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 \chapter{Previous Work}\label{existing}
+Scheduling is the process of assigning resources to incomming requests.
+A very common form of this is assigning available workers to work-requests.
+The need for scheduling is very common in Computer Science, \eg Operating Systems and Hypervisors schedule available CPUs, NICs schedule available bamdwith, but scheduling is also common in other fields.
+For example, in assmebly lines assigning parts in need of assembly to line workers is a form of scheduling.
+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 all these cases, the choice of a scheduling algorithm generally depends first and formost on how much information is available to the scheduler.
 Workloads that are well-kown, consistent and homegenous can benefit from a scheduler that is optimized to use this information while ill-defined inconsistent heterogenous workloads will require general algorithms.
 A secondary aspect to that is how much information can be gathered versus how much information must be given as part of the input.
 There is therefore a 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 limitted information.
 Note that this description includes both infomation about each requests, \eg time to complete or resources needed, and information about the relationships between request, \eg whether or not some request must be completed before another request starts.
+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 requests, \eg time to complete or resources needed, and information about the relationships among request, \eg whether or not some request must be completed before another request starts.
 Scheduling physical resources, for example in assembly lines, is generally amenable to using very 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 of time.
+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 of time.
 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 different communities concentrating on different incarnation of the same problems. As a result, their is no real naming convention for scheduling that is respected across these communities. For this document, I will use the term \newterm{\Gls{at}} to refer to the abstract objects being scheduled and the term \newterm{\Gls{proc}} to refer to the objects which will execute these \glspl{at}.
+Scheduling has been studied by various communities concentrating on different incarnation of the same problems. As a result, there is no standard naming conventions for scheduling that is 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 \glspl{at}.
 \section{Static Scheduling}
 Static schedulers require that \glspl{at} have their dependencies and costs explicitly and exhaustively specified prior schedule.
 The scheduler then processes this input ahead of time and producess a \newterm{schedule} to which the system can later adhere.
 This approach is generally popular in real-time systems since the need for strong guarantees justifies the cost of supplying this information.
 In general, static schedulers are less relavant to this project since they require input from the programmers that \CFA does not have as part of its concurrency semantic.
 Specifying this information explicitly can add a significant burden on the programmers and reduces flexibility, for this reason the \CFA scheduler does not require this information.
+\newterm{Static schedulers} require \gls{at} dependencies and costs 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 a programming language does not have as part of its concurrency semantic.
+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}
+It may be difficult to fulfill the requirements of static scheduler if dependencies are conditionnal. In this case, it may be preferable to detect dependencies at runtime. This detection effectively takes the form of adding one or more new \gls{at}(s) to the system as their dependencies are resolved. As well as potentially halting or suspending a \gls{at} that dynamically detect unfulfilled dependencies. Each \gls{at} has the responsability of adding the dependent \glspl{at} back in the system once completed. As a consequence, the scheduler may have an incomplete view of the system, seeing only \glspl{at} we no pending dependencies. Schedulers that support this detection at runtime are referred to as \newterm{Dynamic Schedulers}.
+\newterm{Dynamic schedulers} determine \gls{at} dependencies and costs (if at all) during scheduling.
+% Schedulers that support this detection at runtime are referred to as \newterm{Dynamic Schedulers}.
+Hence, unlike static scheduling, \gls{at} dependencies are conditional and detected at runtime. This detection takes the form of observing new \gls{at}(s) in the system and determining dependencies from their behaviour, including suspending or halting a \gls{at} that dynamically detects unfulfilled dependencies. Furthermore, each \gls{at} has the responsibility of adding dependent \glspl{at} back into the system once dependencies are fulfilled. As a consequence, the scheduler often has an incomplete view of the system, seeing only \glspl{at} with no pending dependencies.
