It’s often said one should not meet one’s heroes as, all too often, they turn out to be, well, just a bit too human. To be sure, in politics I have often been up close to people who were seen as etherial beings by many but were indeed a bit ordinary close up (though you also can see in some people an inexpressible quality of brilliance – Tony Blair and Ken Clarke both had this).
Well, I have never met Peter J. Denning, the discoverer of the “working set method”, and the man whose work formed the intellectual backdrop to my MSc project last year. But I have now exchanged a few emails with him and I do want to say that they have all increased my admiration for him as one of the great foundational figures of modern computing.
He sought me out after he came across my MSc. I have to say my first section was that he was likely to tear a strip off me (actually my very first reaction was to think he was a recruitment consultant wasting his time – it simply never occurred to me that the Peter Denning emailing me would be that Peter Denning) – as I had described his formulation of the space-time product for memory management as flawed. In fact he just pointed out that I was criticising an approximation which he accepted did not fully represent the space-time needed to manage a working set method of page replacement but also pointed out he had accounted for this in other papers (and he had).
He and I then exchanged a few emails about memory management issues and about my current research interests.
A great man. A giant of computing. And nice to boot. Who would have thought it?
My MSc project was titled “Applying Working Set Heuristics to the Linux Kernel” and my aim was to test some local page replacement policies in Linux, which uses a global page replacement algorithm, based on the “2Q” principle.
There is a precedent for this: the so-called “swap token” is a local page replacement policy that has been used in the Linux kernel for some years.
My aim was to see if a local replacement policy graft could help tackle “thrashing” (when a computer spends so much time trying to manage memory resources – generally swapping pages back and forth to disk – it makes little or no progress with the task itself).
The full report (uncorrected – the typos have made me shudder all the same) is linked at the end, what follows is a relatively brief and simplified summary.
Fundamentally I tried two approaches: acting on large processes when the number of free pages fell to one of the watermark levels used in the kernel and acting on the process last run or most likely to run next.
For the first my thinking – backed by some empirical evidence – was that the largest process tended to consume much more memory than even the second largest. For the second the thought was that make the process next to run more memory efficient would make the system as a whole run faster and that, in any case the process next to run was also quite likely (and again some empirical evidence supported this) to be the biggest consumer of memory in the system.
To begin I reviewed the theory that underlies the claims for the superiority of the working set approach to memory management – particularly that it can run optimally with lower resource use than an LRU (least recently used) policy.
Peter Denning, the discoverer of the “working set” method and its chief promoter, argued that programs in execution do not smoothly and slowly change their fields of locality, but transition from region to region rapidly and frequently.
The evidence I collected – using the Valgrind program and some software I wrote to interpret its output, showed that Denning’s arguments appear valid for today’s programs.
Here, for instance is the memory access pattern of Mozilla Firefox:
Working set size can therefore vary rapidly, as this graph shows:
Denning’s argument is that the local policy suggested by the working set method allows for this rapid change of locality – as the memory space allocated to a given program is free to go up and down (subject to the overall constraint on resources, of course).
He also argued that the working set method will – at least in theory – deliver a better space time product (a measure of overall memory use) than a local LRU policy. Again my results confirmed his earlier findings in that they showed that, for a given average size of a set of pages in memory, the working set method will ensure longer times between page faults, compared to a local LRU policy – as shown in this graph:
Here the red line marks the theoretical performance of a working set replacement policy and the blue line that of a local LRU policy. The y-axis marks the average number of instructions executed between page faults, the x-axis the average resident set size. The working set method clearly outperforms the LRU policy at low resident set values.
The ‘knee’ in either plot where is maximised is also the point of lowest space time product – at this occurs at a much lower value for the working set method than for local LRU.
So, if Denning’s claims for the working set method are valid, why is it that no mainstream operating system uses it? VMS and Windows NT (which share a common heritage) use a local page replacement policy, but both are closer to the page-fault-frequency replacement algorithm – which varies fixed allocations based on fault counts – than a true working set-based replacement policy.
The working set method is just too difficult to implement – pages need to be marked for the time they are used and to really secure the space-time product benefit claimed, they also need to be evicted from memory at a specified time. Doing any of that would require specialised hardware or complex software or both, so approximations must be used.
For my experiments I concentrated on manipulating the “CLOCK” element of the page replacement algorithm: this removes or downgrades pages if they have not been accessed in the time been alternate sweeps of an imaginary second hand of an equally imaginary clock. “Clock pressure” could be increased – ie., pages made more vulnerable to eviction – by systematically marking them as unaccessed, while pages could be preserved in memory by marking them all as having been accessed.
The test environment was compiling the Linux kernel – and I showed that the time taken for this was highly dependent on the memory available in a system:
The red line suggests that, for all but the lowest memory, the compile time is proportional to where is the system memory. I don’t claim this a fundamental relationship, merely what was observed in this particular set up (I have a gut feeling it is related to the number of active threads – this kernel was built using the -j3 switch and at the low memory end the swapper was probably more active than the build, but again I have not explored this).
