\chapter{Previous Work}\label{existing}
As stated, scheduling is the process of assigning resources to incoming requests, where the common example is assigning available workers to work requests or vice versa.
Common scheduling examples in Computer Science are: operating systems and hypervisors schedule available CPUs, NICs schedule available bandwidth, virtual memory and memory allocator schedule available storage, \etc.
Scheduling is also common in most other fields, \eg in assembly lines, assigning parts to line workers is a form of scheduling.

In general, \emph{selecting} a scheduling algorithm depends on how much information is available to the scheduler.
Workloads that are well known, consistent, and homogeneous can benefit from a scheduler that is optimized to use this information, while ill-defined, inconsistent, heterogeneous workloads require general non-optimal algorithms.
A secondary aspect is how much information can be gathered versus how much information must be given as part of the scheduler input.
This information adds to the spectrum of scheduling algorithms, going from static schedulers that are well informed from the start, to schedulers that gather most of the information needed, to schedulers that can only rely on very limited information.
Note, this description includes both information about each request, \eg time to complete or resources needed, and information about the relationships among requests, \eg whether some requests must be completed before another request starts.

Scheduling physical resources, \eg in an assembly line, is generally amenable to using well-informed scheduling since information can be gathered much faster than the physical resources can be assigned and workloads are likely to stay stable for long periods.
When a faster pace is needed and changes are much more frequent gathering information on workloads, up-front or live, can become much more limiting and more general schedulers are needed.

\section{Naming Convention}
Scheduling has been studied by various communities concentrating on different incarnations of the same problems.
As a result, there are no standard naming conventions for scheduling that are respected across these communities.
This document uses the term \newterm{\Gls{at}} to refer to the abstract objects being scheduled and the term \newterm{\Gls{proc}} to refer to the concrete objects executing these \ats.

\section{Static Scheduling}
\newterm{Static schedulers} require \ats dependencies and costs to be explicitly and exhaustively specified prior to scheduling.
The scheduler then processes this input ahead of time and produces a \newterm{schedule} the system follows during execution.
This approach is popular in real-time systems since the need for strong guarantees justifies the cost of determining and supplying this information.
In general, static schedulers are less relevant to this project because they require input from the programmers that the \CFA programming language does not have as part of its concurrency semantics.
Specifying this information explicitly adds a significant burden to the programmer and reduces flexibility.
For this reason, the \CFA scheduler does not require this information.

\section{Dynamic Scheduling}
\newterm{Dynamic schedulers} determine \at dependencies and costs during scheduling, if at all.
Hence, unlike static scheduling, \at dependencies are conditional and detected at runtime.
This detection takes the form of observing new \ats in the system and determining dependencies from their behaviour, including suspending or halting a \at that dynamically detects unfulfilled dependencies.
Furthermore, each \at has the responsibility of adding dependent \ats back into the system once dependencies are fulfilled.
As a consequence, the scheduler often has an incomplete view of the system, seeing only \ats with no pending dependencies.

\subsection{Explicitly Informed Dynamic Schedulers}
While dynamic schedulers may not have an exhaustive list of dependencies for a \at, some information may be available about each \at, \eg expected duration, required resources, relative importance, \etc.
When available, a scheduler can then use this information to direct the scheduling decisions.
For example, when scheduling in a cloud computing context, \ats will commonly have extra information that was manually entered, \eg caps on compute time or \io usage.
However, in the context of user-level threading, most programmers do not determine or even \emph{predict} this information;
at best, the scheduler has only some imprecise information provided by the programmer, \eg, indicating a \at takes approximately 3--7 seconds to complete, rather than exactly 5 seconds.
Providing this kind of information is a significant programmer burden, especially if the information does not scale with the number of \ats and their complexity.
For example, providing an exhaustive list of files read by 5 \ats is an easier requirement than providing an exhaustive list of memory addresses accessed by 10,000 independent \ats.

Since the goal of this thesis is to provide a scheduler as a replacement for \CFA's existing \emph{uninformed} scheduler, explicitly informed schedulers are less relevant to this project. Nevertheless, some strategies are worth mentioning.

\subsubsection{Priority Scheduling}
Common information used by schedulers to direct their algorithm is priorities.
Each \at is given a priority, and higher-priority \ats are preferred to lower-priority ones.
The simplest priority scheduling algorithm is to require that every \at have a distinct pre-established priority and always run the available \ats with the highest priority.
Asking programmers to provide an exhaustive set of unique priorities can be prohibitive when the system has a large number of \ats.
It can therefore be desirable for schedulers to support \ats with identical priorities and/or automatically set and adjust priorities for \ats.
Most common operating systems use some variant on priorities with overlaps and dynamic priority adjustments.
For example, Microsoft Windows uses a pair of priorities~\cite{win:priority}, one specified by users out of ten possible options and one adjusted by the system.