 \subsection{Explicitly Informed Dynamic Schedulers}
+While dynamic schedulers do not have access to an exhaustive list of dependencies for a \gls{at}, they may require to provide more or less information about each \gls{at}, including for example: expected duration, required ressources, relative importance, etc. The scheduler can then use this information to direct the scheduling decisions. \cit{Examples of schedulers with more information} Precisely providing this information can be difficult for programmers, especially \emph{predicted} behaviour, and the scheduler may need to support some amount of imprecision in the provided information. For example, specifying that a \glspl{at} takes approximately 5 seconds to complete, rather than exactly 5 seconds. User provided information can also become a significant burden depending how the effort to provide the information scales with the number of \glspl{at} and there complexity. For example, providing an exhaustive list of files read by 5 \glspl{at} is an easier requirement the providing an exhaustive list of memory addresses accessed by 10'000 distinct \glspl{at}.
+While dynamic schedulers may not have an exhaustive list of dependencies for a \gls{at}, some information may be available about each \gls{at}, \eg expected duration, required resources, relative importance, \etc. When available, a scheduler can then use this information to direct the scheduling decisions. \cit{Examples of schedulers with more information} However, most programmers do not determine or even \emph{predict} this information;
+at best, the scheduler has only some imprecision information provided by the programmer, \eg, indicating a \glspl{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 the information does not scale with the number of \glspl{at} and their complexity. For example, providing an exhaustive list of files read by 5 \glspl{at} is an easier requirement then providing an exhaustive list of memory addresses accessed by 10,000 independent \glspl{at}.
 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 mentionnding.
+Since the goal of this thesis is to provide an \emph{informed} 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{Prority Scheduling}
 A commonly used information that schedulers used to direct the algorithm is priorities. Each Task is given a priority and higher-priority \glspl{at} are preferred to lower-priority ones. The simplest priority scheduling algorithm is to simply require that every \gls{at} have a distinct pre-established priority and always run the available \gls{at} 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 \glspl{at}. It can therefore be diserable for schedulers to support \glspl{at} with identical priorities and/or automatically setting and adjusting priorites for \glspl{at}. The most common operating some variation on priorities with overlaps and dynamic priority adjustments. For example, Microsoft Windows uses a pair of priorities
+\subsubsection{Priority Scheduling}
+Common information used by schedulers to direct their algorithm is priorities. Each task is given a priority and higher-priority \glspl{at} are preferred to lower-priority ones. The simplest priority scheduling algorithm is to require that every \gls{at} have a distinct pre-established priority and always run the available \gls{at} 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 \glspl{at}. It can therefore be desirable for schedulers to support \glspl{at} with identical priorities and/or automatically setting and adjusting priorities for \glspl{at}. The most common adopting some variant on priorities with overlaps and dynamic priority adjustments. For example, Microsoft Windows uses a pair of priorities
 \cit{https://docs.microsoft.com/en-us/windows/win32/procthread/scheduling-priorities,https://docs.microsoft.com/en-us/windows/win32/taskschd/taskschedulerschema-priority-settingstype-element}, 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 additionnal information on each \gls{at}, and instead make scheduling decisions based solely on internal state and/or information implicitly gathered by the scheduler.
+Several scheduling algorithms do not require programmers to provide additional information on each \gls{at}, and instead make scheduling decisions based solely on internal state and/or information implicitly gathered by the scheduler.
 \subsubsection{Feedback Scheduling}
 As mentionned, Schedulers may also gather information about each \glspl{at} to direct their decisions. This design effectively moves the scheduler to some extent into the realm of \newterm{Control Theory}\cite{wiki:controltheory}. This 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 offer the option to programmers to offer additionnal information on certain \glspl{at}, in order to direct scheduling decision. The important distinction being whether or not the scheduler can function without this additionnal information.
+As mentioned, schedulers may also gather information about each \glspl{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 \glspl{at}, in order to direct scheduling decisions. The important distinction being whether or not the scheduler can function without this additional information.
