=== Del 1: styringsregimer uten kjede (tabell 3, avsnitt 8.1 og 9.3) === kp=1.0: a=0.120 b=0.100 tau_c=inf mnd periode=inf mnd kp=3.0: a=0.120 b=0.300 tau_c=7.21 mnd periode=22.9 mnd kp=6.0: a=0.120 b=0.600 tau_c=3.01 mnd periode=10.7 mnd stabil for alle tau hvis kp <= a/c = 1.20 tau=11.0: største stabile kp = 2.28; tommelfingerregel kp < 1.43 p3 tau= 3.0: Kmax=1.116 Kmin=1.002 Tmin=1.00 Tmax=1.35 Lmin=0.787 amp(K,t>60)=0.000 Kend=1.086 Lend=0.787 p6 tau= 6.0: Kmax=1.167 Kmin=1.002 Tmin=1.00 Tmax=1.50 Lmin=0.786 amp(K,t>60)=0.075 Kend=1.093 Lend=0.787 p11 tau=11.0: Kmax=1.405 Kmin=0.911 Tmin=0.73 Tmax=2.20 Lmin=0.467 amp(K,t>60)=0.494 Kend=1.000 Lend=0.659 mpc11 tau=11.0: Kmax=1.224 Kmin=1.002 Tmin=1.00 Tmax=1.39 Lmin=0.783 amp(K,t>60)=0.002 Kend=1.031 Lend=0.795 p11d tau=11.0 kp=1.2: Kmax=1.234 Tmax=1.28 Lmin=0.776 amp(K,t>60)=0.026 Kend=1.155 Lend=0.777 === Del 2: straffesakskjeden koblet til dynamikken (avsnitt 7.3, 7.6, 8.2) === Z_D=0.1053 (ups_0=0.95), m_D=0.233 mnd (kalibrert), tau_D^ref=3.00 mnd, Q_D(0)=0.291, frafall før sjokk=2.9 % av J_D, faktisk utnyttelse R_D/Z_D=0.922 lineær relaksasjonstid for køen: 1/((1-ups)^2/m_D + varsigma) = 28 mnd (uten frafall: 39 mnd) M/M/1-sammenheng: tau_D = m_D/(1-ups): ups=0.8 -> 1.17 mnd, ups=0.95 -> 4.66 mnd --- grensetilfelle: reproduksjon av regime A-D --- Z_D=inf, p3 : max|dK|=0.00e+00 max|dL|=0.00e+00 max|dT|=0.00e+00 Z_D=inf, p6 : max|dK|=1.11e-15 max|dL|=0.00e+00 max|dT|=3.33e-15 Z_D=inf, p11 : max|dK|=2.00e-15 max|dL|=2.44e-15 max|dT|=6.00e-15 Z_D=inf, mpc11 : max|dK|=3.77e-15 max|dL|=2.22e-16 max|dT|=2.89e-14 Z_D=Z_D0, tilbakekoblinger av (theta=chi=mu4=0): max|dK|=0.00e+00 max|dL|=0.00e+00 (køen beregnes, men virker ikke tilbake) Z_D= 1.0 (endelig, m_D=0.233): max|dK|=4.7e-03 max|dL|=2.8e-04 tau_D^ref=0.259 Z_D=10.0 (endelig, m_D=0.233): max|dK|=3.6e-03 max|dL|=1.6e-04 tau_D^ref=0.235 --- scenarioer, regime A (kp=3, tau=3), fig:kjedesim / tabell --- 1 ingen flaskehals (= regime A) Kmax=1.116 Kend=1.086 Tmax=1.35 Tend=1.26 Lmin=0.787 Lend=0.787 tauD(end)= 0.0 tauDmax= 0.0 Qend=0.00 ups_end=1.00 amp(K,t>60)=0.000 2 flaskehals, ingen tiltak Kmax=1.284 Kend=1.284 Tmax=1.85 Tend=1.85 Lmin=0.657 Lend=0.657 tauD(end)= 53.8 tauDmax= 53.8 Qend=5.64 ups_end=1.86 amp(K,t>60)=0.026 3 underordne (xi_D 1->0.8 fra mnd 24) Kmax=1.181 Kend=1.172 Tmax=1.54 Tend=1.51 Lmin=0.707 Lend=0.707 tauD(end)= 15.3 tauDmax= 15.3 Qend=1.59 ups_end=1.21 amp(K,t>60)=0.015 4 utvide (Z_D +34 % over mnd 24-48) Kmax=1.187 Kend=1.146 Tmax=1.56 Tend=1.44 Lmin=0.719 Lend=0.724 tauD(end)= 10.2 tauDmax= 12.0 Qend=1.41 ups_end=1.08 amp(K,t>60)=0.005 5 underordne + utvide Kmax=1.181 Kend=1.087 Tmax=1.54 Tend=1.26 Lmin=0.749 Lend=0.787 tauD(end)= 1.0 tauDmax= 8.2 Qend=0.10 ups_end=1.01 amp(K,t>60)=0.022 s1: tauD@24=0.0 tauD@48=0.0 K@48=1.085 JD_end=0.134 RD_end=0.134 frafall_end=0.000 Umin=0.774 s2: tauD@24=7.8 tauD@48=21.8 K@48=1.242 JD_end=0.195 RD_end=0.105 