Operating Systems

Start Lecture #8

Remark: midterm grades are based on lab1.

3.4.6 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. the one that has been least recently used.

LRU is definitely

1. Implementable: The past is knowable.
2. Good: Simulation studies have shown this.
3. Difficult. Essentially the system needs to either:
   • Keep a time stamp in each PTE, updated on each reference and scan all the PTEs when choosing a victim to find the PTE with the oldest timestamp.
   • Keep the PTEs in a linked list in usage order, which means on each reference moving the corresponding PTE to the end of the list.

Homework: 28, 22.

A hardware cutsie in Tanenbaum

A cleaver hardware method to determine the LRU page.

• For n pages, keep an nxn bit matrix.
• On a reference to page i, set row i to all 1s and column i to all 0s.
• At any time the 1 bits in the rows are ordered by inclusion. I.e. one row's 1s are a subset of another row's 1s, which is a subset of a third. (Tanenbaum forgets to mention this.)
• So the row with the fewest 1s is a subset of all the others and is hence least recently used.
• This row also has the smallest value, when treated as an unsigned binary number. So the hardware can do a comparison of the rows rather than counting the number of 1 bits.
• Cute, but still impractical.

3.4.7 Simulating (Approximating) LRU in Software

The Not Frequently Used (NFU) PRA

Keep a count of how frequently each page is used and evict the one that has been the lowest score. Specifically:

• Include a counter (and reference bit R) in each PTE.
• Set the counter to zero when the page is brought into memory.
• Every k clocks, perform the following for each PTE.
  1. Add R to the counter.
  2. Clear R.
• Choose as victim the PTE with lowest count.

The Aging PRA

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

• Include a counter (and reference bit, R) in each PTE.
• Set the counter to zero when the page is brought into memory.
• Every k clock ticks, perform the following for each PTE.
  1. Shift the counter right one bit.
  2. Insert R as the new high order bit of the counter.
  3. Clear R.
• Choose as victim the PTE with lowest count.

Aging does indeed give more weight to later references, but an n bit counter maintains data for only n time intervals; whereas NFU maintains data for at least 2ⁿ intervals.

Homework: 24, 33.

3.4.8 The Working Set Page Replacement Algorithm (Peter Denning)

The working set policy

The goals are first to specify which pages a given process needs to have memory resident in order for the process to run without too many page faults and second to ensure that these pages are indeed resident.

But this is impossible since it requires predicting the future. So we again make the assumption that the near future is well approximated by the immediate past.

We measure time in units of memory references, so t=1045 means the time when the 1045th memory reference is issued. In fact we measure time separately for each process, so t=1045 really means the time when this process made its 1045th memory reference.

Definition: w(k,t), the working set at time t (with window k) is the set of pages referenced by the last k memory references ending at reference t.

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

• Allocate |w(t,k)| frames to each process. This number differs for each process and changes with time.
• On a fault, evict a page not in the working set. But it is not easy to find such a page quickly.
• Indeed determining w(t,k) precisely is quite time consuming and difficult. It is never done in real systems.
• If a process is suspended, it is often swapped out; the working set then can be used to say which pages should be brought back when the process is resumed.

Homework: Describe a process (i.e., a program) that runs for a long time (say hours) and always has a working set size less than 10. Assume k=100,000 and 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 a working set size greater than 1000. Assume k=100,000 and 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,k) 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:

1. What value should be used for k?
   Experiments have been done and k is surprisingly robust (i.e., for a given system, a fixed value works reasonably for a wide variety of job mixes).
2. How should we calculate w(t,k)?
   Hard to do exactly so ...

... 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 (part of section 3.5.1). In 3.4.9 we will see the popular WSClock algorithm that includes an approximation of the working set as well as several other ideas.

Using Virtual Time

Instead of counting memory referenced and declaring a page in the working set if it was used within k references, we keep track of time, which the system does anyway, and declare a page in the working set if it was used in the past τ seconds. Note that the time is measured only while this process is running, i.e., we are using virtual time.

• Add a field time of last use to the PTE.
• Clear the reference R bit every m milliseconds and set it on every reference, the latter is presumably done by the hardware.
• To choose a victim when a page fault occurs, we proceed as follows (also setting the time of last use field). Scan the page table one PTE at a time (actually we are only interested in resident pages so we would rather look at the page frame table).
  • If the R bit is 1, the page is in the working set so set the time of last use to the current (virtual) time. (We are assuming τ seconds is bigger than m milliseconds.)
  • If the R bit is 0 and the last use was more than τ seconds ago, the page is not in the working set and is evicted (but we keep scanning).
  • If the R bit is 0 but the last use is less than τ seconds ago, the page is in the working set so is not evicted.
  • If no page was chosen for eviction, evict the LRU page.