\subsection{Uninformed and Self-Informed Dynamic Schedulers}
Several scheduling algorithms do not require programmers to provide additional information on each \at, and instead, make scheduling decisions based solely on internal state and/or information implicitly gathered by the scheduler.


\subsubsection{Feedback Scheduling}
As mentioned, schedulers may also gather information about each \at to direct their decisions.
This design effectively moves the scheduler into the realm of \newterm{Control Theory}~\cite{wiki:controltheory}.
This information gathering does not generally involve programmers, and as such, does not increase programmer burden the same way explicitly provided information may.
However, some feedback schedulers do allow programmers to offer additional information on certain \ats, to direct scheduling decisions.
The important distinction is whether the scheduler can function without this additional information.


\section{Work Stealing}\label{existing:workstealing}
One of the most popular scheduling algorithms in practice (see~\ref{existing:prod}) is work stealing.
This idea, introduced by \cite{DBLP:conf/fpca/BurtonS81}, effectively has each worker process its local \ats first but allows the possibility for other workers to steal local \ats if they run out of \ats.
\cite{DBLP:conf/focs/Blumofe94} introduced the more familiar incarnation of this, where each worker has a queue of \ats and workers without \ats steal \ats from random workers\footnote{The Burton and Sleep algorithm has trees of \ats and steals only among neighbours.}.
Blumofe and Leiserson also prove worst-case space and time requirements for well-structured computations.

Many variations of this algorithm have been proposed over the years~\cite{DBLP:journals/ijpp/YangH18}, both optimizations of existing implementations and approaches that account for new metrics.

\paragraph{Granularity} A significant portion of early work-stealing research concentrated on \newterm{Implicit Parallelism}~\cite{wiki:implicitpar}.
Since the system is responsible for splitting the work, granularity is a challenge that cannot be left to programmers, as opposed to \newterm{Explicit Parallelism}\cite{wiki:explicitpar} where the burden can be left to programmers.
In general, fine granularity is better for load balancing and coarse granularity reduces communication overhead.
The best performance generally means finding a middle ground between the two.
Several methods can be employed, but I believe these are less relevant for threads, which are generally explicit and more coarse-grained.

\paragraph{Task Placement} Another aspect of work stealing that has been studied extensively is the mapping between \at and \proc.
In its simplest form, work stealing assumes that all \procs are interchangeable and therefore the mapping between \at and \proc is not interesting.
However, in real-life architectures there are contexts where different \procs can have different characteristics, which makes some mapping more interesting than others.
A common example where this is statically true is architectures with \glsxtrshort{numa}.
In these cases, it can be relevant to change the scheduler to be cognizant of the topology~\cite{vikranth2013topology,min2011hierarchical}.
Another example is energy usage, where the scheduler is modified to optimize for energy efficiency in addition/instead of performance~\cite{ribic2014energy,torng2016asymmetry}.

\paragraph{Complex Machine Architecture} Another aspect that has been examined is how applicable work stealing is to different machine architectures.
This is arguably strongly related to Task Placement but extends into more heterogeneous architectures.
As \CFA offers no particular support for heterogeneous architecture, this is also an area that is less relevant to this thesis.
Although it could be an interesting avenue for future work.

\subsection{Theoretical Results}
There is also a large body of research on the theoretical aspects of work stealing. These evaluate, for example, the cost of \glslink{atmig}{migration}~\cite{DBLP:conf/sigmetrics/SquillanteN91,DBLP:journals/pe/EagerLZ86}, how affinity affects performance~\cite{DBLP:journals/tpds/SquillanteL93,DBLP:journals/mst/AcarBB02,DBLP:journals/ipl/SuksompongLS16} and theoretical models for heterogeneous systems~\cite{DBLP:journals/jpdc/MirchandaneyTS90,DBLP:journals/mst/BenderR02,DBLP:conf/sigmetrics/GastG10}.
\cite{DBLP:journals/jacm/BlellochGM99} examines the space bounds of work stealing and \cite{DBLP:journals/siamcomp/BerenbrinkFG03} shows that for under-loaded systems, the scheduler completes its computations in finite time, \ie is \newterm{stable}.
Others show that work stealing applies to various scheduling contexts~\cite{DBLP:journals/mst/AroraBP01,DBLP:journals/anor/TchiboukdjianGT13,DBLP:conf/isaac/TchiboukdjianGTRB10,DBLP:conf/ppopp/AgrawalLS10,DBLP:conf/spaa/AgrawalFLSSU14}.
\cite{DBLP:conf/ipps/ColeR13} also studied how randomized work-stealing affects false sharing among \ats.

However, as \cite{DBLP:journals/ijpp/YangH18} highlights, it is worth mentioning that this theoretical research has mainly focused on ``fully strict'' computations, \ie workloads that can be fully represented with a direct acyclic graph.
It is unclear how well these distributions represent workloads in real-world scenarios.

