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

2. Theoretical Puzzles - Leiden 10/10/2007 1 Operations are blocking SYSTEM QUEUE Case study basis PUSH time FILTER 1 FILTER 2 PUSH POP PUSH POP Filter 1 : Push(E) Filter 2 : E = Pop() Time physically needed to process an operation Computation Time needed to process an operation

3. Theoretical Puzzles - Leiden 10/10/2007 2 Time between 2 PUSH (δ 1 ) Time between 2 POP(δ 2 ) Time physically needed for a PUSH(λ) Time physically needed for a POP(μ) Exposing each start and end as LOTOS gates 2 Identifying the distribution of the delays 3 Approximating the delays as PH-dist. 4 Embedding each delay into start/end gates 5 Identifying the start and end of relevant timing delays in the model 1 SYSTEM PUSH_RQ GENERATOR Case study performance evaluation QUEUE [ PUSH_RQ, PUSH_RSP, POP_RQ, POP_RSP] CONSUMER PUSH_RSP POP_RQ POP_RSP QUEUE [ PUSH_RQ, PUSH_RSP, POP_RQ, POP_RSP, λ_START, λ_STOP, μ_START, μ_STOP ] GENERATOR […] : δ 1 _START; δ 1 _STOP; PUSH_RQ !DATA; PUSH_RSP; GENERATOR […] CONSUMER […] : δ 2 _START; δ 2 _STOP; POP_RQ; POP_RSP ?Elmt; CONSUMER […] Proba time 1 0 GEN_DELAY δ 1 _STOP δ 1 _START PUSH_DELAY λ _STOP λ _START POP_DELAY μ _STOP μ _START CONS_DELAY δ 2 _START δ 2 _STOP POP_DELAY […] : μ_START; μ_DELAY; μ_STOP; POP_DELAY […] PUSH_DELAY […] : λ_START; λ_DELAY; λ_STOP; PUSH_DELAY […] GEN_DELAY […] : δ 1 _START; δ 1 _DELAY; δ 1 _STOP; GEN_DELAY […] CONS_DELAY […] : δ 2 _START; δ 2 _DELAY; δ 2 _STOP; CONS_DELAY […]

4. Theoretical Puzzles - Leiden 10/10/2007 3 Any distribution can be fitted by a phase-type distribution The longer the erl. dist. is, the better the approx. is. Exposing each start and end as LOTOS gates 2 Identifying the distribution of the delays 3 Identifying the start and end of relevant timing delays in the model 1 Embedding each delay into start/end gates 5 Evaluation of the approximation errors? λ μ λ μ 0 1 2 Estimator of the error on each individual approximation Steady state analysis (Pr 0, Pr 1, Pr 2 ) Approximating the delays as PH-dist. 4 Estimation of the error for the computed results 1 time ERLANG CST DELAY ERROR Why should we increase the size of the erlang distribution if we can not estimate the gain ?

5. Theoretical Puzzles - Leiden 10/10/2007 4 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