Why oPCA? e In our example, oPCa needs less time than EFPa D=3 Calculation task Running time of Running time of ● C-number of channels EFPA in seconds OPCA in seconds pel r trunk Blocking probability of the 0.271 0.197 whole network and c=50 Offered load to each D pair is o5c Blocking probability of the 64.45 12.91 whole network and C=2000 only consider 4 Blocking probability of the B006 significant digits of the whole network and C=10000 fixed-point solutions when b >10 Blocking probability of th 13665 1232 whole network and C=20000 ● When4<10-30,set Comparison of the times used by efpa and opca to 0 calculate the blocking probabilities in the NSFNet J: trunk number k: deflection times
11 Why OPCA? Calculation task Running time of EFPA in seconds Running time of OPCA in seconds Blocking probability of the whole network and C=50 0.271 0.197 Blocking probability of the whole network and C=2000 64.45 12.91 Blocking probability of the whole network and C=10000 3006 397 Blocking probability of the whole network and C=20000 13665 1232 In our example, OPCA needs less time than EFPA Comparison of the times used by EFPA and OPCA to calculate the blocking probabilities in the NSFNet ⚫ D=3 ⚫ C-number of channels per trunk ⚫ Offered load to each SD pair is 0.5C ⚫ only consider 4 significant digits of the fixed-point solutions when ⚫ When , set j: trunk number k: deflection times 50 10− k bj 50 10− k bj = 0 k j b
Why OPCA? In our example, oPCa needs less time than eFpa In practical range, OPCA is more accurate than EFPa and generally it is not worse ●D=3 4日 ●C=50 0 actical loadin range, efPa does not performs better than OPCA ● EFPA is only more accurate than OPCA ① 灯人049 simulation when the offered load EFPA is within 35-40 -日-OPcA when the offered load offered load to each SD pair is within 40-50 EFPA cannot converge
Why OPCA? 12 In our example, OPCA needs less time than EFPA In practical range, OPCA is more accurate than EFPA and generally it is not worse ⚫ D=3 ⚫ C=50 ⚫ in the practical loading range, EFPA does not performs better than OPCA ⚫ EFPA is only more accurate than OPCA when the offered load is within 35–40 ⚫ when the offered load is within 40–50, EFPA cannot converge
Objectives e Provide the upper and lower bounds for the blocking probability obtained by OpCa Understand and mathematically prove the conditions under which the bounds draw near each other Find a way to make the bounds converge faster use them to find solutions for opca
Objectives 13 Provide the upper and lower bounds for the blocking probability obtained by OPCA Understand and mathematically prove the conditions under which the bounds draw near each other Find a way to make the bounds converge faster, use them to find solutions for OPCA
Numerical results C=50 -058 Offered load to each Sd pair: 30 三o00 Erlangs when no. of iterations= distance between two bounds <10-7 lower bound value 兰o064 30z Number of iterations (each layer
Numerical results 14 C=50 Offered load to each SD pair: 30 Erlangs When no. of iterations = 7, 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑡𝑤𝑜 𝑏𝑜𝑢𝑛𝑑𝑠 𝑙𝑜𝑤𝑒𝑟 𝑏𝑜𝑢𝑛𝑑 𝑣𝑎𝑙𝑢𝑒 < 10−7
Summary e Prove that the upper and lower bounds draw near each other ● Numerica lly demonstrate that the bounds become closer to each other very fast
Summary 15 Prove that the upper and lower bounds draw near each other Numerically demonstrate that the bounds become closer to each other very fast