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Theoretical puzzles Estimation of the approximation errors using the IMC theory

Theoretical puzzles Estimation of the approximation errors using the IMC theory. Nicolas Coste - STMicroelectronics -. Filter 1 :. Filter 2 :. E = Pop(). PUSH. PUSH. PUSH. PUSH. Push(E). E = Pop(). Push(E). E = Pop(). Computation. SYSTEM. Computation. Push(E).

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Theoretical puzzles Estimation of the approximation errors using the IMC theory

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  1. Theoretical puzzlesEstimation of the approximation errors using the IMC theory Nicolas Coste- STMicroelectronics -

  2. Filter 1 : Filter 2 : E = Pop() PUSH PUSH PUSH PUSH Push(E) E = Pop() Push(E) E = Pop() Computation SYSTEM Computation Push(E) Time needed to process an operation E = Pop() Push(E) FILTER 1 time FILTER 2 POP POP Case study basis QUEUE • Time physically needed to process an operation • Operations are blocking

  3. Time physically needed for a PUSH (λ) • Time physically needed for a POP (μ) Identifying the start and end of relevant timing delays in the model Proba • Time between 2 PUSH (δ1) • Time between 2 POP (δ2) 1 1 Exposing each start and end as LOTOS gates 2 time 0 Identifying the distribution of the delays SYSTEM 3 Approximating the delays as PH-dist. 4 λ_START μ_START λ_STOP μ_STOP Embedding each delay into start/end gates δ1_START δ1_STOP δ2_STOP POP_DELAY PUSH_DELAY δ2_START PUSH_DELAY […] : λ_START; λ_DELAY; λ_DELAY; λ_STOP; PUSH_DELAY […] POP_DELAY […] : μ_START; μ_DELAY; μ_DELAY; μ_STOP; POP_DELAY […] 5 CONS_DELAY […] : δ2_START; δ2_DELAY; δ2_STOP; CONS_DELAY […] GEN_DELAY […] : δ1_START; δ1_DELAY; δ1_STOP; GEN_DELAY […] GEN_DELAY CONS_DELAY Case study performance evaluation GENERATOR CONSUMER GENERATOR […] : δ1_START; δ1_STOP; PUSH_RQ !DATA; PUSH_RSP; GENERATOR […] CONSUMER […] : δ2_START; δ2_STOP; POP_RQ; POP_RSP ?Elmt; CONSUMER […] QUEUE [ PUSH_RQ, PUSH_RSP, POP_RQ, POP_RSP, λ_START, λ_STOP, μ_START, μ_STOP ] PUSH_RQ QUEUE [ PUSH_RQ, PUSH_RSP, POP_RQ, POP_RSP] POP_RQ PUSH_RSP POP_RSP

  4. λ λ 0 μ μ Steady state analysis (Pr0 , Pr1 , Pr2) 2 1 ERLANG CST DELAY ERROR Estimator of the error on each individual approximation Estimation of the error for the computed results Approximating the delays as PH-dist. 4 • Any distribution can be fitted by a phase-type distribution • The longer the erl. dist. is, the better the approx. is. 1 time Evaluation of the approximation errors? Identifying the start and end of relevant timing delays in the model 1 Exposing each start and end as LOTOS gates 2 Identifying the distribution of the delays 3 Embedding each delay into start/end gates 5 Why should we increase the size of the erlang distribution if we can not estimate the gain ?

  5. CONCLUSION • Industrial needs: • Reduction of development time • Simple and Automated methods to spread the knowledge • Trust indexes to validate the results Industrial success for the IMC theory depends on the answer to this last point

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