Assignment 1 - CS120a
Due Tuesday, February 7, 10:40 AM
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1. 

 a) Compute r |x s (r semi-join s) for the relations shown below:

    +---+---+---+                 +---+---+---+
    | A | B | C |                 | C | D | E |
    +---+---+---+                 +---+---+---+
    | 1 | 2 | 3 |                 | 3 | 4 | 5 |
    | 4 | 5 | 6 |                 | 3 | 6 | 8 |
    | 1 | 2 | 4 |                 | 2 | 3 | 2 |
    | 5 | 3 | 2 |                 | 1 | 4 | 1 |
    | 8 | 9 | 7 |                 | 1 | 2 | 3 |
    +---+---+---+                 +---+---+---+
          r                             s
 
 b)  For any relations t and u, under what conditions
     does (t |x u) = (u |x t)?


2.  Suppose a 10 Mbps (megabits per second) network
    transmits 1024 byte packets that include 
    132 bytes of headers and trailer.  If a workstation
    on the LAN is guaranteed to be able to transmit
    at least one packet every X time units (since
    the network is shared with other workstations), what
    maximum amount of time, as a function of X, should
    be required (based only on these factors) to transfer
    a 3 MB file from a server to a workstation?  What is
    the effective transfer rate from the server to the workstation?


3.  A disk is being utilized 30% of the time, and the average
    time to service a disk request is 20 msec.  If on average,
    60 disk requests are being serviced or in the queue at any one
    time, what is the average response time per disk request?


4.  Consider a RAID-7 disk that distributes data across 6 disks (i.e., 
    a stripe group consists of 6 stripe units), leaving one disk for storing the
    parity.  For n = 1, 2, 3, 4, 5 and 6, compute the minimum number of stripe units (rw (n))
    that must be read as a result of a request to write n stripe units, so
    as to update parity.  Explain each of your answers.

  
5.  To allow for greater enrollment without adding building space,
    the Brandeis Computer Science department adds an internship
    component to its undergraduate degree.  Under this program, 
    students work in industry for one semester for every two
    semesters that they take courses.  Suppose that on average, 
    100 students do an internship every semester, and that on average, students
    complete their degree (including internships) in 6 years.
  
     a)  On average, how many students graduate the program 
         every semester?

     b)  On average, how many students are enrolled in Computer
         Science at the start of a semester?  (You may assume that the average
         number of new enrollments each semester is equal to the
         number of graduating students each semester.)