Optimal TDMA Time Slot and Cycle Length Allocation for Hard RealTime Systems

1
Optimal TDMA Time Slot and Cycle Length
Allocation for Hard Real-Time Systems
26. January 2006 ASP-DAC, Yokohama, Japan
Ernesto Wandeler Lothar Thiele
Computer Engineering and Networks Laboratory ETH
Zurich, Switzerland
2
Time Division Multiple Access (TDMA)
time
M1
M2
M2
M3
M
M
M
M
3
Motivation TDMA as Backbone in DES

• Interconnect a large number of ECUs.
• Interconnect separate communication clusters.
• Serve time- event-triggered messages.

4
Advantages of TDMA

• Supports temporal composability.
• Has deterministic timing behavior.
• Can be made fault tolerant.
• Supports error detection and error contention.

5
Difficulties of TDMA
How do we optimally select the TDMA parameters?

• Optimal parameter selection
• Bandwidth
• Cycle length
• Slot lenghts

6
Related Work
optimal (exact)
real-time messages
stream model
scope
TT
P

• Kopetz et al. 1997
• Obermaisser et al. 2002(Direct share)
• Pop et al. 2004(Heuristic)
• Hamann et al. 2005 (Evolutionary Algorithm)
• This work

TTET
S
TTET
P
TTET
PJD
TTET
any
7
Solution Strategy

• Determine a method to model the service demand of
  an event- or time-triggered real-time message
  stream.
• Determine a method to model the service supply of
  a TDMA resource.
• Based on the two above models, find an analytic
  method to determine the provable smallest slot
  length that must be allocated on a TDMA resource
  to serve a real-time message stream.

8
Solution Strategy

• Determine a method to model the service demand of
  an event- or time-triggered real-time message
  stream.
• Determine a method to model the service supply of
  a TDMA resource.
• Based on the two above models, find an analytic
  method to determine the provable smallest slot
  length that must be allocated on a TDMA resource
  to serve a real-time message stream.

9
Service Demand Arrival Curves
events
Event Stream
deadline d
t ms
2.5
Arrival Curve a Deadline d
au
al
10
Service Demand Arrival Curve Examples
periodic
periodic w/ jitter
periodic w/ burst
complex
11
Service Demand Service Demand Curves
Arrival Curve a Deadline d
au
al
Service Demand Curve bA
bAu
bAl
d
12
Solution Strategy

• Determine a method to model the service demand of
  an event- or time-triggered real-time message
  stream.
• Determine a method to model the service supply of
  a TDMA resource.
• Based on the two above models, find an analytic
  method to determine the provable smallest slot
  length that must be allocated on a TDMA resource
  to serve a real-time message stream.

13
Service Supply Serivce Curves
availability
Resource Availability
t ms
2.5
bu
bl
14
Service Supply of a TDMA Resource
availability
Resource Availability
overhead
t ms
2.5
bu
bl
15
Solution Strategy

• Determine a method to model the service demand of
  an event- or time-triggered real-time message
  stream.
• Determine a method to model the service supply of
  a TDMA resource.
• Based on the two above models, find an analytic
  method to determine the provable smallest slot
  length that must be allocated on a TDMA resource
  to serve a real-time message stream.

16
Computing the Minimum Slot Length
service demand / supply
Cycle Slot
50 5
50 8
50 10
50 9
20 3,6
150 52
D ms

• Given
• Bandwidth
• Cycle Length
• Service Demand

• Find
• Provable smallest slot length

17
Computing the Minimum Slot Length

• Given
• Bandwidth
• Cycle Length
• Service Demand

• Find
• Provable smallest slot length

18
Minimum Slot Lengths vs. Cycle Length
slot length
cycle length ms

• Given
• Bandwidth
• Cycle Length
• Service Demand

• Find
• Provable smallest slot length

19
Finding Feasible Cycle Lengths

• Given
• Bandwidth
• Service Demand

• Find
• Slot lengths
• Feasible Cycle Lengths

20
Finding Feasible Cycle Lengths

• For all cycle lengths compute the minimum
  slot lengths for all message streams.
• Compute total resource utilization
• If and only if is
  feasible

• Given
• Bandwidth
• Service Demand

• Find
• Slot lengths
• Feasible Cycle Lengths

21
Finding Feasible Cycle Lengths
Computation Time up to Upper Bound 1,1
second!(Pentium Mobile 1.6 GHz)
utilization
cycle length ms

• Given
• Bandwidth
• Service Demand

• Find
• Slot lengths
• Feasible Cycle Lengths

22
Finding Optimal Cycle Lengths

• Define an optimality criterion
• E.g. average remaining bandwidth,
• Compute all feasible cycle lengths and select the
  optimal cycle length.

• Given
• Bandwidth
• Service Demand

• Find
• Slot lengths
• Optimal Cycle Length

23
Finding Minimum Total Bandwidth

• Perform a binary search until all feasible cycle
  lengths lead to zero remaining bandwidth.

• Given
• Service Demand

• Find
• Slot lengths
• Optimal Cycle Length
• Bandwidth

24
Conclusions

• We presented an analytic method to determine
  provably smallest possible slot lengths for TDMA.
• The presented analytical method is
  computationally very efficient.
• Based on the computational efficiency, we
  presented constructive methods to find the
  optimal cycle length and the minimum required
  bandwidth for a TDMA resource.

25
Thank you!
Ernesto Wandeler wandeler_at_tik.ee.ethz.ch