Quantitative Evaluation of Embedded Systems

Latency for a delayed periodic source

Calculating a latency bound

• Given a dataflow graph with execution times Ea

• Determine the MCM and choose a period μ ≥ MCM• Determine start-times Ta of a periodic schedule• Determine the minimum number δ

of tokens between input and output

• Latency ≤ Toutput + Eoutput + δ·μ

Latency for a delayed source

MCM = 22ms

St0 = 34ms

A CB

26ms

30ms

t0 = 0ms

t0 = 8ms

Latency = 10ms

Latency for a delayed source

MCM = 22ms

St0 = 34ms

A CB

26ms

30ms

t0 = 0ms

t0 = 8ms

DDelay = 34ms 10ms

Latency =

Calculating a delayed latency bound

• Given a dataflow graph with execution times Ea

• Determine the MCM and choose a period μ ≥ MCM• Determine start-times Ta of a periodic schedule• Determine the minimum number δ

of tokens between input and output

• Delayed latency ≤ Toutput + Eoutput + δ·μ - Tinput

Latency for a delayed source

A CB

26ms

30ms

10ms

E15ms

Latency for a delayed source

MCM = 22ms

S A CB

26ms

30ms

0ms

8ms0ms

DDelay = 10ms

E15ms

34ms

Latency for a delayed source

• Determine the MCM and choose a period μ ≥ MCM• For each actor a initialize a start-time Ta := 0• Repeat for each arc a—i—b :

Tb := Tb max (Ta + Ea – i μ)until there are no more changes

• Repeat for each actor a:Ta := min{all arcs a-i-b} (Tb - Ea + i μ)

until there are no more changes

• Delayed latency ≤ Toutput + Eoutput + δ·μ - Tinput