 \section{Work Stealing}\label{existing:workstealing}
 One of the most popular scheduling algorithm in practice (see~\ref{existing:prod}) is work-stealing. This idea, introduce by \cite{DBLP:conf/fpca/BurtonS81}, effectively has each worker work on its local \glspl{at} first, but allows the possibility for other workers to steal local \glspl{at} if they run out of \glspl{at}. \cite{DBLP:conf/focs/Blumofe94} introduced the more familiar incarnation of this, where each workers has queue of \glspl{at} to accomplish and workers without \glspl{at} steal \glspl{at} from random workers. (The Burton and Sleep algorithm had trees of \glspl{at} and stole only among neighbours). Blumofe and Leiserson also prove worst case space and time requirements for well-structured computations.
+One of the most popular scheduling algorithm in practice (see~\ref{existing:prod}) is work stealing. This idea, introduce by \cite{DBLP:conf/fpca/BurtonS81}, effectively has each worker process its local \glspl{at} first, but allows the possibility for other workers to steal local \glspl{at} if they run out of \glspl{at}. \cite{DBLP:conf/focs/Blumofe94} introduced the more familiar incarnation of this, where each workers has a queue of \glspl{at} and workers without \glspl{at} steal \glspl{at} from random workers. (The Burton and Sleep algorithm had trees of \glspl{at} and steal 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 optmizations of existing implementations and approaches that account for new metrics.
+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 was concentrating on \newterm{Implicit Parellelism}\cite{wiki:implicitpar}. Since the system was responsible to split the work, granularity is a challenge that cannot be left to the programmers (as opposed to \newterm{Explicit Parellelism}\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{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} Since modern computers rely heavily on cache hierarchies\cit{Do I need a citation for this}, migrating \glspl{at} from one core to another can be .  \cite{DBLP:journals/tpds/SquillanteL93}
 …
 \todo{The survey is not great on this subject}
 \paragraph{Complex Machine Architecture} Another aspect that has been looked at is how well Work Stealing is applicable to different machine architectures.
+\paragraph{Complex Machine Architecture} Another aspect that has been examined is how well work stealing is applicable to different machine architectures.
 \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 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 heterogenous systems\cite{DBLP:journals/jpdc/MirchandaneyTS90,DBLP:journals/mst/BenderR02,DBLP:conf/sigmetrics/GastG10}. \cite{DBLP:journals/jacm/BlellochGM99} examine the space bounds of Work Stealing and \cite{DBLP:journals/siamcomp/BerenbrinkFG03} show that for underloaded systems, the scheduler will complete computations in finite time, \ie is \newterm{stable}. Others show that Work-Stealing is applicable 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 \glspl{at}.
+There is also a large body of research on the theoretical aspects of work stealing. These evaluate, for example, the cost of 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 is applicable 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 \glspl{at}.
 However, as \cite{DBLP:journals/ijpp/YangH18} highlights, it is worth mentionning 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.
+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 worth mentionning is preemption since many schedulers rely on it for some of their guarantees. Preemption is the idea of interrupting \glspl{at} that have been running for too long, effectively injecting suspend points in the applications. There are multiple techniques to achieve this but they all aim to have the effect of guaranteeing that suspend points in a \gls{at} are never further apart than some fixed duration. While this helps schedulers guarantee that no \glspl{at} will unfairly monopolize a worker, preemption can effectively added to any scheduler. Therefore, the only interesting aspect of preemption for the design of scheduling is whether or not to require it.
+One last aspect of scheduling is preemption since many schedulers rely on it for some of their guarantees. Preemption is the idea of interrupting \glspl{at} 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 suspend points in a \gls{at} are never further apart than some fixed duration. While this helps schedulers guarantee that no \glspl{at} unfairly monopolizes a worker, preemption can effectively added to any scheduler. Therefore, the only interesting aspect of preemption for the design of scheduling is whether or not to require it.
 \section{Schedulers in Production}\label{existing:prod}
 This section will show a quick overview of several schedulers which are generally available a the time of writing. While these schedulers don't necessarily represent to most recent advances in scheduling, they are what is generally accessible to programmers. As such, I believe that these schedulers are at least as relevant as those presented in published work. I chose both schedulers that operating in kernel space and in user space, as both can offer relevant insight for this project. However, I did not list any schedulers aimed for real-time applications, as these have constraints that are much stricter than what is needed for this project.
