quantitative evaluation of embedded systems
DESCRIPTION
Quantitative Evaluation of Embedded Systems. Buffering. Buffering in streaming applications. Image taken from an online tutorial on the VLC media player. Buffering in dataflow graphs. A. C. B. 30ms. S. 10ms. 26ms. Invariants in a periodic schedule. - PowerPoint PPT PresentationTRANSCRIPT
Quantitative Evaluation of Embedded Systems
Buffering
Buffering in streaming applications
Image taken from an online tutorial on the VLC media player
Buffering in dataflow graphs
S A CB
26ms
30ms
10ms
• 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
Invariants in a periodic schedule
Tb ≥ T
a + Ea – i μ
i ≥ (Ta - T
b + Ea ) / μ
μ = 22ms
St0 = 34ms
A CB
26ms
30ms
t0 = 0ms
t0 = 8ms
10ms i ≥ (Ta – Tc + Ea)/μ
Retaining the invariant when buffering
μ = 22ms
St0 = 34ms
A CB
26ms
30ms
t0 = 0ms
t0 = 8ms
10ms i ≥ (Ta – Tc + Ea)/μi ≥ δ
Retaining the invariant when buffering
A B
Retaining invariant => retaining MCM
By definition of periodic schedule we findfor every arc x-#-y that Ty ≥ Tx + Ex – # μ
Adding these steps over a path B-X-Y----Z-A we find that TA ≥ TB + E(B-X-Y---Z) – #(B-X-Y---Z-A) μ
And so we find that i ≥ (TA - TB + EA)/μ ≥ E(B-X-Y---Z-A) / μ – #(B-X-Y---Z-A)
Which means for the cycle mean on the newly created cycle B-X-Y----Z-A-B:E(B-X-Y---Z-A) / (#(B-X-Y---Z-A) + i) ≤ μ
i
A BReversely, assume that we pick i so that the MCM of the graph does not change.
Then for any cycle B-X-Y----Z-A-B we know:E(B-X-Y---Z-A) / (#(B-X-Y---Z-A) + i) ≤ μ By definition of periodic schedule we havefor every arc x-#-y that Tx ≤ Ty - Ex + # μ
Adding these steps over a path B-X-Y----Z-A we find that TB ≤ TA - E(B-X-Y---Z) + #(B-X-Y---Z-A) μ
And so: (TA - TB + EA)/μ ≤ E(B-X-Y---Z-A) / μ – #(B-X-Y---Z-A) ≤ i
i
Retaining MCM => retaining invariant
How large should a buffer be?
if and only if
the periodic schedule stays unchangedif and only if
the MCM stays unchanged
S A CB
i But be aware of δ…