Remark: Lab 4 (the last lab) is assigned).

3.4.9 The WSClock Page Replacement Algorithm

The WSClock algorithm combines aspects of the working set algorithm and the clock implementation of second chance.

Like clock we create a circular list of nodes with a hand pointing to the next node to examine. There is one such node for every resident page of this process; thus the nodes can be thought of as a list of frames or a kind of inverted page table.

Like working set we store in each node the referenced and modified bits R and M and the time of last use. R and M are initialized to zero when the page is read in. R is set by the hardware on a reference and cleared periodically by the OS (perhaps at the end of each page fault or perhaps every k clock ticks). M is set by the hardware on a write. We indicate below the setting of the time of last use and the clearing of M.

We use virtual time and declare a page old if its last reference is more than τ seconds in the past. Other pages are declared young (i.e., in the working set).

As with clock, on every page fault a victim is found by scanning the list starting with the node indicated by the clock hand.

• If R=1, the page has been recently referenced. R is set to 0, the time of last use is set, and the hand advances.
• If R=0 and M=1, clear M, (schedule an I/O to) write the dirty page and advance the hand.
• If R=M=0 and the page is young, advance the hand.
• If R=M=0 and the page is old, this is our victim; done.

It is possible to go all around the clock without finding a victim. In that case

• If a write was scheduled on old pages, one of these will become the victim once it becomes clean.
• If no writes were scheduled, we will never find a victim (since nothing will change) so pick a page at random (or perhaps the oldest of the young pages).
• If the only young pages are scheduled for writing, no old victim will be chosen so we will need to again pick a page at random (if every page is dirty, we must wait for one to become clean).

An alternative treatment of WSClock, including more details of is interaction with the I/O subsystem, can be found here.

3.4.10 Summary of Page Replacement Algorithms

3.4.A Belady's Anomaly

Consider a system that has no pages loaded and that uses the FIFO PRU.
Consider the following reference string (sequences of pages referenced).

    0 1 2 3 0 1 4 0 1 2 3 4
  

If we have 3 frames this generates 9 page faults (do it).

If we have 4 frames this generates 10 page faults (do it).

Theory has been developed and certain PRA (so called stack algorithms) cannot suffer this anomaly for any reference string. FIFO is clearly not a stack algorithm. LRU is.

Repeat the above calculations for LRU.

3.5 Design Issues for (Demand) Paging Systems

3.5.1 Local vs Global Allocation Policies

A local PRA is one is which a victim page is chosen among the pages of the same process that requires a new frame. That is the number of frames for each process is fixed. So LRU for a local policy means the page least recently used by this process. A global policy is one in which the choice of victim is made among all pages of all processes.

• Of course we can't have a purely local policy, why?
  Answer: A new process has no pages and even if we didn't apply this for the first page loaded, the process would remain with only one page.
• Perhaps wait until a process has been running a while or give the process an initial allocation based on the size of the executable.

In general a global policy seems to work better. For example, consider LRU. With a local policy, the local LRU page might have been more recently used than many resident pages of other processes. A global policy needs to be coupled with a good method to decide how many frames to give to each process. By the working set principle, each process should be given |w(k,t)| frames at time t, but this value is hard to calculate exactly.

If a process is given too few frames (i.e., well below |w(k,t)|), its faulting rate will rise dramatically. If this occurs for many or all the processes, the resulting situation in which the system is doing very little useful work due to the high I/O requirements for all the page faults is called thrashing.

An approximation to the working set policy that is useful for determining how many frames a process needs (but not which pages) is the Page Fault Frequency (PFF) algorithm.

• For each process keep track of the page fault frequency, which is the number of faults divided by the number of references.
• Actually, must use a window or a weighted calculation since you are really interested in the recent page fault frequency.
• Actually, it is too expensive to calculate the number of references so, as above, we approximate this by the amount of (virtual) time.
• If the PFF is exceptionally low, free some of this processes frames (e.g., limit victim selection to this process for a while).
• If the PFF is too high, allocate more frames to this process. Either
  1. Raise its number of frames if using a local policy; or
  2. Bar its frames from eviction (for a while) and use a global policy.
• What if there are not enough frames?
  Answer: Reduce the MPL as we now discuss.

3.5.2 Load Control

To reduce the overall memory pressure, we must reduce the multiprogramming level (or install more memory while the system is running, which is not possible with current technology). That is, we have a connection between memory management and process management. These are the suspend/resume arcs we saw way back when and repeated in the diagram on the right.

