Tong Li wrote:
On Fri, 27 Jul 2007, Chris Snook wrote:
Tong Li wrote:
I'd like to clarify that I'm not trying to push this particular code
to the kernel. I'm a researcher. My intent was to point out that we
have a problem in the scheduler and my dwrr algorithm can potentially
help fix it. The patch itself was merely a proof-of-concept. I'd be
thrilled if the algorithm can be proven useful in the real world. I
appreciate the people who have given me comments. Since then, I've
revised my algorithm/code. Now it doesn't require global locking but
retains strong fairness properties (which I was able to prove
mathematically).
Thanks for doing this work. Please don't take the implementation
criticism as a lack of appreciation for the work. I'd like to see
dwrr in the scheduler, but I'm skeptical that re-introducing expired
runqueues is the most efficient way to do it.
Given the inherently controversial nature of scheduler code,
particularly that which attempts to enforce fairness, perhaps a
concise design document would help us come to an agreement about what
we think the scheduler should do and what tradeoffs we're willing to
make to do those things. Do you have a design document we could discuss?
-- Chris
Thanks for the interest. Attached is a design doc I wrote several months
ago (with small modifications). It talks about the two pieces of my
design: group scheduling and dwrr. The description was based on the
original O(1) scheduler, but as my CFS patch showed, the algorithm is
applicable to other underlying schedulers as well. It's interesting that
I started working on this in January for the purpose of eventually
writing a paper about it. So I knew reasonably well the related research
work but was totally unaware that people in the Linux community were
also working on similar things. This is good. If you are interested, I'd
like to help with the algorithms and theory side of the things.
tong
-------------------------------------------
Overview:
Trio extends the existing Linux scheduler with support for
proportional-share scheduling. It uses a scheduling algorithm, called
Distributed Weighted Round-Robin (DWRR), which retains the existing
scheduler design as much as possible, and extends it to achieve
proportional fairness with O(1) time complexity and a constant error
bound, compared to the ideal fair scheduling algorithm. The goal of Trio
is not to improve interactive performance; rather, it relies on the
existing scheduler for interactivity and extends it to support MP
proportional fairness.
Trio has two unique features: (1) it enables users to control shares of
CPU time for any thread or group of threads (e.g., a process, an
application, etc.), and (2) it enables fair sharing of CPU time across
multiple CPUs. For example, with ten tasks running on eight CPUs, Trio
allows each task to take an equal fraction of the total CPU time. These
features enable Trio to complement the existing Linux scheduler to
enable greater user flexibility and stronger fairness.
Background:
Over the years, there has been a lot of criticism that conventional Unix
priorities and the nice interface provide insufficient support for users
to accurately control CPU shares of different threads or applications.
Many have studied scheduling algorithms that achieve proportional
fairness. Assuming that each thread has a weight that expresses its
desired CPU share, informally, a scheduler is proportionally fair if (1)
it is work-conserving, and (2) it allocates CPU time to threads in exact
proportion to their weights in any time interval. Ideal proportional
fairness is impractical since it requires that all runnable threads be
running simultaneously and scheduled with infinitesimally small quanta.
In practice, every proportional-share scheduling algorithm approximates
the ideal algorithm with the goal of achieving a constant error bound.
For more theoretical background, please refer to the following papers:
I don't think that achieving a constant error bound is always a good thing. We
all know that fairness has overhead. If I have 3 threads and 2 processors, and
I have a choice between fairly giving each thread 1.0 billion cycles during the
next second, or unfairly giving two of them 1.1 billion cycles and giving the
other 0.9 billion cycles, then we can have a useful discussion about where we
want to draw the line on the fairness/performance tradeoff. On the other hand,
if we can give two of them 1.1 billion cycles and still give the other one 1.0
billion cycles, it's madness to waste those 0.2 billion cycles just to avoid
user jealousy. The more complex the memory topology of a system, the more
"free" cycles you'll get by tolerating short-term unfairness. As a crude
heuristic, scaling some fairly low tolerance by log2(NCPUS) seems appropriate,
but eventually we should take the boot-time computed migration costs into
consideration.
[1] A. K. Parekh and R. G. Gallager. A generalized processor sharing
approach to flow control in integrated services networks: The single-node
case. IEEE/ACM Transactions on Networking, 1(3):344-357, June 1993.
[2] C. R. Bennett and H. Zhang. WF2Q: Worst-case fair weighted fair
queueing. In Proceedings of IEEE INFOCOM '94, pages 120-128, Mar. 1996.
Previous proportional-share scheduling algorithms, however, suffer one
or more of the following problems:
(1) Inaccurate fairness with non-constant error bounds;
(2) High run-time overhead (e.g., logarithmic);
(3) Poor scalability due to the use of a global thread queue;
(4) Inefficient support for latency-sensitive applications.
Since the Linux scheduler has been successful at avoiding problems 2 to
4, this design attempts to extend it with support for accurate
proportional fairness while retaining all of its existing benefits.
If we allow a little short-term fairness (and I think we should) we can still
account for this unfairness and compensate for it (again, with the same
tolerance) at the next rebalancing.
User Interface:
By default, each thread is assigned a weight proportional to its static
priority. A set of system calls also allow users to specify a weight or
reservation for any thread. Weights are relative. For example, for two
threads with weights 3 and 1, the scheduler ensures that the ratio of
their CPU time is 3:1. Reservations are absolute and in the form of X%
of the total CPU time. For example, a reservation of 80% for a thread
means that the thread always receives at least 80% of the total CPU time
regardless of other threads.
The system calls also support specifying weights or reservations for
groups of threads. For example, one can specify an 80% reservation for a
group of threads (e.g., a process) to control the total CPU share to
which the member threads are collectively entitled. Within the group,
the user can further specify local weights to different threads to
control their relative shares.
