Prepare for this assignment by reading
(1) You are waiting in a line at an
airline terminal. You count 80 people ahead of you in the line.
You observe that there are 5 ticket agents and that the average
transaction with a ticket agent takes 2 minutes. What is your
expected wait until you are finished with the ticket agent?
(2) By observing people standing in the security line in the
airport, you measure that out of every 101 people, 100 require 1
minute of service from the agent and 1 requires an astounding 1
hour, 40 minutes of service. You arrive at a random moment and
find there are 10 people ahead of you in line before the single
security gate. What is the probability that the long customer
is being served when you arrive? What is your expected time
until you clear security?
(3) A restaurant open every day of the year
has a wine cellar. The owner wants to age
all red wines 7 years before serving them, to assure maximum
flavor. The restaurant sells 1 case of red wine every night.
How many cases of red wine must the cellar accommodate?
(4) A server in a computer system is processing 100 jobs per
hour. The average job requires 10 seconds. For how many minutes
per hour is the server idle?
(5) A computer system serves two kinds of jobs. The large
jobs, averaging 1 minute each, flow through at 20 per hour. The
small jobs, averaging 1.2 sec each, flow through at 1500 per
hour. The server gives preemptive priority to the small jobs.
What is the utilization of this server? For how many minutes per
hour is the server idle?
(6) A time sharing system is serving 1500 jobs per hour. Each
of the 100 users spends an average 30 seconds from the previous system
response until typing the next command. What is the response
time of the system to a user command?
(7) A company internal network consists of 1000 routers in 300
branch offices around the world. A job flow analysis
shows that, averaged over all transactions processed in the
network, a typical transaction in the network sends 10 messages
to the router in Princeton, NJ. The Princeton router is observed to
be processing 15,000 transactions per minute. How many
transactions per minute is the entire network processing?
(8) In the same network, the router in Burbank, CA, is used
twice per minute and is operating with utilization 67%. What is
the maximum possible transaction rate for the entire network?
Can this rate be achieved?
(9) A hard disk with rotation time T
is laid out with K sectors per revolution.
The disk driver has one FIFO queue for each sector. Disk
requests are for page transfers that take up one sector each.
As requests
come in, they are immediately sorted into the proper sector
queues. When the disk is in the rotational position of a given
sector, it processes the request at the head of that sector
queue. Suppose that the disk has a fixed load of N requests --
as soon as one is finished, another request is submitted for a
random sector. Find an expression for U(N), the utilization of this
disk. (Hint: divide the response time into three parts: time for
disk to rotate to your sector, time for queue ahead of you to
empty, and time for you to receive your sector service. Then
apply Little's law.)
(10) Repeat the analysis for the disk except now there is only
one FIFO queue in which all sector requests are placed. Compare
this efficiency with the sector-scheduled queue (previous question).