Hard Real-Time Scheduling for LowEnergy Using Stochastic Data and DVS
Processors
Flavius Gruian
Department of Computer Science, Lund University
Box 118
S-221 00 Lund, Sweden
Tel.: +46 046 2224673
e-mail: Flavius.Gruian@cs.lth.se
Dynamic Voltage Scaling (DVS)
2
Pd  Cef Vdd
 f
P: dynamic power dissipation for CMOS
C: effective switched capacitance
V: voltage
f: frequency of the clock
Different Abstraction Level for Power
Saving
• Task set level
– Scheduling at inter-task level
• Task level
– Scheduling at intra task level. Insert rescheduling points inside a task
Different Abstraction Level for Power
Saving
• DVS for soft real-time systems
– Deadline misses are allowed
– QoS is kept
• DVS for hard real-time systems
– No deadline miss is allowed
Three execution mode for a task
Mode 1: ideal schedule ; Mode 2: WCET oriented schedule;
Mode 3: stochastic schedule
Obtaining Stochastic Schedule
• Obtained off-line
• Obtained by simulation
• Built and improved at runtime
Obtaining Stochastic Schedule
E
 (1  cdf
0 y W X
y
)  ey
E: average energy for the whole task
WX: worst case number of clock cycles of
a task
cdf : cumulative density of probability
function, cdfx=P(X<=x)
e: energy consumption for clock cycle y
Obtaining Stochastic Schedule
k
0 y W X
y
E
 A,
k V

(1  cdf y )
0 y W X
(1  )
,
e V
2
k y2
Ky: the clock length associated to clock cycle y
A: the maximum execution time for a task to
complete
Goal of DVS: to minimize E
Obtaining Stochastic Schedule
by mathematical induction:
1
2
E  2 (  1  cdf y )
A 0 y W X
when :
k y  A  ( 1  cdf y ) /(

0 y W X
1  cdf y )
Optimal Values -> Real Case Values
• Optimal clock length ky may not overlap
with the available clock lengths, need to be
converted to real clock cycles
• Find two bounding available clock cycles
CKi<Ky<=CKj
• Distribute the work of the ideal cycle into
two parts:
k y  wi  CKi  (1  wi )  CK j
Off-line Task Stretching
• Computing stretching factors in an iterative
manner, from the higher to the lower priority
tasks ( priority computed by RMS)
• For the tasks which already have assigned a
stretching factor, we use that one  r
• For the rest of the tasks, assume they will all
use the same and yet to be computed
stretching factor  ij
 S ij 
 S ij 
 r Cr     ij   C p     Sij

1 r  q
q  p i
 Tp 
 Tr 
Off-line Task Stretching
On-line Slack Distribution
• An early finishing task may pass on its unused
processor time for any of the tasks executing
next
• Not all the slacks can be used by any task at any
time, because deadlines have to be met at the
same time
On-line Slack Distribution
• Multiple levels slacks
• If the tasks in the task set have m different
priorities, we use m levels of slacks
• The slack in each level is a cumulative value: the
sum of the unused processor times remaining
from the tasks with higher priority
Run-time Management of Slack
Level
• Whenever an instance k of a task Ti starts executing
(with priority i), it can use an arbitrary part Cik of the
slack available at level i, Si.
• Allowed executing time for Ti : Aik  Ci  Cik
• Remaining slack from level I will degrade into level
i+1 slack. Update each level slack with:
0, j  i

Sj  
k
S j  Ci , j  i

Run-time Management of Slack
Level
• Whenever a task instance finishes its execution, if it
finishes before its allowed time, it will generate some
k
k
k
slack: Ai  Ai  Ei
• This slack can be used by the lower priority tasks.
The level slacks are updated according to:
Sj

 Sj, j  i

k
S j  Ai , j  i
Slack Assignment
• Greedy: the task gets all the slack available for its
level
Cik  S i
• Mean proportional: the task gets the slack according
to the proportion of their mean execution time  i
C  S i  i /(
k
i
 j )
jRe adyQ
Experimental Results ---Example 1
Experimental Results ---Example 2
Conclusions
• DVS policy for hard real-time systems
• Both off-line and on-line scheduling
decisions are taken
• Scheduling at both task level and task set
level
• Task splitting
• Multi-level slacks