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 \chapter{Scheduling Core}\label{core}
+Before discussing scheduling in general, where it is important to address systems that are changing states, this document discusses scheduling in a somewhat ideal scenario, where the system has reached a steady state. For this purpose, a steady state is loosely defined as a state where there are always \glspl{thrd} ready to run and the system has the resources necessary to accomplish the work, \eg, enough workers. In short, the system is neither overloaded nor underloaded.
+It is important to discuss the steady state first because it is the easiest case to handle and, relatedly, the case in which the best performance is to be expected. As such, when the system is either overloaded or underloaded, a common approach is to try to adapt the system to this new load and return to the steady state, \eg, by adding or removing workers. Therefore, flaws in scheduling the steady state tend to be pervasive in all states.
+Before discussing scheduling in general, where it is important to address systems that are changing states, this document discusses scheduling in a somewhat ideal scenario, where the system has reached a steady state.
+For this purpose, a steady state is loosely defined as a state where there are always \glspl{thrd} ready to run and the system has the resources necessary to accomplish the work, \eg, enough workers.
+In short, the system is neither overloaded nor underloaded.
+It is important to discuss the steady state first because it is the easiest case to handle and, relatedly, the case in which the best performance is to be expected.
+As such, when the system is either overloaded or underloaded, a common approach is to try to adapt the system to this new load and return to the steady state, \eg, by adding or removing workers.
+Therefore, flaws in scheduling the steady state tend to be pervasive in all states.
 \section{Design Goals}
+As with most of the design decisions behind \CFA, an important goal is to match the expectation of the programmer according to their execution mental-model. To match expectations, the design must offer the programmer sufficient guarantees so that, as long as they respect the execution mental-model, the system also respects this model.
+As with most of the design decisions behind \CFA, an important goal is to match the expectation of the programmer according to their execution mental-model.
+To match expectations, the design must offer the programmer sufficient guarantees so that, as long as they respect the execution mental-model, the system also respects this model.
 For threading, a simple and common execution mental-model is the ``Ideal multi-tasking CPU'' :
 …
 Applied to threads, this model states that every ready \gls{thrd} immediately runs in parallel with all other ready \glspl{thrd}. While a strict implementation of this model is not feasible, programmers still have expectations about scheduling that come from this model.
+In general, the expectation at the center of this model is that ready \glspl{thrd} do not interfere with each other but simply share the hardware. This assumption makes it easier to reason about threading because ready \glspl{thrd} can be thought of in isolation and the effect of the scheduler can be virtually ignored. This expectation of \gls{thrd} independence means the scheduler is expected to offer two guarantees:
+In general, the expectation at the center of this model is that ready \glspl{thrd} do not interfere with each other but simply share the hardware.
+This assumption makes it easier to reason about threading because ready \glspl{thrd} can be thought of in isolation and the effect of the scheduler can be virtually ignored.
+This expectation of \gls{thrd} independence means the scheduler is expected to offer two guarantees:
 \begin{enumerate}
         \item A fairness guarantee: a \gls{thrd} that is ready to run is not prevented by another thread.
 …
 \end{enumerate}
+It is important to note that these guarantees are expected only up to a point. \Glspl{thrd} that are ready to run should not be prevented to do so, but they still share the limited hardware resources. Therefore, the guarantee is considered respected if a \gls{thrd} gets access to a \emph{fair share} of the hardware resources, even if that share is very small.
+Similar to the performance guarantee, the lack of interference among threads is only relevant up to a point. Ideally, the cost of running and blocking should be constant regardless of contention, but the guarantee is considered satisfied if the cost is not \emph{too high} with or without contention. How much is an acceptable cost is obviously highly variable. For this document, the performance experimentation attempts to show the cost of scheduling is at worst equivalent to existing algorithms used in popular languages. This demonstration can be made by comparing applications built in \CFA to applications built with other languages or other models. Recall programmer expectation is that the impact of the scheduler can be ignored. Therefore, if the cost of scheduling is competitive to other popular languages, the guarantee is consider achieved.
+It is important to note that these guarantees are expected only up to a point.
+\Glspl{thrd} that are ready to run should not be prevented to do so, but they still share the limited hardware resources.