+\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. Schedulers that operate in kernel space and in user space are considered, as both can offer relevant insight for this project. However, real-time schedulers as 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 schedulers, they generally support some amount of real-time, aim to balance interactive and non-interactive \glspl{at} and support for 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 operating systems behind closed source.
+Operating System Schedulers tend to be fairly complex as they generally support some amount of real-time, aim to balance interactive and non-interactive \glspl{at} 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 operating systems with closed source.
 \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 \glspl{at} waiting to run, ordering them by amount of CPU time spent. The scheduler schedules the \gls{at} that has spent the least CPU time. It also supports the concept of \newterm{Nice values}, which are effectively multiplicative factors on the CPU time spent. The ordering of \glspl{at} is also impacted by a group based notion of fairness, where \glspl{at} belonging to groups having spent less CPU time are preferred to \glspl{at} beloning to groups having spent more CPU time. Linux achieves load-balancing by regularly monitoring the system state\cite{MAN:linux/cfs/balancing} and using some heuristic on the load (currently CPU time spent in the last millisecond plus decayed version of the previous time slots\cite{MAN:linux/cfs/pelt}.).
+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 \glspl{at} waiting to run, ordering them by the amount of CPU time used. The \gls{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 \glspl{at} is also affected by a group based notion of fairness, where \glspl{at} belonging to groups having used less CPU time are preferred to \glspl{at} 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 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 processors, but the paper argues this aspect can be improved significantly. The issues highlighted sem to stem from Linux's need to support fairness across \glspl{at} \emph{and} across users\footnote{Enforcing fairness across users means, for example, that given two users: one with a single \gls{at} and the other with one thousand \glspl{at}, the user with a single \gls{at} does not receive one one thousandth of the CPU time.}, increasing the complexity.
+\cite{DBLP:conf/eurosys/LoziLFGQF16} shows that Linux's CFS also does work stealing to balance the workload of each processors, but the paper argues this aspect can be improved significantly. The issues highlighted stem from Linux's need to support fairness across \glspl{at} \emph{and} across users\footnote{Enforcing fairness across users means that given two users, one with a single \gls{at} and the other with one thousand \glspl{at}, the user with a single \gls{at} does not receive one thousandth of the CPU time.}, increasing the complexity.
 Linux also offers a FIFO scheduler, a real-time schedulerwhich runs the highest-priority \gls{at}, and a round-robin scheduler, which is an extension of the fifo-scheduler that adds fixed time slices. \cite{MAN:linux/sched}
+Linux also offers a FIFO scheduler, a real-time scheduler, which runs the highest-priority \gls{at}, 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 spent and niceness values. It also periodically balances the load of the system(according to a different heuristic), but uses a simpler Work Stealing approach.
+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 prviliged applications. It schedules \glspl{at} based on the highest priorities (lowest number) and how much cpu time each \glspl{at} have used. The scheduler may also temporarily adjust priorities after certain effects like the completion of I/O requests.
+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 \glspl{at} based on the highest priorities (lowest number) and how much CPU time each \gls{at} has used. The scheduler may also temporarily adjust priorities after certain effects like the completion of I/O requests.
 \todo{load balancing}
 …
 By comparison, user level schedulers tend to be simpler, gathering fewer metrics and avoid complex notions of fairness. Part of the simplicity is due to the fact that all \glspl{at} have the same user, and therefore cooperation is both feasible and probable.
 \paragraph{Go}
 Go's scheduler uses a Randomized Work Stealing algorithm that has a global runqueue(\emph{GRQ}) and each processor(\emph{P}) has both a fixed-size runqueue(\emph{LRQ}) and a high-priority next ``chair'' holding a single element.\cite{GITHUB:go,YTUBE:go} Preemption is present, but only at function call boundaries.
+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 function call boundaries.
 The algorithm is as follows :
 \begin{enumerate}
         \item Once out of 61 times, directly pick 1 element from the \emph{GRQ}.
