy-speciﬁc aspects of the problem, and an op-

timisation problem deﬁnition based on that formal-

ism.

3 CONCEPTS AND

FORMALISMS

3.1 Manual vs Automatic Scheduling

The process of scheduling university and institutional

telescopes typically goes as follows. A Time Allo-

cation Committee (TAC) is responsible for allocating

to each scientiﬁc project a total amount of time to be

used over a semester on their resources, and for as-

signing a numerical priority to each project. Before

the semester begins, individual investigators contact a

human scheduler and, in English, request exclusive

use of particular resources for particular intervals.

They usually assign their requests their own, usually

three tier, level of priority (“High, Medium, Low”).

The human scheduler then resolves scheduling con-

ﬂicts by taking into account a subjectively weighted

mix of the conﬂicting projects’ TAC-assigned prior-

ities, the investigators’ self-assigned priority for the

particular observation, and the urgency (expressed in

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terms of expectation of future opportunities to per-

form an observation) and importance (expressed as

number of past observations that become useless if

this observation is not performed) of the requests, if

those are available. Observing programmes requiring

near-real-time access to resources are allocated Target

of Opportunity (ToO) time on the resources, allowing

them to manually pre-empt ongoing observations, and

assume control. The human scheduler patches up the

schedule in response to disruption from ToO requests

and weather, to whatever extent possible.

In the following section we develop an “assem-

bly language” for specifying users’ resource and time

requirements. Higher level speciﬁcations of users’

needs can be “compiled” into this language by inter-

faces, and automated systems can encode their needs

directly in it.

3.2 The Reservation Formalism

At the core of advance scheduling of all types is the

concept of a reservation, a representation of a request

for exclusive use of a resource at a particular time. In

this paper reservation with a lowercase ’r’ will refer to

the concept, whereas Reservation with an uppercase

’R’ will refer to a formalism, or data structure.

Formally, a Reservation is a 4-tuple (d, p, t, W),

where:

• d is the duration of the exclusive use of the re-

source,

• p is the priority,

• t is the resource, and

• W is a list of “windows of opportunity”,

, . . . , w

}, where w

≥ d, ∀ j ∈ [1, i].

Windows of opportunity give the times during

which the observation can occur; that is, the concrete

start and end times of the Reservation must both ﬁt

within a single window of opportunity.

In the vocabulary of astronomy, a Reservation is a

request by a project with priority p to use telescope t

for duration d during one of the windows listed in W.

To explain the design considerations that led us to

adopt this particular formalism, let us consider two

typical examples of requests made via email to the

human scheduler of the Faulkes North telescope in the

ﬁrst semester of 2011.

In both examples the ﬁrst column gives the date,

the second the start time and the third the end time.

A different window is speciﬁed on each line. Note

that an informal English sentence further specifying

the intended meaning of each request was necessary.

Note also – and we will not dwell on this aspect of

transitioning from human language to automated in-

terfaces, although it is interesting and possibly impor-

tant to human computer interface design – that in the

ﬁrst example, “or two” is redundant and can be omit-

ted without loss of information, since, if one night is

sufﬁcient, two are clearly also sufﬁcient.

Example 1. “[For this observation] one or two of the

nights should be sufﬁcient.”

11-05-01 05:30 15:30

11-04-27 05:30 15:30

11-05-03 05:30 15:30

The next request invents a notation for a date

range. This range implicitly contains ﬁve windows

of opportunity (on consecutive days between May 1st

and 5th). The investigator also wishes to include so-

called “slack”, i.e. some ﬂexibility in the start and end

times, but that has to be expressed in English.

Example 2. “[This observation] can also start (and

end) up to 2 hours later if that ﬁts better.”

2011-05-01<->2011-05-05 06:30 11:00

The Reservation formalism allows us to com-

pactly capture these two typical request scenarios,

which previously had to be expressed in a mix of

machine-readable notation and English. Both exam-

ples illustrate the need for multiple windows of op-

portunity. Example 2 illustrates the additional need to

accommodate slack in the windows, which we meet

by including a duration ﬁeld that is separate from the

start and end of the windows.

3.3 The Compound Reservation

Formalism

Intuition and experience suggest that the astronomical

observations being requested by a particular project

are usually not independent of each other, since they

are components of a larger scientiﬁc programme.

Aside from having a common target, requests from

the same project are often linked to each other in ways

that are more complicated. In what follows we de-

scribe two types of “scheduling-time dependencies”,

so called because they can be resolved at the time the

schedule is being assembled.

The ﬁrst kind of scheduling-time dependency is

one in which the scheduling status of a request (“did

it get scheduled or not?”) depends on the schedul-

ing status of the other requests in the dependency.

For example, it can be the case that two observations

are useful only if both of them are successfully com-

pleted; if only one can be scheduled, then it will be of

no value. Or it can be the case that the same data can

be obtained using either of two different telescopes, a

TelescopeNetworkScheduling-RationaleandFormalisms

167

logical disjunction between observations that cannot

be captured within a single Reservation, as deﬁned

above.