Adding system calls, while great for research, is not something which is done
lightly in the published kernel. If we're going to implement a user interface
beyond simply interpreting existing priorities more precisely, it would be nice
if this was part of a framework with a broader vision, such as a scheduler economy.
Scheduling Algorithm:
The scheduler keeps a set data structures, called Trio groups, to
maintain the weight or reservation of each thread group (including one
or more threads) and the local weight of each member thread. When
scheduling a thread, it consults these data structures and computes (in
constant time) a system-wide weight for the thread that represents an
equivalent CPU share. Consequently, the scheduling algorithm, DWRR,
operates solely based on the system-wide weight (or weight for short,
hereafter) of each thread. Having a flat space of system-wide weights
for individual threads avoids performing seperate scheduling at each
level of the group hierarchy and thus greatly simplies the
implementation for group scheduling.
Implementing a flat weight space efficiently is nontrivial. I'm curious to see
how you reworked the original patch without global locking.
For each processor, besides the existing active and expired arrays, DWRR
keeps one more array, called round-expired. It also keeps a round number
for each processor, initially all zero. A thread is said to be in round
R if it is in the active or expired array of a round-R processor. For
each thread, DWRR associates it with a round slice, equal to its weight
multiplied by a system constant, called base round slice, which controls
the total time that the thread can run in any round. When a thread
exhausts its time slice, as in the existing scheduler, DWRR moves it to
the expired array. However, when it exhausts its round slice, DWRR moves
it to the round-expired array, indicating that the thread has finished
round R. In this way, all threads in the active and expired array on a
round-R processor are running in round R, while the threads in the
round-expired array have finished round R and are awaiting to start
round R+1. Threads in the active and expired arrays are scheduled the
same way as the existing scheduler.
I had a feeling this patch was originally designed for the O(1) scheduler, and
this is why. The old scheduler had expired arrays, so adding a round-expired
array wasn't a radical departure from the design. CFS does not have an expired
rbtree, so adding one *is* a radical departure from the design. I think we can
implement DWRR or something very similar without using this implementation
method. Since we've already got a tree of queued tasks, it might be easiest to
basically break off one subtree (usually just one task, but not necessarily) and
migrate it to a less loaded tree whenever we can reduce the difference between
the load on the two trees by at least half. This would prevent both
overcorrection and undercorrection.
When a processor's active array is empty, as usual, the active and
expired arrays are switched. When both active and expired are empty,
DWRR eventually wants to switch the active and round-expired arrays,
thus advancing the current processor to the next round. However, to
guarantee fairness, it needs to maintain the invariant that the
differences of all processors' rounds are bounded by a constant, where
the smaller this constant is, the stronger fairness it can guarantee
(the following assumes the constant is 1). With this invariant, it can
be shown that, during any time interval, the number of rounds that any
two threads go through differs by the constant, which is key to ensuring
DWRR's constant error bound compared to the ideal algorithm.
To enforce the above invariant, DWRR keeps track of the highest round
(referred to as highest) among all processors at any time and ensures
that no processor in round highest can advance to round highest+1 (thus
updating highest), if there exists at least one thread in the system
that is still in round highest. There are at least two approaches to
maintain a global highest round variable. One is to associate it with a
global lock to ensure consistency of its value. However, this may be not
be scalable. Thus, a second approach is to use no locking, but it could
lead to inconsistencies in the value. However, such inconsistencies
don't affect correctness of the kernel and the only impact is that the
fairness error of the scheduler can be twice as big as the locking
approach, but the error is still bounded by a constant and thus
sufficient in most cases. The following describes the operations of
DWRR, assuming the locking approach, while the non-locking approach
requires only simple changes.
The idea of rounds was another implementation detail that bothered me. In the
old scheduler, quantizing CPU time was a necessary evil. Now that we can
account for CPU time with nanosecond resolution, doing things on an as-needed
basis seems more appropriate, and should reduce the need for global synchronization.
On any processor p, whenever both the active and expired arrays become
empty, DWRR compares the round of p with highest. If equal, it performs
idle load balancing in two steps: (1) It Identifies runnable threads
that are in round highest but not currently running. Such threads can be
in the active or expired array of a round highest processor, or in the
round-expired array of a round highest - 1 processor. (2) Among those
threads from step 1, move X of them to the active array of p, where X is
a design choice and does not impact the fairness properties of DWRR. If
step 1 returns no suitable threads, DWRR proceeds as if the round of
processor p is less than highest, in which case DWRR switches p's active
and round-expired arrays, and increments p's round by one, thus allowing
all threads in its round-expired array to advance to the next round.
Whenever the system creates a new thread or awakens an existing one,
DWRR inserts the thread into the active array of an idle processor and
sets the processor's round to the current value of highest. If no idle
processor exists, it starts the thread on the least loaded processor
among those in round highest.
Whenever a processor goes idle (i.e., all of its three arrays are
empty), DWRR resets its round to zero. Similar to the existing
scheduler, DWRR also performs periodic load balancing but only among
processors in round highest. Unlike idle load balancing, periodic load
balancing only improves performance and is not necessary for fairness.
In summary, I think the accounting is sound, but the enforcement is sub-optimal
for the new scheduler. A revision of the algorithm more cognizant of the
capabilities and design of the current scheduler would seem to be in order.
I've referenced many times my desire to account for CPU/memory hierarchy in
these patches. At present, I'm not sure we have sufficient infrastructure in
the kernel to automatically optimize for system topology, but I think whatever
design we pursue should have some concept of this hierarchy, even if we end up
using a depth-1 tree in the short term while we figure out how to optimize this.
-- Chris
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