Real-Time Systems Group
Accounting for
Cache Related Pre-emption Delays in
Hierarchal Scheduling
Will Lunniss1 Sebastian Altmeyer2 Giuseppe Lipari3,4 Robert I. Davis1
1Department
of Computer Science, University of York, UK
{wl510, rob.davis}@york.ac.uk
2Computer Systems Architecture Group, University of Amsterdam, Netherlands
altmeyer@uva.nl
3Scuola Superiore, Sant'Anna, IT
g.lipari@sssup.it
4LSV – ENS Cachan, FR
giuseppe.lipari@lsv.ens-cachan.fr
Real-Time Systems Group
Outline
 Hierarchical Scheduling
 Cache Related Pre-emption Delays (CRPD)
 Accounting for CRPD in Hierarchical Scheduling
 Evaluation
 Conclusions
2
Real-Time Systems Group
Outline
 Hierarchical Scheduling
 Cache Related Pre-emption Delays (CRPD)
 Accounting for CRPD in Hierarchical Scheduling
 Evaluation
 Conclusions
3
Real-Time Systems Group
Hierarchical Scheduling
 Hierarchical scheduling provides a means of composing
multiple real-time components (applications) on a single
processor
 Components should be isolated and not interfere with
each other
 Divide up access to the processor using a global
scheduler
 Schedule tasks in each component using a local
scheduler
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Real-Time Systems Group
Hierarchical Scheduling
 Assume single processor
 Assume each component has a dedicated server, S,
that allocates processor capacity to it
 Assume servers are scheduled globally using non-preemptive scheduler
 Assume tasks are scheduled locally using pre-emptive
FP scheduler
 Each server SG, has a budget QG, and a period PG
5
Real-Time Systems Group
Hierarchical Scheduling
Components scheduled
globally using non preemptive scheduling
Tasks scheduled locally
using pre-emptive FP
scheduling
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Real-Time Systems Group
Supply Bound Function
 Accounts for non dedicated access to the processor
 inverse supply bound function (isbf)
 determine the maximum amount of time needed by a specific server
to supply some capacity c
[1] I. Shin and I. Lee, "Periodic Resource Model for Compositional Real-Time Guarantees," in Proceedings of the
24th IEEE Real-Time Systems Symposium (RTSS), Cancun, Mexico, 2003, pp. 2-13.
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Real-Time Systems Group
Schedulability Analysis for Hierarchical Systems




R
i Jj
 1
G
Ri  isbf Ci   
Cj 



T
j

j

hp
(
G
,
i
)

 

Wrap response time
analysis in the inverse
supply bound function
8
Restrict the set of tasks to
those in the same
component
Real-Time Systems Group
Outline
 Hierarchical Scheduling
 Cache Related Pre-emption Delays (CRPD)
 Accounting for CRPD in Hierarchical Scheduling
 Evaluation
 Conclusions
9
Real-Time Systems Group
Cache Related Pre-emption Delays (CRPD)
 Pre-empting task can evict cache blocks belonging to
the pre-empted task
 CRPD are introduced when the pre-empted task has to
reload some of those evicted cache blocks after
resuming
 Tasks in other components could evict cache blocks,
causing ‘inter-component’ CRPD
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Real-Time Systems Group
Cache Block Categorisation
 Evicting Cache Blocks (ECBs)
 Loaded into cache and can therefore evict other blocks
 Useful Cache Blocks (UCBs)
 Reused once they have been loaded into cache before potentially
being evicted by the task
 If evicted by another task, they may have to be reloaded which
introduces CRPD
 UCBs are always also ECBs
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Real-Time Systems Group
CRPD in Hierarchical Scheduling
Component-level CRPD
Task-level CRPD
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Real-Time Systems Group
Outline
 Hierarchical Scheduling
 Cache Related Pre-emption Delays (CRPD)
 Accounting for CRPD in Hierarchical Scheduling
 Evaluation
 Conclusions
13
Real-Time Systems Group
Integrating CRPD Analysis

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



R

J
i
j
G

Ri 1  isbf G  Ci    
C




j
i
,
j
i





T
j
jhp ( G , i )  




