Operating Systems

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Our final is currently scheduled for 5-7PM on tues 11 May. This would prove difficult for students who wish to attend the GSAS convocation on that same afternoon.

I have received permissions to give the exam instead on 4 May (same room, again 5pm). Either date is OK with me (but not both).

Is there anyone who can *NOT* make 4 May (it is "reading day" with no classes or exams)?

Is there anyone who will have a conflict with GSAS convocation if we have the exam as scheduled on 11 May.

End of important conflict

4.4: Page Replacement Algorithms (PRAs)

These are solutions to the replacement question.

Good solutions take advantage of locality.

Pages belonging to processes that have terminated are of course perfect choices for victims.

Pages belonging to processes that have been blocked for a long time are good choices as well.

Random PRA

A lower bound on performance. Any decent scheme should do better.

4.4.1: The optimal page replacement algorithm (opt PRA) (aka Belady's min PRA)

Replace the page whose next reference will be furthest in the future.

4.4.2: The not recently used (NRU) PRA

Divide the frames into four classes and make a random selection from the lowest nonempty class.

  1. Not referenced, not modified
  2. Not referenced, modified
  3. Referenced, not modified
  4. Referenced, modified

Assumes that in each PTE there are two extra flags R (sometimes called U, for used) and M (often called D, for dirty).

Also assumes that a page in a lower priority class is cheaper to evict.

We again have the prisoner problem, we do a good job of making little ones out of big ones, but not the reverse. Need more resets.

Every k clock ticks, reset all R bits

What if the hardware doesn't set these bits?

4.4.3: FIFO PRA

Simple but poor since usage of the page is ignored.

Belady's Anomaly: Can have more frames yet generate more faults. Example given later.

The natural implementation is to have a queue of nodes each pointing to a page.

4.4.4: Second chance PRA

Similar to the FIFO PRA, but altered so that a page recently referenced is given a second chance.

4.4.5: Clock PRA

Same algorithm as 2nd chance, but a better implementation for the nodes: Use a circular list with a single pointer serving as both head and tail.

Let us begin by assuming that the number of pages loaded is constant.

What if the number of pages is not constant?


This is terrible! Why?
Ans: All but the last frame are frozen once loaded so you can replace only one frame. This is especially bad after a phase shift in the program when it is using all new pages.

4.4.6: Least Recently Used (LRU) PRA

When a page fault occurs, choose as victim that page that has been unused for the longest time, i.e. that has been least recently used.

LRU is definitely

Homework: 29, 23

A hardware cutsie in Tanenbaum

4.4.7: Simulating (Approximating) LRU in Software

The Not Frequently Used (NFU) PRA

R counter

The Aging PRA

NFU doesn't distinguish between old references and recent ones. The following modification does distinguish.

Homework: 25, 34

4.4.8: The Working Set Page Replacement Problem (Peter Denning)

The working set policy (Peter Denning)

The goal is to specify which pages a given process needs to have memory resident in order for the process to run without too many page faults.

The idea of the working set policy is to ensure that each process keeps its working set in memory.

Homework: Describe a process (i.e., a program) that runs for a long time (say hours) and always has w<10[ Assume ω=100,000, the page size is 4KB. The program need not be practical or useful.

Homework: Describe a process that runs for a long time and (except for the very beginning of execution) always has w>1000. Assume ω=100,000, the page size is 4KB. The program need not be practical or useful.

The definition of Working Set is local to a process. That is, each process has a working set; there is no system wide working set other than the union of all the working sets of each process.

However, the working set of a single process has effects on the demand paging behavior and victim selection of other processes. If a process's working set is growing in size, i.e. w(t,ω) is increasing as t increases, then we need to obtain new frames from other processes. A process with a working set decreasing in size is a source of free frames. We will see below that this is an interesting amalgam of local and global replacement policies.

Interesting questions concerning the working set include:

... Various approximations to the working set, have been devised. We will study two: using virtual time instead of memory references (immediately below) and Page Fault Frequency (section 4.6). In 4.4.9 we will see the popular WSClock algorithm that includes an approximation of the working set as well as several other ideas.

Using virtual time

4.4.9: The WSClock Page Replacement Algorithm

This treatment is based on one by Prof. Ernie Davis.