+        \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}.
+        \item If it was empty steal (len(\emph{GRQ}) / \#of\emph{P}) + 1 items (max 256) from the \emph{GRQ}.
+        \item If it was empty steal \emph{half} the \emph{LRQ} of another \emph{P} chosen randomly.
+        \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 functionnal language that supports concurrency in the form of processes, threads that share no data. It seems to be some kind of Round-Robin Scheduler. It currently uses some mix of Work Sharing and Work Stealing to achieve load balancing\cite{:erlang}, where underloaded workers steal from other workers, but overloaded workers also push work to other workers. This migration logic seems to be directed by monitoring logic that evaluates the load a few times per seconds.
+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 migration logic is directed by monitoring logic that evaluates the load a few times per seconds.
 \paragraph{Intel\textregistered ~Threading Building Blocks}
 \newterm{Thread Building Blocks}(TBB) is Intel's task parellelism\cite{wiki:taskparallel} framework. It runs \newterm{jobs}, uninterruptable \glspl{at}, schedulable objects 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 \glspl{at} as follows (where \textit{t} is the last \gls{at} completed):
+\newterm{Thread Building Blocks} (TBB) is Intel's task parallelism \cite{wiki:taskparallel} framework. It runs \newterm{jobs}, which are uninterruptable \glspl{at} 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 \glspl{at} as follows (where \textit{t} is the last \gls{at} completed):
 \begin{displayquote}
         \begin{enumerate}
                 \item The task returned by \textit{t}\texttt{.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 deque.
+                \item A task popped from the end of the thread's own deque.
                 \item A task with 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 deque.
+                \item A task popped from the beginning of another randomly chosen thread's deque.
         \end{enumerate}
 …
 \paragraph{Quasar/Project Loom}
 Java has two projects that are attempting to introduce lightweight threading into java in the form of Fibers, Quasar\cite{MAN:quasar} and Project Loom\cite{MAN:project-loom}\footnote{It is unclear to me if these are distinct projects or not}. Both projects seem to be based on the \texttt{ForkJoinPool} in Java which appears to be a simple incarnation of Randomized Work Stealing\cite{MAN:java/fork-join}.
+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 \texttt{ForkJoinPool} in Java, which appears to be a simple incarnation of randomized work-stealing~\cite{MAN:java/fork-join}.
 \paragraph{Grand Central Dispatch}
 This is an API produce by Apple\cit{Official GCD source} that offers task parellelism\cite{wiki:taskparallel}. Its distinctive aspect is that it uses multiple ``Dispatch Queues'', some of which are created by programmers. These queues each have their own local ordering guarantees, \eg \glspl{at} on queue $A$ are executed in \emph{FIFO} order.
+An Apple\cit{Official GCD source} 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 \glspl{at} on queue $A$ are executed in \emph{FIFO} order.
 \todo{load balancing and scheduling}
 …
 % http://web.archive.org/web/20090920043909/http://images.apple.com/macosx/technology/docs/GrandCentral_TB_brief_20090903.pdf
 In terms of semantics, the Dispatch Queues seem to be very similar in semantics to Intel\textregistered ~TBB \texttt{execute()} and predecessor semantics. Where it would be possible to convert from one to the other.
+In terms of semantics, the Dispatch Queues seem to be very similar in semantics to Intel\textregistered ~TBB \texttt{execute()} and predecessor semantics. % Where it would be possible to convert from one to the other.
 \paragraph{LibFibre}
+LibFibre\cite{DBLP:journals/pomacs/KarstenB20} is a light-weight user-level threading framework developt at the University of Waterloo. Similarly to Go, it uses a variation of Work Stealing with a global queue that is higher priority than stealing. Unlock Go it does not have the high-priority next ``chair'' and does not use Randomized Work Stealing.
+LibFibre~\cite{DBLP:journals/pomacs/KarstenB20} is a light-weight 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 is higher priority than stealing. Unlike Go, it does not have the high-priority next ``chair'' and does not use randomized work-stealing.

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