\section{Preemption}
One last aspect of scheduling is preemption since many schedulers rely on it for some of their guarantees.
Preemption is the idea of interrupting \ats that have been running too long, effectively injecting suspend points into the application.
There are multiple techniques to achieve this effect, but they all aim to guarantee that the suspend points in a \at are never further apart than some fixed duration.
While this helps schedulers guarantee that no \ats unfairly monopolize a worker, preemption can effectively be added to any scheduler.
Therefore, the only interesting aspect of preemption for the design of scheduling is whether to require it.

\section{Production Schedulers}\label{existing:prod}
This section presents a quick overview of several current schedulers.
While these schedulers do not necessarily represent the most recent advances in scheduling, they are what is generally accessible to programmers.
As such, I believe these schedulers are at least as relevant as those presented in published work.
Both Schedulers that operate in kernel space and user space are considered, as both can offer relevant insight for this project.
However, real-time schedulers are not considered, as these have constraints that are much stricter than what is needed for this project.

\subsection{Operating System Schedulers}
Operating System Schedulers tend to be fairly complex as they generally support some amount of real time, aim to balance interactive and non-interactive \ats and support multiple users sharing hardware without requiring these users to cooperate.
Here are more details on a few schedulers used in the common operating systems: Linux, FreeBSD, Microsoft Windows and Apple's OS X.
The information is less complete for closed source operating systems.

\paragraph{Linux's CFS}
The default scheduler used by Linux, the Completely Fair Scheduler~\cite{MAN:linux/cfs,MAN:linux/cfs2}, is a feedback scheduler based on CPU time.
For each processor, it constructs a Red-Black tree of \ats waiting to run, ordering them by the amount of CPU time used.
The \at that has used the least CPU time is scheduled.
It also supports the concept of \newterm{Nice values}, which are effectively multiplicative factors on the CPU time used.
The ordering of \ats is also affected by a group-based notion of fairness, where \ats belonging to groups having used less CPU time are preferred to \ats belonging to groups having used more CPU time.
Linux achieves load-balancing by regularly monitoring the system state~\cite{MAN:linux/cfs/balancing} and using some heuristic on the \gls{load}, currently CPU time used in the last millisecond plus a decayed version of the previous time slots~\cite{MAN:linux/cfs/pelt}.

\cite{DBLP:conf/eurosys/LoziLFGQF16} shows that Linux's CFS also does work stealing to balance the workload of each \proc, but the paper argues this aspect can be improved significantly.
The issues highlighted stem from Linux's need to support fairness across \ats \emph{and} across users\footnote{Enforcing fairness across users means that given two users, one with a single \at and the other with one thousand \ats, the user with a single \at does not receive one-thousandth of the CPU time.}, increasing the complexity.

Linux also offers a FIFO scheduler, a real-time scheduler, which runs the highest-priority \ats, and a round-robin scheduler, which is an extension of the FIFO scheduler that adds fixed time slices. \cite{MAN:linux/sched}

\paragraph{FreeBSD}
The ULE scheduler used in FreeBSD\cite{DBLP:conf/bsdcon/Roberson03} is a feedback scheduler similar to Linux's CFS.
It uses different data structures and heuristics but also schedules according to some combination of CPU time used and niceness values.
It also periodically balances the load of the system (according to a different heuristic) but uses a simpler work stealing approach.

\paragraph{Windows(OS)}
Microsoft's Operating System's Scheduler~\cite{MAN:windows/scheduler} is a feedback scheduler with priorities.
It supports 32 levels of priorities, some of which are reserved for real-time and privileged applications.
It schedules \ats based on the highest priorities (lowest number) and how much CPU time each \at has used.
The scheduler may also temporarily adjust priorities after certain effects like the completion of I/O requests.

In~\cite{russinovich2009windows}, Chapter 1 section 2.3 ``Processes, Threads, and Jobs'' discusses the scheduling policy more in-depth.
Multicore scheduling is based on a combination of priorities and \proc preference.
Each \at is assigned an initial processor using a round-robin policy, called the \at's \newterm{ideal} \proc.
\Glspl{at} are distributed among the \procs according to their priority, preferring to match \ats to their ideal \proc and then to the last \proc they ran on.
This approach is a variation of work stealing, where the stealing \proc restores the \at to its original \proc after running it, but mixed with priorities.

\paragraph{Apple OS X}
Apple programming documentation describes its kernel scheduler as follows:
\begin{displayquote}
	OS X is based on Mach and BSD. [...]. It contains an advanced scheduler based on the CMU Mach 3 scheduler. [...] Mach scheduling is based on a system of run queues at various priorities.

	\begin{flushright}
		-- Kernel Programming Guide \cite{MAN:apple/scheduler}
	\end{flushright}
\end{displayquote}

There is very little documentation on the internals of this scheduler.
However, the documentation does describe a feature set that is very similar to the Windows and Linux OS schedulers.
Presumably, this means that the internals are also fairly similar overall.