When the PFF (or another indicator) is too high, we choose a process and suspend it, thereby swapping it to disk and releasing all its frames. When the frequency gets low, we can resume one or more suspended processes. We also need a policy to decide when a suspended process should be resumed even at the cost of suspending another.

This is called medium-term scheduling. Since suspending or resuming a process can take seconds, we clearly do not perform this scheduling decision every few milliseconds as we do for short-term scheduling. A time scale of minutes would be more appropriate.

3.5.3 Page size

Page size must be a multiple of the disk block size. Why?
Answer: When copying out a page if you have a partial disk block, you must do a read/modify/write (i.e., 2 I/Os).

Characteristics of a large page size.

• Good for demand paging I/O.
  • It is better to swap in/out one big page than several small pages. We will learn later this term that the total time for performing 8 I/O operations each of size 1KB is much larger that the time for a single 8KB I/O.
  • But if page is too big you will be swapping in data that is really not local and hence might well not be used.
• Large internal fragmentation (1/2 page size).
• Small page table (process size / page size * size of PTE).
• These last two can be analyzed by setting the derivative of the sum = 0. The minimum overhead occurs at a page size of
  sqrt(2 * process size * size of PTE)
  Since the term inside the sqrt is typically megabytes, we see that modern practice of having the page size a few kilobytes is near the minimum point.
• A very large page size leads to very few pages. A process will have many faults if using demand paging and if the process frequently references more regions than the number of (large) frames that the process has been allocated.

A small page size has the opposite characteristics.

Homework: Consider a 32-bit address machine using paging with 8KB pages and 4 byte PTEs. How many bits are used for the offset and what is the size of the largest page table? Repeat the question for 128KB pages.

3.5.4 Separate Instruction and Data (I and D) Spaces

This was used when machine have very small virtual address spaces. Specifically the PDP-11, with 16-bit addresses, could address only 2₁₆ bytes or 64KB, a severe limitation. With separate I and D spaces there could be 64KB of instructions and 64KB of data.

Separate I and D are no longer needed with modern architectures having large address spaces.

3.5.5 Shared pages

Permit several processes to each have a page loaded in the same frame. Of course this can only be done if the processes are using the same program and/or data.

• Really should share segments.
• Must keep reference counts or something so that when a process terminates, pages (even dirty pages) it shares with another process are not automatically discarded.
• Similarly, a reference count would make a widely shared page (correctly) look like a poor choice for a victim.
• A good place to store the reference count would be in a structure pointed to by both PTEs. If stored in the PTEs themselves, we must keep somehow keep the count consistent between processes.
• If you want the pages to be initially shared for reading but want each process's updates to be private, then use so called copy on write techniques.

Homework: Can a page shared between two processes be read-only for one process and read-write for the other?

3.5.6 Shared Libraries (Dynamic-Linking)

In addition to sharing individual pages, process can share entire library routines. The technique used is called dynamic linking and the objects produced are calledshared libraries or dynamically-linked libraries (DLLs). (The traditional linking you did in lab1 is today often called static linking).

• With dynamic linking, frequently used routines are not linked into the program. Instead, just a stub is linked.
• When the routine is called (or when the process begins), the stub checks to see if the real routine has been loaded by another program).
  • If it has not been loaded, load it (really page it in as needed).
  • If it is already loaded, share it. Only the text is loaded, data is not shared.
• Advantages of dynamic linking.
  • Saves RAM: Only one copy of a routing is in memory once even when it is used concurrently by many processes. For example even a big server with hundreds of active processes will have only one copy of printf in memory. (In fact with demand paging only part of the routine will be in memory.)
  • Saves disk space: Files containing executable programs no longer contain copies of the shared libraries.
  • A bug fix to a dynamically linked library fixes all applications that use that library, without having to relink these applications.
• Disadvantages of dynamic linking.
  • New bugs in dynamically linked library infect all applications.
  • Applications change even when they haven't changed.
• A Technical Difficulty with dynamic linking. The shared library has different virtual addresses in each process so addresses relative to the beginning of the module cannot be used (they would need to be relocated to different addresses in the multiple copies of the module). Instead position-independent code must be used. For example, jumps within the module would use PC-relative addresses.

3.5.7 Mapped Files

The idea of memory-mapped files is to use the mechanisms in place for demand paging (and segmentation, if present) to implement I/O.

A system call is used to map a file into a portion of the address space. (No page can be part of a file and part of regular memory; the mapped file would be a complete segment if segmentation is present).

The implementation of demand paging we have presented assumes that the entire process is stored on disk. This portion of secondary storage is called the backing store for the pages. Sometimes it is called a paging disk. For memory-mapped files, the file itself is the backing store.

Once the file is mapped into memory, reads and writes become loads and stores.