The second type of scheduling-timedependencyis

one in which the times of observations participating in

the dependency are related by some formula. This is

a use case commonly known in astronomy as a “time

series with cadence”, and it is used when the timing of

the ﬁrst observation is ﬂexible, but the gaps between

subsequent observations must obey some mathemati-

cal rule. The Reservation formalism as deﬁned above,

given its ﬁxed windows of opportunity, cannot help

encode such a dependency. Our practical way of deal-

ing with this limitation is by allowing astronomers to

request such a dependency at a higher level, and then

“compiling” it into the ﬁxed windows of Reservations

after making some (arbitrary or intelligent) constrain-

ing decisions about the position of one of the obser-

vations in the dependency.

Scheduling-time dependencies are distinct from

another class of dependencies that we do not address

in this paper, and which cannot be captured by our

formalisms, namely those for which the decision of

whether to schedule an observation participating in a

dependency hinges on some post-completion function

(not the mere scheduling status) of its antecedents.

To take full advantage of the fact that a scientiﬁc

programme can include the ﬁrst type of scheduling-

time dependencies between observations, we deﬁne

a second formalism, the Compound Reservation. A

Compound Reservation is a logical sentence contain-

ing Reservations connected by a logical operator. The

two logical operators that we have found relevant to

the telescope network scheduling problem are AND

and ONE-OF. Luckily, most astronomy use-cases are

covered by Compound Reservations that include only

one level of logical operators, although, with minor

changes to the model, multiple levels of nesting are

possible.

We call a Compound Reservation containing a sin-

gle Reservation and no operators a singleton.

The AND operator in our formalism is the tradi-

tional conjunction operator. The Compound Reserva-

tion (r

AND r

) means simply that either both r

and

should be scheduled, or neither should be sched-

uled. (r

AND r

AND . . . AND r

) is also deﬁned as

one would expect.

The ONE-OF operator in our formalism is equiv-

alent to a “one-hot circuit” in digital circuit design.

ONE-OF r

) means that either r

or r

should be

scheduled, but not both. For two arguments ONE-OF

is equivalent to XOR. The reason we use the notation

ONE-OF rather than XOR is that most implementa-

tions of an XOR for more than two arguments yield a

parity checker (by chaining many two-argument XOR

gates). A parity checker is a circuit that evaluates to

True when an odd number of its arguments are True,

whereas what we want is a circuit that evaluates to

True when exactly one of its arguments is True. Since

the term “one-hot” is not commonly used outside dig-

ital design, we use the more intuitive label ONE-OF

for this operator.

Note that independent Compound Reservations,

which we join in a list by separating them with com-

mas, i.e. R

, R

, are implicitly linked by a regular

logical OR, since any non-overlappingsubset of them

may be scheduled.

Some examples of the kinds of astronomical ob-

servation requests that the Compound Reservation

formalism enables are:

• observing a target from one of multiple alternative

telescopes (using ONE-OF)

• generic time-series of observations (using AND)

• concurrent observation of the same target from

multiple locations or using multiple instruments

(using AND)

• tracking a stationary target in spite of the earth’s

rotation, or a moving target, using a succession of

telescopes (using AND)

4 THE TELESCOPE NETWORK

SCHEDULING PROBLEM

We deﬁne the telescope network scheduling problem

as the following: given a list of Compound Reserva-

tions {R

, . . . , R

}, produce a consistent schedule, i.e.

one that satisﬁes the logical constraints and contains

no overlaps, that maximises the sum of the priorities

of the scheduled Reservations.

Similar problems have been formulated in op-

erations research and computer science (e.g. truck

scheduling (Lee et al., 2012) and satellite schedul-

ing (Barbulescu et al., 2004; Frank et al., 2001)).

The telescope network scheduling problem combines

four attributes of previously formulated scheduling

problems. First, it concerns interval scheduling, i.e.

scheduling events that must occur at particular points

in time, in a non-overlapping fashion. Second, it

allows slack, that is, ﬂexibility in the start and end

times. This is captured in the Reservation formalism

by allowing windows of opportunity to be of greater

length than the separately deﬁned duration of a Reser-

vation. Third, it is a multi-resource problem. Multi-

ple resources may be available concurrently, but they

are not interchangeable due to their distinct locations.

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Thus, the resource being requested in a Reservation

must always be speciﬁed. Fourth, through the use of

ANDs and ONE-OFs, the multiple telescope schedul-

ing problem contains one type of logical scheduling-

time dependencies between reservations.

For the purposes of the LCOGT scheduler, we are

interested in the ofﬂine version of the telescope net-

work scheduling problem, that is, the version in which

the full list of Compound Reservations is provided at

the outset. Thus, we seek algorithms that take as in-

put a list of Compound Reservations and return one

or more consistent schedules that maximise the sum

priority of the scheduled Reservations. In practice,

such an algorithm will be wrapped in a control algo-

rithm that triggers the re-calculation of the schedule

in response to observation failure, resource availabil-

ity changes, requests for near-real-time observations

and other user actions, which can be thought of as

changes to the input list.

5 SUMMARY

In this paper we have described a formalism that

allows astronomers to express their complex scien-

tiﬁc needs and preferences regarding resource and

time allocation on a telescope network. This formal-

ism serves as the assembly language into which even

higher-level descriptions of astronomers’ needs can

be translated.

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