\subsection{User-Level Schedulers}
By comparison, user-level schedulers tend to be simpler, gather fewer metrics and avoid complex notions of fairness. Part of the simplicity is due to the fact that all \ats have the same user, and therefore cooperation is both feasible and probable.

\paragraph{Go}\label{GoSafePoint}
Go's scheduler uses a randomized work-stealing algorithm that has a global run-queue (\emph{GRQ}) and each processor (\emph{P}) has both a fixed-size run-queue (\emph{LRQ}) and a high-priority next ``chair'' holding a single element~\cite{GITHUB:go,YTUBE:go}.
Preemption is present, but only at safe points,~\cite{go:safepoints} which are detection code inserted at various frequent access boundaries.

The algorithm is as follows :
\begin{enumerate}
	\item Once out of 61 times, pick 1 element from the \emph{GRQ}.
	\item If there is an item in the ``chair'' pick it.
	\item Else pick an item from the \emph{LRQ}.
	\begin{itemize}
	\item If it is empty steal (len(\emph{GRQ}) / \#of\emph{P}) + 1 items (max 256) from the \emph{GRQ}
	\item and steal \emph{half} the \emph{LRQ} of another \emph{P} chosen randomly.
	\end{itemize}
\end{enumerate}

\paragraph{Erlang}
Erlang is a functional language that supports concurrency in the form of processes: threads that share no data.
It uses a kind of round-robin scheduler, with a mix of work sharing and stealing to achieve load balancing~\cite{:erlang}, where under-loaded workers steal from other workers, but overloaded workers also push work to other workers.
This \glslink{atmig}{migration} logic is directed by monitoring logic that evaluates the load a few times per second.

\paragraph{Intel\textregistered ~Threading Building Blocks}
\newterm{Thread Building Blocks} (TBB) is Intel's task parallelism \cite{wiki:taskparallel} framework.
It runs \newterm{jobs}, which are uninterruptible \ats that must always run to completion, on a pool of worker threads.
TBB's scheduler is a variation of randomized work-stealing that also supports higher-priority graph-like dependencies~\cite{MAN:tbb/scheduler}.
It schedules \ats as follows (where \textit{t} is the last \at completed):
\begin{displayquote}
	\begin{enumerate}
		\item The task returned by \textit{t}@.execute()@
		\item The successor of t if \textit{t} was its last completed predecessor.
		\item A task popped from the end of the thread's own queue.
		\item A task with an affinity for the thread.
		\item A task popped from approximately the beginning of the shared queue.
		\item A task popped from the beginning of another randomly chosen thread's queue.
	\end{enumerate}

	\begin{flushright}
		-- Intel\textregistered ~TBB documentation \cite{MAN:tbb/scheduler}
	\end{flushright}
\end{displayquote}

\paragraph{Quasar/Project Loom}
Java has two projects, Quasar~\cite{MAN:quasar} and Project Loom~\cite{MAN:project-loom}\footnote{It is unclear if these are distinct projects.}, that are attempting to introduce lightweight thread\-ing in the form of Fibers.
Both projects seem to be based on the @ForkJoinPool@ in Java, which appears to be a simple incarnation of randomized work-stealing~\cite{MAN:java/fork-join}.

\paragraph{Grand Central Dispatch}
An Apple~\cite{apple:gcd} API that offers task parallelism~\cite{wiki:taskparallel}.
Its distinctive aspect is multiple ``Dispatch Queues'', some of which are created by programmers.
Each queue has its own local ordering guarantees, \eg \ats on queue $A$ are executed in \emph{FIFO} order.

While the documentation only gives limited insight into the scheduling and load balancing approach, \cite{apple:gcd2} suggests a fairly classic approach.
Each \proc has a queue of \ats to run, called \newterm{blocks}, which are drained in \glsxtrshort{fifo}.
GCD also has secondary queues, called \newterm{Dispatch Queues}, with clear ordering, where executing a block ends up scheduling more blocks.
In terms of semantics, these Dispatch Queues seem to be very similar to Intel\textregistered ~TBB \lstinline{execute()} and predecessor semantics.

The similarity of API and semantics between GCD and Intel\textregistered ~TBB suggest the underlying scheduling algorithms are similar.

\paragraph{LibFibre}
LibFibre~\cite{DBLP:journals/pomacs/KarstenB20} is a lightweight user-level threading framework developed at the University of Waterloo.
Similarly to Go, it uses a variation of work stealing with a global queue that has a higher priority than stealing.
Unlike Go, it does not have the high-priority next ``chair'' and does not use randomized work-stealing.