Task-level CRPD determined using the
Combined Multiset approach [1]
Component-level CRPD
[1] Altmeyer, S., Davis, R.I., and Maiza, C. Improved Cache Related Pre-emption Delay Aware Response Time
Analysis for Fixed Priority Pre-emptive Systems. Real-Time Systems, 48, 5 (September 2012), 499-512.
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Real-Time Systems Group
Approach Variation 1 ‘-All’
 Assume that every time server SG is suspended, all of
the other servers run and their tasks evict all the cache
blocks that they use
This approach could be pessimistic
if servers do not have equal
periods
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Real-Time Systems Group
Approach Variation 1 ‘-All’
 Assume that every time server SG is suspended, all of
the other servers run and their tasks evict all the cache
blocks that they use
Ri 

E Ri   1   G 
P 
G
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Real-Time Systems Group
UCB-ECB-ALL
Multiplied by the number of times
component G is suspended and
resumed during the response time
of task τi
 iG



 
G
Z
 BRT  E Ri     UCBk     ECB 

 khepG ,i 
   ZZ
G


Multiplied by the cost incurred
when reloading a block, the Block
Reload Time (BRT)
Calculate the union of UCBs of task τi
and all tasks that are part of component
G that could pre-empt it
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Calculate the union of ECBs of all
other components
Real-Time Systems Group
Approach Variation 2 ‘-Counted’
 Consider each component separately by calculating the
number of disruptive executions that server SZ can have
on task τi in component G during the response time of
task τi
Tasks in component Z cannot evict
the same cache block multiple
times even if component Z runs
more than once while component
G is suspended
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Real-Time Systems Group
Approach Variation 2 ‘-Counted’
 Consider each component separately by calculating the
number of disruptive executions that server SZ can have
on task τi in component G during the response time of
task τi
X
19
Z


 G 
 t
S , t  min  E  t  , 1   Z
P

G




 

Real-Time Systems Group
UCB-ECB-Counted
Summed for all other components
 iG  BRT 
 Z G


Z



X
S
,
R

UCB

ECB
i
k
 



Z 
khepG ,i 



 Z G

Multiplied by the number of disruptive
executions of component Z during the
response time of task τi
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




Calculate the union of UCBs of
task τi and all tasks that are part of
component G that could pre-empt
it, intersected with the ECBs of
component Z
Real-Time Systems Group
Approach Variation 3 ‘-Open’
 Ignore details of other components, assume all blocks
are evicted by the other components
 Variation of ‘-All’ approaches
 The union of ECBs of the other components is assumed to contain all
cache blocks
 Allows the analysis to be used when no information
about the other components is available
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Real-Time Systems Group
Outline
 Hierarchical Scheduling
 Cache Related Pre-emption Delays (CRPD)
 Accounting for CRPD in Hierarchical Scheduling
 Evaluation
 Conclusions
22
Real-Time Systems Group
Evaluation Methodology
 Assign equal server periods to all components
 Split tasks equally between components
 Default of 24 tasks and 3 components
 Determine if the system is schedulable
 Perform a binary search to find the minimum server capacity required
to schedule each component
 As server periods are equal, if the total capacity of all servers is less
than 100% then the system is schedulable
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Real-Time Systems Group
Evaluation
Accounting for all of the
other components at
once, or assuming that
the cache is flushed,
performs the best
Considering just the other
components, and doing so
individually performs the
worst
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Real-Time Systems Group
Number of Components
Assuming the cache
if flushed every time
a component is
suspended is not
effective with one
component
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There is no difference
between the ‘-All’ and ‘Counted’ variants when there
are two components
Real-Time Systems Group
Server Period
Minimising the server
periods maximises
schedulability when
component CRPD is
not considered
In practice, the
server period must
be carefully selected
26
Real-Time Systems Group
Cache Utilisation
When the cache
utilisation is low, not
considering the other
components can be
overly pessimistic
27
Once the cache utilisation of the other
components is > 1, assuming the cache
is flushed each time a component is
suspended can be as effective as the
more sophisticated approach
Real-Time Systems Group
Outline
 Hierarchical Scheduling
 Cache Related Pre-emption Delays (CRPD)
 Accounting for CRPD in Hierarchical Scheduling
 Evaluation
 Conclusions
28
Real-Time Systems Group
Conclusions
 Presented a number of approaches for bounding CRPD
under hierarchical scheduling with a local FP scheduler
 Shown that it is important to consider inter-component
CRPD
 Note that minimising server periods does not maximise
schedulability, as is the case when inter-component
CRPD is not considered
 Must select the server period carefully
 If the components fill the cache, simply assuming the
cache is flushed each time a component is suspended
can be very effective with equal server periods
 Allows a bound on CRPD to be calculated without any information
about the other components in the system
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Real-Time Systems Group
Thank you for listening
Any Questions?
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