frafall_end=0.056 Umin=0.715 s3: tauD@24=7.8 tauD@48=10.4 K@48=1.151 JD_end=0.125 RD_end=0.104 frafall_end=0.016 Umin=0.749 s4: tauD@24=7.8 tauD@48=11.7 K@48=1.158 JD_end=0.149 RD_end=0.138 frafall_end=0.014 Umin=0.745 s5: tauD@24=7.8 tauD@48=3.9 K@48=1.066 JD_end=0.108 RD_end=0.107 frafall_end=0.001 Umin=0.751 s1: J_D i ny likevekt=0.134 (ups_D=1.28); med xi=0.8: 0.107 (ups_D=1.02); Z_D for ups=0.95: 0.141 (+34 %), med xi=0.8: 0.113 (+7 %) --- trommel-buffer-tau (T begrenses slik at J_D <= 0.95 Z_D) og MPC (tau=3) --- 6 TBT, xi_D=1 Kmax=2.661 Kend=2.661 Tmax=1.00 Tend=0.54 Lmin=0.557 Lend=0.557 tauD(end)= 3.4 tauDmax= 4.1 Qend=0.33 ups_end=1.03 amp(K,t>60)=0.528 7 TBT + underordne Kmax=1.589 Kend=1.589 Tmax=1.00 Tend=0.89 Lmin=0.712 Lend=0.712 tauD(end)= 3.1 tauDmax= 3.7 Qend=0.30 ups_end=1.03 amp(K,t>60)=0.085 MPC uten kjedemodell (flaskehals) Kmax=1.515 Kend=1.515 Tmax=1.55 Tend=1.55 Lmin=0.627 Lend=0.627 tauD(end)= 46.6 tauDmax= 46.6 Qend=4.88 ups_end=1.76 amp(K,t>60)=0.091 MPC med kjedemodell (flaskehals) Kmax=1.215 Kend=1.215 Tmax=1.96 Tend=1.96 Lmin=0.667 Lend=0.667 tauD(end)= 56.6 tauDmax= 56.6 Qend=5.93 ups_end=1.89 amp(K,t>60)=0.043 MPC med kjedemodell + underordne Kmax=1.131 Kend=1.068 Tmax=1.70 Tend=1.70 Lmin=0.716 Lend=0.716 tauD(end)= 18.2 tauDmax= 18.2 Qend=1.89 ups_end=1.25 amp(K,t>60)=0.001 --- følsomhet for celerity-parameteren chi_D (tabell): K_end / Lambda_end / tau_D(end) --- 2 flaskehals, ingen tiltak chi=0.00: 1.193 / 0.679 / 35.6 | chi=0.15: 1.284 / 0.657 / 53.8 | chi=0.30: 1.378 / 0.638 / 74.3 3 underordne (xi_D 1->0.8 fra mnd 24) chi=0.00: 1.113 / 0.741 / 7.9 | chi=0.15: 1.172 / 0.707 / 15.3 | chi=0.30: 1.255 / 0.677 / 27.0 5 underordne + utvide chi=0.00: 1.087 / 0.787 / 1.0 | chi=0.15: 1.087 / 0.787 / 1.0 | chi=0.30: 1.087 / 0.787 / 1.0 --- følsomhet for vartheta og mu_4 (scenario 2) --- vartheta=0.00: Kend=1.164 Lend=0.690 tauD=27.7 Tend=1.49 vartheta=0.25: Kend=1.207 Lend=0.676 tauD=36.7 Tend=1.62 vartheta=0.50: Kend=1.284 Lend=0.657 tauD=53.8 Tend=1.85 vartheta=0.75: Kend=1.477 Lend=0.614 tauD=98.8 Tend=2.43 mu4=0.00: Kend=1.228 Lend=0.766 tauD=55.5 mu4=0.06: Kend=1.254 Lend=0.712 tauD=54.7 mu4=0.12: Kend=1.284 Lend=0.657 tauD=53.8 mu4=0.24: Kend=1.356 Lend=0.548 tauD=51.6 varsigma=0.00: Kend=1.293 Lend=0.650 tauD=87.9 varsigma=0.01: Kend=1.284 Lend=0.657 tauD=53.8 varsigma=0.02: Kend=1.274 Lend=0.666 tauD=36.1 --- stabilitet: regime B (tau=6) og C (tau=11) med mettet domstol --- tau= 6.0 uten kjede Kmax=1.167 Kend=1.093 Tmax=1.50 Tend=1.29 Lmin=0.786 Lend=0.787 tauD(end)= 0.0 tauDmax= 0.0 Qend=0.00 ups_end=1.00 amp(K,t>60)=0.075 topper [(19, 1.166), (39, 1.146), (58, 1.13), (78, 1.118), (97, 1.11), (116, 1.104)] bunner [(29, 1.017), (49, 1.035), (68, 1.048), (87, 1.058), (107, 1.065)] tau= 6.0 flaskehals (scen. 2) Kmax=1.284 Kend=1.284 Tmax=1.85 Tend=1.85 Lmin=0.657 Lend=0.657 tauD(end)= 53.7 tauDmax= 53.7 Qend=5.63 ups_end=1.86 