+Therefore, the guarantee is considered respected if a \gls{thrd} gets access to a \emph{fair share} of the hardware resources, even if that share is very small.
+Similar to the performance guarantee, the lack of interference among threads is only relevant up to a point.
+Ideally, the cost of running and blocking should be constant regardless of contention, but the guarantee is considered satisfied if the cost is not \emph{too high} with or without contention.
+How much is an acceptable cost is obviously highly variable.
+For this document, the performance experimentation attempts to show the cost of scheduling is at worst equivalent to existing algorithms used in popular languages.
+This demonstration can be made by comparing applications built in \CFA to applications built with other languages or other models.
+Recall programmer expectation is that the impact of the scheduler can be ignored.
+Therefore, if the cost of scheduling is competitive to other popular languages, the guarantee is consider achieved.
 More precisely the scheduler should be:
 \begin{itemize}
 …
         \item Faster than other schedulers that have equal or better fairness.
 \end{itemize}
-(Everything should be made as fair as possible, but not fairer. Chuck Einstein, Albert's younger brother)
 \subsection{Fairness Goals}
 For this work, fairness is considered to have two strongly related requirements: true starvation freedom and ``fast'' load balancing.
 \paragraph{True starvation freedom} means as long as at least one \proc continues to dequeue \ats, all ready \ats should be able to run eventually (eventual progress).
+\paragraph{True starvation freedom} means as long as at least one \proc continues to dequeue \ats, all ready \ats should be able to run eventually, \ie, eventual progress.
 In any running system, a \proc can stop dequeuing \ats if it starts running a \at that never blocks.
 Without preemption, traditional work-stealing schedulers do not have starvation freedom in this case.
 …
 \subsection{Fairness vs Scheduler Locality} \label{fairnessvlocal}
+An important performance factor in modern architectures is cache locality. Waiting for data at lower levels or not present in the cache can have a major impact on performance. Having multiple \glspl{hthrd} writing to the same cache lines also leads to cache lines that must be waited on. It is therefore preferable to divide data among each \gls{hthrd}\footnote{This partitioning can be an explicit division up front or using data structures where different \glspl{hthrd} are naturally routed to different cache lines.}.
+For a scheduler, having good locality {\color{red}PAB: I think you should fold this footnote into the paragraph}\footnote{This section discusses \emph{internal locality}, \ie, the locality of the data used by the scheduler versus \emph{external locality}, \ie, how the data used by the application is affected by scheduling. External locality is a much more complicated subject and is discussed in the next section.}, \ie, having the data local to each \gls{hthrd}, generally conflicts with fairness. Indeed, good locality often requires avoiding the movement of cache lines, while fairness requires dynamically moving a \gls{thrd}, and as consequence cache lines, to a \gls{hthrd} that is currently available.
+However, I claim that in practice it is possible to strike a balance between fairness and performance because these goals do not necessarily overlap temporally. Figure~\ref{fig:fair} shows a visual representation of this behaviour. As mentioned, some unfairness is acceptable; therefore it is desirable to have an algorithm that prioritizes cache locality as long as thread delay does not exceed the execution mental-model.
+An important performance factor in modern architectures is cache locality.
+Waiting for data at lower levels or not present in the cache can have a major impact on performance.
+Having multiple \glspl{hthrd} writing to the same cache lines also leads to cache lines that must be waited on.
+It is therefore preferable to divide data among each \gls{hthrd}\footnote{This partitioning can be an explicit division up front or using data structures where different \glspl{hthrd} are naturally routed to different cache lines.}.
+For a scheduler, having good locality, \ie, having the data local to each \gls{hthrd}, generally conflicts with fairness.
+Indeed, good locality often requires avoiding the movement of cache lines, while fairness requires dynamically moving a \gls{thrd}, and as consequence cache lines, to a \gls{hthrd} that is currently available.
+Note that this section discusses \emph{internal locality}, \ie, the locality of the data used by the scheduler versus \emph{external locality}, \ie, how the data used by the application is affected by scheduling.
+External locality is a much more complicated subject and is discussed in the next section.
+However, I claim that in practice it is possible to strike a balance between fairness and performance because these goals do not necessarily overlap temporally.
+Figure~\ref{fig:fair} shows a visual representation of this behaviour.
+As mentioned, some unfairness is acceptable; therefore it is desirable to have an algorithm that prioritizes cache locality as long as thread delay does not exceed the execution mental-model.
 \begin{figure}
 …
         \input{fairness.pstex_t}
         \vspace*{-10pt}
+        \caption[Fairness vs Locality graph]{Rule of thumb Fairness vs Locality graph \smallskip\newline The importance of Fairness and Locality while a ready \gls{thrd} awaits running is shown as the time the ready \gls{thrd} waits increases, Ready Time, the chances that its data is still in cache decreases, Locality. At the same time, the need for fairness increases since other \glspl{thrd} may have the chance to run many times, breaking the fairness model. Since the actual values and curves of this graph can be highly variable, the graph is an idealized representation of the two opposing goals.}
+        \caption[Fairness vs Locality graph]{Rule of thumb Fairness vs Locality graph \smallskip\newline The importance of Fairness and Locality while a ready \gls{thrd} awaits running is shown as the time the ready \gls{thrd} waits increases, Ready Time, the chances that its data is still in cache decreases, Locality.
+        At the same time, the need for fairness increases since other \glspl{thrd} may have the chance to run many times, breaking the fairness model.
+        Since the actual values and curves of this graph can be highly variable, the graph is an idealized representation of the two opposing goals.}
         \label{fig:fair}
 \end{figure}
 \subsection{Performance Challenges}\label{pref:challenge}
+While there exists a multitude of potential scheduling algorithms, they generally always have to contend with the same performance challenges. Since these challenges are recurring themes in the design of a scheduler it is relevant to describe the central ones here before looking at the design.
+While there exists a multitude of potential scheduling algorithms, they generally always have to contend with the same performance challenges.
+Since these challenges are recurring themes in the design of a scheduler it is relevant to describe the central ones here before looking at the design.
 \subsubsection{Scalability}
 …
 \section{Inspirations}
+In general, a na\"{i}ve \glsxtrshort{fifo} ready-queue does not scale with increased parallelism from \glspl{hthrd}, resulting in decreased performance. The problem is a single point of contention when adding/removing \glspl{thrd}. As shown in the evaluation sections, most production schedulers do scale when adding \glspl{hthrd}. The solution to this problem is to shard the ready-queue: create multiple \emph{subqueues} forming the logical ready-queue and the subqueues are accessed by multiple \glspl{hthrd} without interfering.
+In general, a na\"{i}ve \glsxtrshort{fifo} ready-queue does not scale with increased parallelism from \glspl{hthrd}, resulting in decreased performance.
+The problem is a single point of contention when adding/removing \ats.
+As shown in the evaluation sections, most production schedulers do scale when adding \glspl{hthrd}.
+The solution to this problem is to shard the ready-queue: create multiple \emph{subqueues} forming the logical ready-queue and the subqueues are accessed by multiple \glspl{hthrd} without interfering.
 Before going into the design of \CFA's scheduler, it is relevant to discuss two sharding solutions that served as the inspiration scheduler in this thesis.
 …
 \subsection{Work-Stealing}
 As mentioned in \ref{existing:workstealing}, a popular pattern in work-stealing is sharding the ready-queue.
 In this pattern, each \gls{proc} has its own local ready-queue and \glspl{proc} only access each other's ready-queue if they run out of work on their local ready-queue.
+As mentioned in \ref{existing:workstealing}, a popular sharding approach for the ready-queue is work-stealing.
+In this approach, each \gls{proc} has its own local subqueue and \glspl{proc} only access each other's subqueue if they run out of work on their local ready-queue.
 The interesting aspect of work stealing happens in the steady-state scheduling case, \ie all \glspl{proc} have work and no load balancing is needed.
 In this case, work stealing is close to optimal scheduling: it can achieve perfect locality and have no contention.
 …
 \subsection{Relaxed-FIFO}
 A different scheduling approach is to create a ``relaxed-FIFO'' queue as in \todo{cite Trevor's paper}. This approach forgoes any ownership between \gls{proc} and ready-queue, and simply creates a pool of ready-queues from which \glspl{proc} pick.
