Tham khảo tài liệu 'petri nets applications part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Reachability Analysis of Time-Critical Systems 271 Ttim tenti tfti ff We denote be p ti - generated TI after j-th firing of ti in the stable loop Ơ and Ttỉỉ tenti W tfti 0 According to Lemma 1 Lemma 2 . due to properties of TB nets and the stabile selffeded loops we have that Tt Tti j 1 and also teni ffl teni i 1 e sq Assume tent tt i Tt ữ . To calculate tent j 1 in the case of the stabile loop we have to consider the contribution of Ơ to the lower and upper bound of ten. The contribution is denoted by tfiL t and tfaL t to be the contribution to the lower and upper bound respectively. In our example for t5-generated t4 we get P 1 r 1 ĩen n 1 f 0 4 4 4t5 tent5 fy rent 1 rfi a To compute t6 n i and t7 n a we first compute t6 1 t7 1 . Notice t6 is t3 - generated . t6 tt3 t7 is t7 - generated . t7 tt7 We compute Tt 1i for all te T ơ in this particular case. We start with the calculation of initial values for ơ uơơ . provided Ơ tfatsts and u t3t7t2t6t7t6 rh r6 tf3 0 ren3 dti2 10 18 18 rt7 tf7 0 ren7 8 10 10 18 rt6 tf6 0 ren2 Tt7 10 18 r f7 0 ren7 8 rt 8 rt5 f5 0 ren5 max r6i r2i r7i 47a 01 max 18 We are going now to construct i- and a- determinate loops for the TB net of the voice station Fig. 7 . We are choosing first ơ trtĩtstg. For the loop chosen we have T ơ t1 t3 t5 t7 and p v P1 P2 Pi P4 P6 Pl P8 . We can see Fig. 7 that in P ơ there will be both mono-generated TIs ti t2 t3 by ti while t7 by t7 and also non mono-generated TIs t4 either by t5 or t2 while t8 either by t5 or t6 272 Petri Nets Applications In the following calculations based on the loop Ơ we choose for r4 and r8 to be tj-generated. In the table below you can see the values of tfti 0 for i 1 2 3 5 6 7. i a tfti 0 10 10 10 tf2 0 10 10 10 tft3 0 Ú .2 0 tft5 0 04 0 tfte p tft7 0 8 0 8 Table 1. Values of tfn 0 Now we can calculate íGl Í5 0 f 0 f 0 tf5 0 10 0 0 10 tfaL W f 0 a tft5 0