amp(K,t>60)=0.026 topper [(22, 1.233), (48, 1.25)] bunner [(31, 1.19), (51, 1.25)] tau= 6.0 underordne+utvide (scen. 5) Kmax=1.233 Kend=1.074 Tmax=1.70 Tend=1.31 Lmin=0.750 Lend=0.786 tauD(end)= 1.1 tauDmax= 8.0 Qend=0.12 ups_end=1.00 amp(K,t>60)=0.071 topper [(22, 1.233), (42, 1.1), (67, 1.126), (89, 1.115), (111, 1.107)] bunner [(34, 1.063), (54, 1.034), (78, 1.055), (100, 1.064)] tau=11.0 uten kjede Kmax=1.405 Kend=1.000 Tmax=2.20 Tend=2.17 Lmin=0.467 Lend=0.659 tauD(end)= 0.0 tauDmax= 0.0 Qend=0.00 ups_end=1.00 amp(K,t>60)=0.494 topper [(24, 1.228), (54, 1.324), (83, 1.399), (111, 1.405)] bunner [(38, 0.93), (67, 0.911), (95, 0.934)] tau=11.0 flaskehals (scen. 2) Kmax=1.322 Kend=1.279 Tmax=1.97 Tend=1.81 Lmin=0.658 Lend=0.658 tauD(end)= 53.6 tauDmax= 53.6 Qend=5.62 ups_end=1.81 amp(K,t>60)=0.088 topper [(26, 1.321), (61, 1.322), (96, 1.307)] bunner [(42, 1.163), (77, 1.234), (112, 1.266)] tau=11.0 underordne+utvide (scen. 5) Kmax=1.310 Kend=1.162 Tmax=1.93 Tend=0.75 Lmin=0.670 Lend=0.750 tauD(end)= 0.4 tauDmax= 7.0 Qend=0.03 ups_end=0.98 amp(K,t>60)=0.396 topper [(24, 1.31), (61, 1.207), (95, 1.304)] bunner [(41, 0.969), (78, 0.949), (111, 0.908)] lineær analyse i sluttilstanden til scen. 2 (Lambda=0.657, T=1.85, K=1.28): mettet domstol a'=0.096 b'=0.158 tau_c'=17.7 mnd; samme tilstand uten metning a=0.172 b=0.316 tau_c=8.1 mnd === Del 3: robusthet (avsnitt 8.3 og 8.4) === --- (a) politimetning: lineær analyse i referanselikevekten (b uendret, a = 0.10 s + delta, s = 1/(1+1/K_sat)) --- K_sat= 1.0: s=0.500 a=0.070 b=0.300 tau_c=6.192 mnd (periode 21.5); stabil for alle tau hvis kp<=0.70; største stabile kp ved tau=11: 1.90 K_sat= 1.5: s=0.600 a=0.080 b=0.300 tau_c=6.366 mnd (periode 21.7); stabil for alle tau hvis kp<=0.80; største stabile kp ved tau=11: 1.98 K_sat= 3.0: s=0.750 a=0.095 b=0.300 tau_c=6.652 mnd (periode 22.1); stabil for alle tau hvis kp<=0.95; største stabile kp ved tau=11: 2.09 K_sat= inf: s=1.000 a=0.120 b=0.300 tau_c=7.210 mnd (periode 22.9); stabil for alle tau hvis kp<=1.20; største stabile kp ved tau=11: 2.28 oppklaringsintensitet h(K)/h(1) = (1+1/K_sat)/(1+K/K_sat) ved fast T: K_sat=1.5: K=1.3 -> 0.893, K=1.5 -> 0.833, K=2 -> 0.714 K_sat=3.0: K=1.3 -> 0.930, K=1.5 -> 0.889, K=2 -> 0.800 --- (a) grensetilfelle K_sat=inf: regime A-C og scenario 2 gjenskapes --- K_sat=inf p3: max|dK|=0.00e+00 max|dT|=0.00e+00 K_sat=inf p6: max|dK|=0.00e+00 max|dT|=0.00e+00 K_sat=inf p11: max|dK|=0.00e+00 max|dT|=0.00e+00 K_sat=inf scen. 2: max|dK|=0.00e+00 --- (a) regime A/B/C med politimetning (K_sat = 1.5 og 3; gamma rekalibrert) --- K_sat=3.0 regime A tau= 3.0: Kmax=1.125 Kmin=1.002 Tmax=1.37 Lmin=0.786 amp(K,t>60)=0.000 Kend=1.093 Lend=0.786 h(Kmax)/h(1)=0.970 | lin. etter sjokk: a=0.110 b=0.315 tau_c=6.5 K_sat=3.0 regime B tau= 6.0: Kmax=1.184 Kmin=1.002 Tmax=1.55 Lmin=0.784 amp(K,t>60)=0.121 Kend=1.129 Lend=0.787 h(Kmax)/h(1)=0.956 | lin. etter sjokk: