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\markright{\footnotesize CS 481 Operating Systems Principles, Fall 2000}

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\section*{Homework 7 --- due on Tuesday 5 December 2000}

Total number of points available on this homework is 150. Full credit
is equivalent to 100 points.

\begin{enumerate}


\item (15 pts) Suppose a physical page frame is shared by multiple
processes. 
If the OS uses global page replacement with the clock algorithm,
how does page 
sharing affect the page replacement algorithm?
If the OS uses per-process page replacement with the clock
algorithm, how does page 
sharing affect the page replacement algorithm?


\item (10 pts) Assume a page reference string
for a process with $m$ frames, initially empty.  The page reference
string has length $p$ with $n$ distinct page numbers occurring in it.
\begin{enumerate}
\item What is a lower bound on the number of page faults?
\item What is an upper bound on the number of page faults?
\end{enumerate}


\item (15 pts)  You are designing an operating system for a database
server.  The entire system is to be devoted to serving database
queries on one large database.  Users of the database may also add and
delete entries in the database.  How would you design your file index
structure to support fast random access for this application?  How
expensive are additions and deletions in your scheme?
 

\item (15 pts)   Consider a file system on a
disk that has both logical and physical block sizes of 512 bytes.
Assume that the information about each file is already in memory.  For
each of the three allocation strategies (contiguous, linked, and
indexed), answer these questions:
\begin{enumerate}
\item How is the logical-to-physical address mapping accomplished in
this system?  (For indexed allocation, assume that no file 
needs more than one index block.)  
\item If we are currently at logical block 10 (the last block accessed
was block 10) and want to access logical block 4, how many physical
blocks must be read from the disk?
\end{enumerate}


\item (10 pts) When the average queue length is small, do all
disk-scheduling algorithms reduce to FCFS?  Why or Why not?  Does
locality of reference exaggerate differences in scheduling algorithms?
Why or why not?


\item (20 pts) Disk requests are not usually uniformly distributed.
For example, users access the file directory
structures more frequently than other files.  Assume that accesses
to the file directory structures account for 50\% of all accesses.  
(1)
For each of the following algorithms, how would it perform,
assuming that the
file directory structures are co-located at a random spot on the disk
and why?  
(2) 
Which algorithm takes best advantage of this locality?  
(3)
For each algorithm, also specify where you would locate the file
directory structure to improve the algorithm's performance, if some
such placement exists.  

\begin{enumerate}
\item FCFS
\item SSTF
\item SCAN 
\item C-SCAN 
\end{enumerate}

Assume that SCAN and C-SCAN use their LOOK
variations (i.e., they only continue to seek in a direction if there
is a request in that direction).


\item (15 pts) Do problem 11.2 in Stallings. (Then look at the next question 
in this homework 
to see why 11.2 in Stallings is too simplistic.)


\item (Extra credit, 50 pts, due on Friday 8 December, should be handed in
separately) 
Suppose that a disk is dedicated for use as backing store
in a virtual memory system. Suppose further that the sequence of disk 
accesses is determined by the page faults experienced by your favorite
program under your favorite page replacement algorithm of Project 2
(other than OPT).

Let $a$ be the lowest page number in the virtual address space of the
program, and $b$ the highest, such that $N=b-a+1$ is the number of
pages in the program's address space. 
Suppose that the entire disk is used to store pages of the program.
The disk has $M=10000$ cylinders, numbered 1 through $M$.
Suppose that pages are laid out almost linearly on disk, such that
page number $n$ is on cylinder     
$ \textsf{round} (\frac{M}{N} (n-a+1) )$,
where $\textsf{round}$ rounds to the nearest integer in the range 1 through $M$.
(This assumes that there
are no big gaps in your program's address space. If you discover that
there are gaps, consider not mapping them to disk.)



Suppose that seek time, the time for disk arm movement, is independent of the 
absolute position of the disk arm, and only dependent on the relative
distance travelled, given by the difference in cylinder coordinates $d$,
as follows: $f(d)= C + L \sqrt{d/M}$, 
where $C=3\textrm{ms}$ and $L=17\textrm{ms}$, 
except that $f(0)=0$.

\epsfig{file=graph.eps,width=4in}

Ignore rotational delay, transfer delay, and any other delays but seek delay.

Assume that page faults occur exactly every 3ms. (Note: pretend that
the sequence of page faults is actually an aggregate stream from a
multitude of programs. Otherwise it would be difficult to explain
how a program can generate new faults while it is waiting for a
fault to be serviced.)

Assume there is no difference between disk reads and writes.

What is the total seek time for processing the entire stream of
requests, if the set of pending disk requests is managed by the
following algorithms:
\begin{enumerate}
\item FCFS
\item SSTF
\item SCAN 
\item C-SCAN 
\end{enumerate}

Plot the distributions of seek distances and seek times in each case.
Calculate the average seek distance and average seek time.



\end{enumerate}

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