Tannenbaum suggests that the WSClock Page Replacement Algorithm is a natural outgrowth of the idea of a working set. However, reality is less clear cut. WSClock is actually embodies several ideas one of which is connected to the idea of a working set. As the name suggests another of the ideas is the clock implementation of 2nd chance.

The actual implemented algorithm is somewhat complicated and not a clean elegant concept. It is important because

  1. It works well and is in common use.
  2. The embodied ideas are themselves interesting.
  3. Inelegant amalgamations of ideas are more commonly used in real systems than clean, elegant, one-idea algorithms.

Since the algorithm is complicated we present it in stages. As stated above this is an important algorithm since it works well and is used in practice. However, I certainly do not assume you remember all the details.

  1. We start by associating a node with every page loaded in memory (i.e., with every frame given to this process). In the node are stored R and M bits that we assume are set by the hardware. (Of course we don't design the hardware so really the R and M bits are set in a hardware defined table and the nodes reference the entries in that table.) Every k clock ticks the R bit is reset. So far this looks like NRU.

    To ease the explanation we will assume k=1, i.e., actions are done each clock tick.

  2. We now introduce an LRU aspect (with the virtual time approximation described above for working set): At each clock tick we examine all the nodes for the running process and store the current virtual time in all nodes for which R is 1.

    Thus, the time field is an approximation to the time of the most recent reference, accurate to the clock period. Note that this is done every clock tick (really every k ticks) and not every memory reference. That is why it is feasible.

    If we chose as victim the page with the smallest time field, we would be implementing a virtual time approximation to LRU. But in fact we do more

  3. We now introduce some working set aspects into the algorithm by first defining a time constant τ (analogous to ω in the working set algorithm) and consider all pages older than τ (i.e., their stored time is smaller than the current time minus τ) as candidate victims. The idea is that these pages are not in the working set.

    The OS designer needs to tune τ just as one would need to tune ω and, like ω, τ is quite robust (the same value works well for a variety of job mixes).

    The advantage of introducing τ is that a victim search can stop as soon as a page older than τ is found.

    If no pages have a reference time older than Tau, then the page with the earliest time is the victim.

  4. Next we introduce the other aspect of NRU, preferring clean to dirty victims. We search until we find a clean page older than τ, if there is one; if not, we use a dirty page older than τ.

  5. Now we introduce an optimization similar to prefetching (i.e., speculatively fetching some data before it is known to be needed). Specifically, when we encounter a dirty page older than τ (while looking for a clean old page), we write the dirty page back to disk (and clear the M bit, which Tanenbaum forgot to mention) without evicting the page, on the presumption that, since the page is not in (our approximation to) the working set, this I/O will be needed eventually. The down side is that the page could become dirty again, rendering our speculative I/O redundant.

    Suppose we've decided to write out old dirty pages D1 through Dd and to replace old clean page C with new page N.

    We must block the current process P until N is completely read in, but P can run while D1 through Dd are being written. Hence we would desire the I/O read to be done the writes, but we shall see later that there are other considerations for choosing the order to perform I/O operations.

    Similarly, suppose we can not find an old clean page and have decided to replace old dirty page D0 with new page N, and have detected additional old dirty pages D1 through Dd (recall that we were searching for an old clean page). Then P must block until D0 has been written and N has been read, but can run while D1 through Dd are being written.

  6. We throttle the previous optimization to prevent overloading the I/O subsystem. Specifically we set a limit on the number of dirty pages the previous optimization can request be written.

  7. Finally, as in the clock algorithm, we keep the data structure (nodes associated with pages) organized as a circular list with a single pointer (the hand of the clock). Hence we start each victim search where the previous one left off.

    It is not so clear why this is important. As with the clock algorithm, using both front and rear pointers would cause extra work when skipping over nodes, but why not simply use a linear list with just a single pointer to the beginning and always starting there? Perhaps keeping a bit of FIFO is helpful (recall that the first old clean page is chosen, so where we start does effect the choice).

4.4.10: Summary of Page Replacement Algorithms

RandomPoor, used for comparison
OptimalUnimplementable, use for comparison
LIFOHorrible, useless
FIFONot good ignores frequency of use
Second ChanceImprovement over FIFO
ClockBetter implementation of Second Chance
LRUGreat but impractical
NFUCrude LRU approximation
AgingBetter LRU approximation
Working SetGood, but expensive
WSClockGood approximation to working set