a=0.106 b=0.323 tau_c=6.2 topper [(20, 1.184), (40, 1.17), (60, 1.157), (80, 1.146), (100, 1.137)] bunner [(30, 1.01), (50, 1.024), (70, 1.036), (90, 1.046), (110, 1.054)] K_sat=3.0 regime C tau=11.0: Kmax=1.472 Kmin=0.908 Tmax=2.42 Lmin=0.365 amp(K,t>60)=0.541 Kend=0.991 Lend=0.549 h(Kmax)/h(1)=0.894 | lin. etter sjokk: a=0.140 b=0.204 tau_c=15.6 topper [(24, 1.262), (56, 1.419), (83, 1.472), (109, 1.439)] bunner [(39, 0.908), (67, 0.932), (94, 0.981)] K_sat=1.5 regime A tau= 3.0: Kmax=1.131 Kmin=1.002 Tmax=1.39 Lmin=0.785 amp(K,t>60)=0.000 Kend=1.098 Lend=0.785 h(Kmax)/h(1)=0.950 | lin. etter sjokk: a=0.091 b=0.311 tau_c=6.3 K_sat=1.5 regime B tau= 6.0: Kmax=1.196 Kmin=1.002 Tmax=1.59 Lmin=0.783 amp(K,t>60)=0.152 Kend=1.136 Lend=0.787 h(Kmax)/h(1)=0.927 | lin. etter sjokk: a=0.081 b=0.318 tau_c=5.9 topper [(20, 1.196), (41, 1.186), (61, 1.177), (82, 1.167), (102, 1.16)] bunner [(30, 1.005), (51, 1.016), (71, 1.025), (92, 1.033), (112, 1.041)] K_sat=1.5 regime C tau=11.0: Kmax=1.514 Kmin=0.900 Tmax=2.54 Lmin=0.326 amp(K,t>60)=0.557 Kend=0.999 Lend=0.484 h(Kmax)/h(1)=0.829 | lin. etter sjokk: a=0.106 b=0.181 tau_c=14.9 topper [(24, 1.285), (56, 1.479), (83, 1.513), (108, 1.455)] bunner [(39, 0.9), (67, 0.958), (94, 1.02)] --- (a) MPC (regime D, tau=11) når det styrte systemet er mettet, men MPC-ens interne modell ikke er det --- K_sat=3.0: Kmax=1.254 Kend=1.041 Tmax=1.39 Tend=1.32 Lmin=0.780 Lend=0.794 amp(K,t>60)=0.006 (K_sat=inf: Kmax=1.224 Kend=1.031 Lmin=0.783) K_sat=1.5: Kmax=1.273 Kend=1.051 Tmax=1.39 Tend=1.32 Lmin=0.778 Lend=0.792 amp(K,t>60)=0.011 (K_sat=inf: Kmax=1.224 Kend=1.031 Lmin=0.783) --- (a) kjedescenarioer (regime A) med politimetning: Kend / Lend / tauD(end) / Tend / R_D-andel --- K_sat= inf: s2: 1.284/0.657/53.8/1.85 | s3: 1.172/0.707/15.3/1.51 | s4: 1.146/0.724/10.2/1.44 | s5: 1.087/0.787/ 1.0/1.26 K_sat= 3.0: s2: 1.316/0.653/52.7/1.95 | s3: 1.187/0.706/14.8/1.56 | s4: 1.157/0.724/ 9.8/1.47 | s5: 1.094/0.786/ 1.0/1.28 K_sat= 1.5: s2: 1.338/0.650/52.0/2.01 | s3: 1.197/0.705/14.5/1.59 | s4: 1.164/0.724/ 9.5/1.49 | s5: 1.099/0.785/ 1.0/1.30 --- (b) domstol med to sakstyper: kontrolltall --- FIFO, theta_A=theta_B=0.5, c=1: max|dK| mot scenario 2 = 2.22e-15, max|dtau| = 2.77e-13 FIFO, theta_A=0.8, theta_B=0.3 (vektet 0.5): Kend=1.300 (scen. 2: 1.284), tau(end)=57.4 kalibrert m: c=1 -> 0.2330 (Del 2: 0.2330); c=10 -> 1.540 mnd; M/M/10: tau ved ups=0.8: 1.85 c=10, FIFO: tau_ref=3.00 mnd --- FIFO, c=1 (referanse, vektet theta) --- 2 flaskehals, ingen tiltak Kend=1.300 KA_end=0.609 KB_end=0.691 Lend=0.654 Tend=1.90 tauA(end)= 57.4 tauB(end)= 57.4 tauAmax=57.4 tauBmax= 57.4 QA=2.82 QB=3.20 3 underordne (B: xi_B 1->0.67) Kend=1.190 KA_end=0.511 KB_end=0.679 Lend=0.697 Tend=1.57 tauA(end)= 18.9 tauB(end)= 18.9 tauAmax=18.9 tauBmax= 18.9 QA=1.04 QB=0.92 4 utvide Kend=1.147 KA_end=0.469 KB_end=0.678 Lend=0.723 Tend=1.44 tauA(end)= 10.4 tauB(end)= 10.4 