+A different scheduling approach is to create a ``relaxed-FIFO'' queue, as in \todo{cite Trevor's paper}.
+This approach forgoes any ownership between \gls{proc} and subqueue, and simply creates a pool of ready-queues from which \glspl{proc} pick.
 Scheduling is performed as follows:
 \begin{itemize}
 \item
+All ready queues are protected by TryLocks.
+\item
+Timestamps are added to each element of a ready queue.
+\item
+A \gls{proc} randomly tests ready queues until it has acquired two queues.
+\item
+The older of the two \ats at the front the acquired queues is dequeued.
+All subqueues are protected by TryLocks.
+\item
+Timestamps are added to each element of a subqueue.
+\item
+A \gls{proc} randomly tests ready queues until it has acquired one or two queues.
+\item
+If two queues are acquired, the older of the two \ats at the front the acquired queues is dequeued.
+\item
+Otherwise the \ats from the single queue is dequeued.
 \end{itemize}
 The result is a queue that has both good scalability and sufficient fairness.
 The lack of ownership ensures that as long as one \gls{proc} is still able to repeatedly dequeue elements, it is unlikely any element will delay longer than any other element.
+This guarantee contrasts with work-stealing, where a \gls{proc} with a long ready queue results in unfairness for its \ats in comparison to a \gls{proc} with a short ready queue. This unfairness persists until a \gls{proc} runs out of work and steals.
+This guarantee contrasts with work-stealing, where a \gls{proc} with a long subqueue results in unfairness for its \ats in comparison to a \gls{proc} with a short subqueue.
+This unfairness persists until a \gls{proc} runs out of work and steals.
 An important aspects of this scheme's fairness approach is that the timestamps make it possible to evaluate how long elements have been on the queue.
 However, \glspl{proc} eagerly search for these older elements instead of focusing on specific queues, which affects locality.
+However, \glspl{proc} eagerly search for these older elements instead of focusing on specific queues, which negatively affects locality.
 While this scheme has good fairness, its performance suffers.
 …
 The inherent fairness and good performance with many \ats, makes the relaxed-FIFO queue a good candidate to form the basis of a new scheduler.
 The problem case is workloads where the number of \ats is barely greater than the number of \procs.
 In these situations, the wide sharding of the ready queue means most of its (relaxed) subqueues are empty.
+In these situations, the wide sharding of the ready queue means most of its subqueues are empty.
 Furthermore, the non-empty subqueues are unlikely to hold more than one item.
 The consequence is that a random dequeue operation is likely to pick an empty subqueue, resulting in an unbounded number of selections.
 …
 \subsection{Dynamic Entropy}\cit{https://xkcd.com/2318/}
 The Relaxed-FIFO approach can be made to handle the case of mostly empty subqueues by tweaking the \glsxtrlong{prng} (PRNG).
+The Relaxed-FIFO approach can be made to handle the case of mostly empty subqueues by tweaking the \glsxtrlong{prng}.
 The \glsxtrshort{prng} state can be seen as containing a list of all the future subqueues that will be accessed.
 While this concept is not particularly useful on its own, the consequence is that if the \glsxtrshort{prng} algorithm can be run \emph{backwards}, then the state also contains a list of all the subqueues that were accessed.
 …
         \centering
         \input{base.pstex_t}
+        \caption[Base \CFA design]{Base \CFA design \smallskip\newline A pool of subqueues offers the sharding, two per \glspl{proc}. Each \gls{proc} can access all of the subqueues. Each \at is timestamped when enqueued.}
+        \caption[Base \CFA design]{Base \CFA design \smallskip\newline A pool of subqueues offers the sharding, two per \glspl{proc}.
+        Each \gls{proc} can access all of the subqueues.
+        Each \at is timestamped when enqueued.}
         \label{fig:base}
 \end{figure}
 …
 This structure is similar to classic work-stealing except the subqueues are placed in an array so \procs can access them in constant time.
 Sharding width can be adjusted based on contention.
 Note, as an optimization, the TS of a \at is store in the \at in front of it, so the first TS is in the array and the last \at has no TS.
 This organization keeps the highly accessed front TSs close together in the array.
+Note, as an optimization, the TS of a \at is stored in the \at in front of it, so the first TS is in the array and the last \at has no TS.