The first set of patches I tried were based on waiting for free memory in the system to sink to one of the “watermarks” the kernel uses to trigger page replacement. My patches looked for the largest process then either looked to increase clock pressure – ie., make the pages from this large process more likely to be removed – or to decrease it, ie., to make it more likely these pages would be preserved in memory.
In fact the result in either case was similar – at higher memory values there seemed to be a small but noticeable decline in performance but at low memory values performance declined sharply – possibly because moving pages from one of the “queues” of cached pages involves locking (though, as later results showed also likely because the process simply is not optimal in its interaction with the existing mechanisms to keep or evict pages).
The graph below shows a typical result of an attempt to increase clock pressure – patched times are marked with a blue cross.
The CFS orders processes in a red-black tree (a semi-balanced tree) and the rightmost node is the process least likely to run next and the leftmost the process most likely to run next (as it has run for the shortest amount of virtual time).
As before the idea was to either free memory (increase clock pressure) or hold needed pages in memory (decrease clock pressure). The flowchart below illustrates the mechanism used for the leftmost process (and decreasing clock pressure):
But again the results were generally similar – a general decline, and a sharp decline at low memory values.
(In fact, locking in memory of the leftmost process actually had little effect – as shown below:)
But when the same approach was taken to the rightmost process – ie the process that has run for the longest time (and presumably may also run for a long time in the future), the result was a catastrophic decline in performance at small memory values:
And what is behind the slowdown? Using profiling tools the biggest reason seems to be that the wrong pages are being pushed out of the caches and need to be fetched back in. At 40MB of free memory both patched and unpatched kernels show similar profiles with most time spent scheduling and waiting for I/O requests – but the slowness of the patched kernel shows that this has to be done many more times there.
There is much more in the report itself – including an examination of Denning’s formulation of the space-time product - I conclude his is flawed (update: in fairness to Peter Denning, who has pointed this out to me, this is as regards his approximation of the space-time product: Denning’s modelling in the 70s also accounted for the additional time that was required to manage the working set) as it disregards the time required to handle page replacement – and the above is all a (necessary) simplification of what is in the report – so if you are interested please read that.
- Best book on Linux kernel internals (cartesianproduct.wordpress.com)
- Is the time pages are in the working set stochastic? (cartesianproduct.wordpress.com)
- Counting soft and hard faults (cartesianproduct.wordpress.com)
- Building The Linux Kernel In 60 Seconds (phoronix.com)
- Update Your Linux Kernel Without Reboot (hackstips.wordpress.com)
The graphs look similar but the differences are important – this one (the correct one), appears to confirm that Peter Denning‘s findings about the working set model versus LRU still hold good, at least in broad terms – though this still suggests LRU has better performance characteristics than might be expected.
But it’s late now and I am going to bed – perhaps more later.
- The graph is wrong (cartesianproduct.wordpress.com)
I have a serious problem with my MSc project.
The graphs on other blogs here are some of the output of the test cases I have been using and they seem to work well.
In addition, though, I want to show what Peter Denning refers to as a “lifetime curve” for a process – essentially showing how increasing the size of the resident set (or in my case increasing the time for which pages remain resident) changes the time between page faults.
This should not (and early results of mine show) it isn’t linear (though it is monotonic). But to calculate this seems, under the algorithm I am using, to require vast amounts of computing power.
My algorithm (in Groovy) is essentially this:
1. Set time (if we are plotting 600 points then first time would be 1/600th of the process lifetime) for page expiry
2. Reading the lackeyml file and using a groovy/java map, store the page number and the reference time -if the page wasn’t referred to in the map, increase the fault count
3. Look through the map to see if there are any pages which are older than the page expiry times, and evict them from the map
4. Move to the next record in the lackeyml file and return to 2
5. Get to the end of the file and count the total faults.
The problem with all this is (2) above – typically it is being called millions of times and iterating through a map in this way is extremely slow. I think on a dual AMD64 box here with the 48 million instruction count for xterm (pretty much a ‘toy’ application in this context) – this will take 20 days to run, even with a decent bit of parallelization in the code.
Hence I need a better algorithm or massive (and affordable) computing power. Anyone have a cluster they could lend me for a few hours?
- Introducing the lackeyml format (cartesianproduct.wordpress.com)
- Eighteen million lines of XML! (cartesianproduct.wordpress.com)
- Patterns of locality in xterm (cartesianproduct.wordpress.com)
- Bob Morris and stream algorithms (geomblog.blogspot.com)
- When is an algorithm not an algorithm? (jrvarma.wordpress.com)
- Simple algorithms, illustrated (sathyasays.com)
- Optimizing the A* algorithm (takinginitiative.net)