tauAmax=12.5 tauBmax= 12.5 QA=0.58 QB=0.84 5 begge Kend=1.087 KA_end=0.436 KB_end=0.651 Lend=0.787 Tend=1.26 tauA(end)= 1.0 tauB(end)= 1.0 tauAmax= 8.5 tauBmax= 8.5 QA=0.05 QB=0.05 6 TBT via T (J_D <= 0.95 Z_D) Kend=2.659 KA_end=1.070 KB_end=1.589 Lend=0.563 Tend=0.53 tauA(end)= 3.0 tauB(end)= 3.0 tauAmax= 3.0 tauBmax= 3.0 QA=0.12 QB=0.17 scen. 2: tau_ref A/B = 3.00/3.00; tauA@48=22.9 tauB@48=22.9; RA_end=0.049 RB_end=0.056 frafall B=0.032 --- prioritet, c=1 --- 2 flaskehals, ingen tiltak Kend=1.182 KA_end=0.399 KB_end=0.783 Lend=0.709 Tend=1.55 tauA(end)= 0.5 tauB(end)= 71.2 tauAmax= 0.5 tauBmax= 71.2 QA=0.03 QB=3.61 3 underordne (B: xi_B 1->0.67) Kend=1.131 KA_end=0.423 KB_end=0.708 Lend=0.737 Tend=1.39 tauA(end)= 0.5 tauB(end)= 15.9 tauAmax= 0.5 tauBmax= 15.9 QA=0.03 QB=0.80 4 utvide Kend=1.107 KA_end=0.430 KB_end=0.678 Lend=0.758 Tend=1.32 tauA(end)= 0.4 tauB(end)= 6.5 tauAmax= 0.5 tauBmax= 13.3 QA=0.02 QB=0.55 5 begge Kend=1.086 KA_end=0.435 KB_end=0.651 Lend=0.787 Tend=1.26 tauA(end)= 0.4 tauB(end)= 0.6 tauAmax= 0.5 tauBmax= 11.3 QA=0.02 QB=0.03 6 TBT via T (J_D <= 0.95 Z_D) Kend=2.616 KA_end=1.045 KB_end=1.571 Lend=0.569 Tend=0.54 tauA(end)= 0.4 tauB(end)= 2.3 tauAmax= 0.4 tauBmax= 2.3 QA=0.01 QB=0.13 scen. 2: tau_ref A/B = 0.37/2.26; tauA@48=0.5 tauB@48=30.0; RA_end=0.054 RB_end=0.051 frafall B=0.036 --- FIFO, c=10 --- 2 flaskehals, ingen tiltak Kend=1.300 KA_end=0.609 KB_end=0.691 Lend=0.654 Tend=1.90 tauA(end)= 56.9 tauB(end)= 56.9 tauAmax=56.9 tauBmax= 56.9 QA=2.79 QB=3.18 3 underordne (B: xi_B 1->0.67) Kend=1.187 KA_end=0.508 KB_end=0.679 Lend=0.699 Tend=1.56 tauA(end)= 18.0 tauB(end)= 18.0 tauAmax=18.0 tauBmax= 18.0 QA=0.99 QB=0.89 4 utvide Kend=1.140 KA_end=0.464 KB_end=0.677 Lend=0.728 Tend=1.42 tauA(end)= 9.4 tauB(end)= 9.4 tauAmax=12.1 tauBmax= 12.1 QA=0.53 QB=0.77 5 begge Kend=1.088 KA_end=0.438 KB_end=0.650 Lend=0.787 Tend=1.26 tauA(end)= 1.7 tauB(end)= 1.7 tauAmax= 8.3 tauBmax= 8.3 QA=0.09 QB=0.09 6 TBT via T (J_D <= 0.95 Z_D) Kend=2.659 KA_end=1.070 KB_end=1.589 Lend=0.563 Tend=0.53 tauA(end)= 3.0 tauB(end)= 3.0 tauAmax= 3.0 tauBmax= 3.0 QA=0.12 QB=0.17 scen. 2: tau_ref A/B = 3.00/3.00; tauA@48=22.5 tauB@48=22.5; RA_end=0.049 RB_end=0.056 frafall B=0.032 --- prioritet, c=10 --- 2 flaskehals, ingen tiltak Kend=1.182 KA_end=0.401 KB_end=0.781 Lend=0.710 Tend=1.55 tauA(end)= 1.6 tauB(end)= 70.2 tauAmax= 1.6 tauBmax= 70.2 QA=0.08 QB=3.58 3 underordne (B: xi_B 1->0.67) Kend=1.130 KA_end=0.425 KB_end=0.704 Lend=0.739 Tend=1.39 tauA(end)= 1.6 tauB(end)= 14.9 tauAmax= 1.6 tauBmax= 14.9 QA=0.08 QB=0.76 4 utvide Kend=1.104 KA_end=0.434 KB_end=0.670 Lend=0.763 Tend=1.31 tauA(end)= 1.5 tauB(end)= 5.6 tauAmax= 1.6 tauBmax= 13.0 QA=0.08 QB=0.47 5 begge Kend=1.088 KA_end=0.437 KB_end=0.651 Lend=0.787 Tend=1.26 tauA(end)= 1.5 tauB(end)= 1.6 tauAmax= 1.6 tauBmax= 11.4 QA=0.08 QB=0.08 6 TBT via T (J_D <= 0.95 Z_D) Kend=2.634 KA_end=1.056 KB_end=1.578 Lend=0.566 