Identification of Stochastic Timed Discrete Event Systems with st-IPN

Algorithm 2

Subroutine Case.

Inputs:   𝑢_𝑙,𝑠; 𝑦_𝑙,𝑗; 𝑘_𝑙; 𝑞_𝑙; 𝜑_𝑙𝑀_{𝑙,𝑘𝑙}; 𝜑_𝑙(𝑀); 𝜆_𝑙(tr)

Outputs:   Pre_𝑙; Post_𝑙; 𝜑_𝑙𝑀_{𝑙,𝑘𝑙}; 𝜑_𝑙(𝑀); 𝜆_𝑙(tr)

Case  1.

read (𝑙)

𝑘^′_𝑙=𝑘_𝑙+1;

𝑞^′_𝑙=𝑞_𝑙+1;

𝑢_𝑙,𝑠={cc₁,…,cc_𝑚𝑔,cc_𝑙,1,…,cc_{𝑙,𝑚𝑙}};

𝑦_𝑙,𝑗={sr_𝑙,1,…,sr_{𝑙,𝑛𝑙}};

 (1) 𝜑_𝑙𝑀_{𝑙,𝑘′𝑙}=𝑦^𝑖_𝑙,𝑗/𝑦^𝑖_𝑙,𝑗−𝑦^𝑖−1_𝑙,𝑗=𝑦^𝑖_𝑙,𝑗/𝑑𝑦_𝑙,𝑗

 (2) 𝑡^𝑖_{𝑙,𝑞𝑙}=𝜏_𝑖−𝜏_𝑖−1

 (3) 𝜆_𝑙tr_{𝑙,𝑞′𝑙}=𝑢_𝑙,𝑠⋅𝑡^𝑖_{𝑙,𝑞𝑙}

 (4) Update Pre_𝑙; Post_𝑙; 𝜑_𝑙(𝑀); 𝜆_𝑙(tr); 𝛿_𝑜𝑖tr_{𝑙,𝑞𝑙}.

Case  2.

read (𝑙)

𝑘^′_𝑙=𝑘_𝑙;

𝑞^′_𝑙=𝑞_𝑙+1;

𝑢_𝑙,𝑠={cc₁,…,cc_𝑚𝑔,cc_𝑙,1,…,cc_{𝑙,𝑚𝑙}};

 (1) 𝑡^𝑖_{𝑙,𝑞𝑙}=𝜏_𝑖−𝜏_𝑖−1

 (2) 𝜆_𝑙tr_{𝑙,𝑞′𝑙}=𝑢_𝑙,𝑠⋅𝑡^𝑖_{𝑙,𝑞𝑙}

 (3) Update Pre_𝑙; Post_𝑙; 𝜑_𝑙(𝑀); 𝜆_𝑙(tr); 𝛿_𝑜𝑖tr_{𝑙,𝑞𝑙}

The updating of Pre_𝑙; Post_𝑙; 𝜑_𝑙(𝑀); 𝜆_𝑙(tr); 𝛿_𝑜𝑖tr_{𝑙,𝑞𝑙} can be seen in Figure 4.