Homework I
1.
Five jobs are waiting to be run. Their expected run times are 9, 6, 3, 5 and X. In
what order should they be run in order to minimize average waiting time? (Hint:
Though the answer is simple, you need to consider all cases).
In class we’ve discussed that shortest job first leads to
minimum
average waiting time.
See class text, p 159. You don’t need to prove it for this question, just remember that
fact. In that case the answer is
a.
0 < X
β
3
: X, 3, 5, 6, 9
b.
3 < X
β
5
: 3, X, 5, 6, 9
c.
5 < X
β
6
: 3, 5, X, 6, 9
d.
6 < X
β
9
: 3, 5, 6, X, 9
e.
X > 9
: 3, 5, 6, 9, X
2.
This problem deals with real time systems with N CPU’s. Events that real time
systems have to respond to are classified as
periodic
or
aperiodic
. Consider the
first case where jobs occur at regular intervals: Let there be
m
periodic events and
event
i
occurs with period
P
i
and
C
i
seconds of CPU time are required to handle
each event, derive an inequality that can be used to show the conditions under
which the periodic load can be handled. (
Hint
: Define CPU utilization, ignore
context switch overhead.)
Utilization is defined as
∑
=
m
i
i
i
P
C
1
and this must be less than or equal to N, i.e., CPU
utilization cannot exceed the number of CPU’s available, and we have assumed N
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 Spring '07
 Chandra
 Algorithms, Virtual memory, Central processing unit, real time systems, N CPU

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