Tend=0.54 tauA(end)= 1.5 tauB(end)= 2.4 tauAmax= 1.5 tauBmax= 2.4 QA=0.06 QB=0.14 scen. 2: tau_ref A/B = 1.54/2.43; tauA@48=1.6 tauB@48=29.5; RA_end=0.054 RB_end=0.051 frafall B=0.036 tabell (K, K_A/0.4, K_B/0.6, Lambda, tauA, tauB): FIFO, c=1 (referanse, vektet theta) scen.2: K=1.300 K_A/0.4=1.524 K_B/0.6=1.151 L=0.654 tauA=57.42 tauB=57.42 FIFO, c=1 (referanse, vektet theta) scen.3: K=1.190 K_A/0.4=1.278 K_B/0.6=1.132 L=0.697 tauA=18.89 tauB=18.89 FIFO, c=1 (referanse, vektet theta) scen.4: K=1.147 K_A/0.4=1.172 K_B/0.6=1.131 L=0.723 tauA=10.35 tauB=10.35 FIFO, c=1 (referanse, vektet theta) scen.5: K=1.087 K_A/0.4=1.090 K_B/0.6=1.085 L=0.787 tauA=0.96 tauB=0.96 FIFO, c=1 (referanse, vektet theta) scen.6: K=2.659 K_A/0.4=2.674 K_B/0.6=2.649 L=0.563 tauA=3.00 tauB=3.00 prioritet, c=1 scen.2: K=1.182 K_A/0.4=0.999 K_B/0.6=1.305 L=0.709 tauA=0.48 tauB=71.25 prioritet, c=1 scen.3: K=1.131 K_A/0.4=1.057 K_B/0.6=1.180 L=0.737 tauA=0.48 tauB=15.88 prioritet, c=1 scen.4: K=1.107 K_A/0.4=1.074 K_B/0.6=1.129 L=0.758 tauA=0.38 tauB=6.52 prioritet, c=1 scen.5: K=1.086 K_A/0.4=1.087 K_B/0.6=1.086 L=0.787 tauA=0.38 tauB=0.60 prioritet, c=1 scen.6: K=2.616 K_A/0.4=2.613 K_B/0.6=2.619 L=0.569 tauA=0.37 tauB=2.26 FIFO, c=10 scen.2: K=1.300 K_A/0.4=1.522 K_B/0.6=1.151 L=0.654 tauA=56.91 tauB=56.91 FIFO, c=10 scen.3: K=1.187 K_A/0.4=1.271 K_B/0.6=1.131 L=0.699 tauA=17.99 tauB=17.99 FIFO, c=10 scen.4: K=1.140 K_A/0.4=1.160 K_B/0.6=1.128 L=0.728 tauA=9.35 tauB=9.35 FIFO, c=10 scen.5: K=1.088 K_A/0.4=1.094 K_B/0.6=1.084 L=0.787 tauA=1.74 tauB=1.74 FIFO, c=10 scen.6: K=2.659 K_A/0.4=2.674 K_B/0.6=2.649 L=0.563 tauA=3.00 tauB=3.00 prioritet, c=10 scen.2: K=1.182 K_A/0.4=1.003 K_B/0.6=1.302 L=0.710 tauA=1.55 tauB=70.23 prioritet, c=10 scen.3: K=1.130 K_A/0.4=1.063 K_B/0.6=1.174 L=0.739 tauA=1.55 tauB=14.86 prioritet, c=10 scen.4: K=1.104 K_A/0.4=1.084 K_B/0.6=1.117 L=0.763 tauA=1.54 tauB=5.56 prioritet, c=10 scen.5: K=1.088 K_A/0.4=1.093 K_B/0.6=1.084 L=0.787 tauA=1.54 tauB=1.58 prioritet, c=10 scen.6: K=2.634 K_A/0.4=2.639 K_B/0.6=2.631 L=0.566 tauA=1.54 tauB=2.43 merbelastning mot scen. 1 (1.086): FIFO 0.214, prioritet 0.097; tillitstap mot scen. 1 (0.787): FIFO 0.133, prioritet 0.078 --- (b) regime C (tau=11) med to sakstyper: lånt stabilitet med og uten forrang --- FIFO, c=1 scen. 2: amp(K,t>60)=0.049 topper [(26, 1.324), (61, 1.317), (96, 1.308)] bunner [(42, 1.194), (77, 1.268), (112, 1.293)] Lmin=0.654 tauB(end)=57 prioritet, c=1 scen. 2: amp(K,t>60)=0.209 topper [(25, 1.281), (58, 1.292), (91, 1.285)] bunner [(41, 1.053), (74, 1.077), (108, 1.089)] Lmin=0.703 tauB(end)=61 --- (c) rekruttering/smitte: Omega_soc = eps K^p/(K_h^p+K^p), eps=0.30 K_h=2.0 p=4 --- Omega_0'=0.1024; eps*H'(1)=0.0664 -> a_eff = a - eps H'(1) = 0.0536 (mot 0.12); max H' ved K=1.760: 0.5326, nødvendig betingelse eps > a/max H' = 0.225 likevekter, fast T=1 (åpen sløyfe): [1. 