1. Q uantitative E valuation of E mbedded S ystems 1.Periodic schedules are linear programs 2.Latency analysis of a periodic source 3.Latency analysis of a sporadic source 4.Latency analysis of a bursty source

2. Determine the MCM and choose a period μ ≥ MCM For each actor a initialize a start-time T a := 0 Repeat for each arc a—i—b : T b := T b max (T a + E a – i μ) until there are no more changes Here, i denotes the number of initial tokens on an arc, and E a is the execution time of an actor a

3. A S B C 1ms 2ms x3x3 y x1x1 x2x2 3ms µ Choose a period μ ≥ MCM Initialize a start-time T a := 0 Repeat for each arc a—i—b : T b := T b max (T a + E a – i μ) until there are no more changes

4. Q uantitative E valuation of E mbedded S ystems 1.Periodic schedules and linear programs 2.Latency analysis of a periodic source 3.Latency analysis of a sporadic source 4.Latency analysis of a bursty source

5. Time (s) Tokens Latency Throughput

6. Time (s) Tokens Latency Throughput

7. And a periodic schedule: Given a source: We inductively derive the following latency bound:

8. We derive the following latency bound: And a periodic schedule: Given a source:

9. We derive the following latency bound: And a periodic schedule: Given a source:

10. And a periodic schedule: Given a source: We inductively derive the following latency bound: Theorem (monotonicity 2): Larger inter-arrival times in the source will not worsen the latency.

11. And a periodic schedule: Given a source: As an exercise, derive that: