
Reacting to Randomly Observed Events 261
Exercise 5. Modify the task scheduling algorithm of Section 9.1.7 to allow the
controller to serve more than one task per frame. Specifically, every frame k the
controller chooses a service action s[k] from a set S of possible actions. Each
service action s ∈Sdetermines a clearance vector c(s)=(c
1
(s),...,c
N
(s)),
where c
i
(s) is the number of tasks of type i served if action s is used on a
given frame. It also incurs a delay
ˆ
D(s) and energy ˆe(s).
Exercise 6. Consider the linear fractional problem of finding a vec-
tor (x
1
,...,x
M
) to minimize (a
0
+
!
M
i=1
a
i
x
i
)/(b
0
+
!
M
i=1
b
i
x
i
) subject to
!
M
i=1
c
il
x
i
≤ d
l
for l ∈{1,...,L