1.668 2.883] (lav stabil, vippepunkt, høy stabil) likevekter med P-regel kp=3.0 og T<= 3.0: [1.] likevekter med P-regel kp=1.0 og T<= 3.0: [1.] likevekter med P-regel kp=3.0 og T<= 1.5: [1.] likevekter med P-regel kp=3.0 og T<= 1.2: [1.] likevekter med P-regel kp=3.0 og T<= 1.1: [1.] likevekter med P-regel kp=3, T<=1.5 og politimetning K_sat=1.5: [1. 2.023 5.232] likevekter, fast T=1 og politimetning K_sat=1.5: [1. 1.124 9.319] lineær analyse i K=1 med rekruttering: a=0.0536 b=0.30 tau_c=5.93 mnd (mot 7.21) simulering: forbigående sjokk Omega x1.6 i mnd 12-36 fast T=1 K@36=2.778 K@48=3.415 Kmax=5.634 Kend=5.634 Tmax=1.00 Tend=1.00 Lmin=0.400 Lend=0.400 P kp=3 tau=3 K@36=1.162 K@48=1.024 Kmax=1.242 Kend=1.000 Tmax=1.73 Tend=1.00 Lmin=0.778 Lend=0.800 P kp=3 tau=6 K@36=1.300 K@48=0.836 Kmax=1.398 Kend=1.116 Tmax=2.19 Tend=0.57 Lmin=0.652 Lend=0.802 P kp=3 tau=3, T<=1.5, K_sat=1.5 K@36=1.682 K@48=1.409 Kmax=1.682 Kend=1.000 Tmax=1.50 Tend=1.00 Lmin=0.725 Lend=0.800 P kp=3 tau=6, T<=1.5, K_sat=1.5 K@36=2.407 K@48=3.383 Kmax=9.820 Kend=9.820 Tmax=1.50 Tend=1.50 Lmin=0.400 Lend=0.400 === Del 4: endogene tiltak -- fra observasjon til beslutning (avsnitt 8.5) === --- grensetilfelle: faste tidsplaner gjenskaper scenario 2 og 5 --- sched = scen. 2: max|dK|=0.00e+00 max|dtauD|=0.00e+00 sched = scen. 5: max|dK|=0.00e+00 max|dtauD|=0.00e+00 --- beslutningsregler, regime A (kp=3, tau=3), 180 måneder (tabell og figur i 8.5) --- parametre: lagD=3.0, xi_min=0.8, tau_thr=6.0, k_xi=0.0167/mnd, tau_xi=6.0, ups*=0.95, dødsone [0.85, 1.0], kZ=1.0, realisering [6, 24] mnd, tau_down=36.0, T_clear=24.0, H_pred=36.0 2 flaskehals, ingen tiltak Kmean=1.259 Kend=1.290 Lmin=0.651 Lend=0.651 tauDmax= 68.7 tauDend=68.7 Zmax=1.00 Zend=1.00 xi_min=1.00 xi_end=1.00 frafall=7.32 kap.år=0.00 Tend=1.87 5 faste vedtak (mnd 24) Kmean=1.092 Kend=1.087 Lmin=0.749 Lend=0.787 tauDmax= 8.2 tauDend= 1.0 Zmax=1.34 Zend=1.34 xi_min=0.80 xi_end=0.80 frafall=0.44 kap.år=4.08 Tend=1.26 desentralisert (observert strøm) Kmean=1.106 Kend=1.095 Lmin=0.719 Lend=0.786 tauDmax= 13.4 tauDend= 2.6 Zmax=1.75 Zend=1.36 xi_min=0.80 xi_end=1.00 frafall=1.03 kap.år=4.85 Tend=1.28 mnd 24: bestill +27 % (ups_obs=1.21) mnd 36: bestill +48 % (ups_obs=1.52) mnd 60: bygg ned mot 1.05 (ups_obs=0.57) mnd 72: bygg ned mot 0.79 (ups_obs=0.49) mnd 96: bestill +18 % (ups_obs=1.10) mnd 108: bestill +13 % (ups_obs=1.14) mnd 144: bygg ned mot 1.28 (ups_obs=0.82) mnd 156: bygg ned mot 1.27 (ups_obs=0.84) desentralisert, kZ=0.5 Kmean=1.114 Kend=1.109 Lmin=0.714 Lend=0.785 tauDmax= 14.8 tauDend= 2.2 Zmax=1.50 Zend=1.25 xi_min=0.80 xi_end=0.97 frafall=1.24 kap.år=3.75 Tend=1.31 mnd 24: bestill +13 % (ups_obs=1.21) mnd 36: bestill +31 % (ups_obs=1.59) mnd 48: bestill +6 % (ups_obs=1.20) mnd 72: bygg ned mot 0.95 (ups_obs=0.60) mnd 84: bygg ned mot 0.90 (ups_obs=0.63) mnd 108: bestill +13 % (ups_obs=1.17) mnd 120: bestill +15 % (ups_obs=1.26) mnd 132: bestill +9 % (ups_obs=1.15) mnd 156: bygg ned mot 1.04 (ups_obs=0.66) mnd 168: bygg ned mot 0.95 (ups_obs=0.66) desentralisert med prognose Kmean=1.099 Kend=1.092 Lmin=0.724 Lend=0.786 tauDmax= 12.2 tauDend= 2.9 Zmax=1.76 Zend=1.36 xi_min=0.80 xi_end=1.00 frafall=0.78 kap.