+This organization keeps the highly accessed front TSs directly in the array.
 When a \proc attempts to dequeue a \at, it first picks a random remote subqueue and compares its timestamp to the timestamps of its local subqueue(s).
 The oldest waiting \at (possibly within some range) is dequeued to provide global fairness.
+The oldest waiting \at is dequeued to provide global fairness.
 However, this na\"ive implemented has performance problems.
 First, it is necessary to have some damping effect on helping.
 Random effects like cache misses and preemption can add spurious but short bursts of latency negating the attempt to help.
 These bursts are caused by increased migrations and make this work stealing approach slowdown to the level of relaxed-FIFO.
+These bursts can cause increased migrations and make this work stealing approach slowdown to the level of relaxed-FIFO.
 \begin{figure}
 …
 With these additions to work stealing, scheduling can be made as fair as the relaxed-FIFO approach, avoiding the majority of unnecessary migrations.
 Unfortunately, the work to achieve fairness has a performance cost, especially when the workload is inherently fair, and hence, there is only short-term or no starvation.
 The problem is that the constant polling (reading) of remote subqueues generally entail a cache miss because the TSs are constantly being updated (written).
 To make things worst, remote subqueues that are very active, \ie \ats are frequently enqueued and dequeued from them, the higher the chances are that polling will incur a cache-miss.
+The problem is that the constant polling, \ie reads, of remote subqueues generally entail a cache miss because the TSs are constantly being updated, \ie, writes.
+To make things worst, remote subqueues that are very active, \ie \ats are frequently enqueued and dequeued from them, lead to higher chances that polling will incur a cache-miss.
 Conversely, the active subqueues do not benefit much from helping since starvation is already a non-issue.
 This puts this algorithm in the awkward situation of paying for a cost that is largely unnecessary.
 …
         \centering
         \input{base_ts2.pstex_t}
+        \caption[\CFA design with Redundant Timestamps]{\CFA design with Redundant Timestamps \smallskip\newline An array is added containing a copy of the timestamps. These timestamps are written to with relaxed atomics, so there is no order among concurrent memory accesses, leading to fewer cache invalidations.}
+        \caption[\CFA design with Redundant Timestamps]{\CFA design with Redundant Timestamps \smallskip\newline An array is added containing a copy of the timestamps.
+        These timestamps are written to with relaxed atomics, so there is no order among concurrent memory accesses, leading to fewer cache invalidations.}
         \label{fig:base-ts2}
 \end{figure}
 …
 The correctness argument is somewhat subtle.
 The data used for deciding whether or not to poll a queue can be stale as long as it does not cause starvation.
 Therefore, it is acceptable if stale data makes queues appear older than they really are but not fresher.
+Therefore, it is acceptable if stale data makes queues appear older than they really are but appearing fresher can be a problem.
 For the timestamps, this means missing writes to the timestamp is acceptable since they make the head \at look older.
 For the moving average, as long as the operations are just atomic reads/writes, the average is guaranteed to yield a value that is between the oldest and newest values written.
 …
 \subsection{Per CPU Sharding}
 Building a scheduler that is cache aware poses two main challenges: discovering the cache topology and matching \procs to this cache structure.
 Unfortunately, there is no portable way to discover cache topology, and it is outside the scope of this thesis to solve this problem.
 …
 The simplest approach for mapping subqueues to cache structure is to statically tie subqueues to CPUs.
 Instead of having each subqueue local to a specific \proc (kernel thread), the system is initialized with subqueues for each hardware hyperthread/core up front.
+Instead of having each subqueue local to a specific \proc, the system is initialized with subqueues for each hardware hyperthread/core up front.
 Then \procs dequeue and enqueue by first asking which CPU id they are executing on, in order to identify which subqueues are the local ones.
 \Glspl{proc} can get the CPU id from \texttt{sched\_getcpu} or \texttt{librseq}.
 …
 \subsection{Topological Work Stealing}
 Therefore, the approach used in the \CFA scheduler is to have per-\proc subqueues, but have an explicit data-structure track which cache substructure each subqueue is tied to.
 This tracking requires some finesse because reading this data structure must lead to fewer cache misses than not having the data structure in the first place.

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