år=5.67 Tend=1.28 mnd 24: bestill +47 % (F_pred=0.134 Q_exc=0.30) mnd 36: bestill +29 % (F_pred=0.134 Q_exc=0.99) mnd 60: bygg ned mot 1.34 (F_pred=0.134 Q_exc=0.00) mnd 72: bygg ned mot 1.34 (F_pred=0.134 Q_exc=0.00) mnd 84: bygg ned mot 1.34 (F_pred=0.134 Q_exc=0.00) koordinert (T_clear=24) Kmean=1.098 Kend=1.090 Lmin=0.743 Lend=0.786 tauDmax= 8.3 tauDend= 3.0 Zmax=1.31 Zend=1.31 xi_min=0.80 xi_end=0.96 frafall=0.83 kap.år=3.52 Tend=1.27 mnd 24: bestill +19 % (F_pred=0.134 Q_exc=0.27) mnd 36: bestill +12 % (F_pred=0.134 Q_exc=0.56) koordinert (T_clear=12) Kmean=1.096 Kend=1.090 Lmin=0.746 Lend=0.786 tauDmax= 8.1 tauDend= 3.0 Zmax=1.53 Zend=1.35 xi_min=0.80 xi_end=0.99 frafall=0.70 kap.år=4.66 Tend=1.27 mnd 24: bestill +30 % (F_pred=0.134 Q_exc=0.27) mnd 36: bestill +23 % (F_pred=0.134 Q_exc=0.54) mnd 60: bygg ned mot 1.34 (F_pred=0.134 Q_exc=0.00) koordinert (T_clear=48) Kmean=1.102 Kend=1.090 Lmin=0.740 Lend=0.787 tauDmax= 8.5 tauDend= 3.0 Zmax=1.19 Zend=1.19 xi_min=0.80 xi_end=0.88 frafall=0.86 kap.år=2.22 Tend=1.27 mnd 24: bestill +13 % (F_pred=0.134 Q_exc=0.27) mnd 36: bestill +6 % (F_pred=0.134 Q_exc=0.58) koordinert (T_clear=inf) Kmean=1.128 Kend=1.118 Lmin=0.735 Lend=0.751 tauDmax= 8.8 tauDend= 6.0 Zmax=1.07 Zend=1.07 xi_min=0.80 xi_end=0.80 frafall=1.35 kap.år=0.88 Tend=1.36 mnd 24: bestill +7 % (F_pred=0.134 Q_exc=0.28) koordinert + kvalitetssløyfe Kmean=1.095 Kend=1.090 Lmin=0.743 Lend=0.787 tauDmax= 8.3 tauDend= 3.0 Zmax=1.31 Zend=1.31 xi_min=0.80 xi_end=0.96 frafall=0.83 kap.år=3.52 Tend=1.27 mnd 24: bestill +19 % (F_pred=0.134 Q_exc=0.27) mnd 36: bestill +12 % (F_pred=0.134 Q_exc=0.56) desentralisert + kvalitetssløyfe Kmean=1.100 Kend=1.094 Lmin=0.721 Lend=0.788 tauDmax= 13.4 tauDend= 2.6 Zmax=1.75 Zend=1.36 xi_min=0.80 xi_end=1.00 frafall=1.02 kap.år=4.88 Tend=1.28 mnd 24: bestill +27 % (ups_obs=1.21) mnd 36: bestill +48 % (ups_obs=1.52) mnd 60: bygg ned mot 1.05 (ups_obs=0.57) mnd 72: bygg ned mot 0.80 (ups_obs=0.49) mnd 96: bestill +18 % (ups_obs=1.10) mnd 108: bestill +13 % (ups_obs=1.14) mnd 144: bygg ned mot 1.28 (ups_obs=0.81) mnd 156: bygg ned mot 1.28 (ups_obs=0.85) des: xi<0.99 fra mnd 31, xi<0.81 fra mnd 54, kapasitet øker fra mnd 30, xi>0.9 igjen fra mnd 79; J_D ved mnd 33 (budsjettsignal)=0.173, ups ved mnd 60=0.44 ko: xi<0.99 fra mnd 17, xi<0.81 fra mnd 36, kapasitet øker fra mnd 30, xi>0.9 igjen fra mnd 62; J_D ved mnd 33 (budsjettsignal)=0.124, ups ved mnd 60=0.80 des: kapasitetstopper [(60, 1.75)] bunner []; K-topper [(32, 1.202), (72, 1.129), (105, 1.137)] des: Z/Z0 og xi ved mnd 36: 1.09/0.95, 48: 1.43/0.83, 60: 1.75/0.80, 72: 1.55/0.83, 96: 1.18/0.99, 108: 1.24/1.00, 120: 1.41/1.00, 138: 1.49/1.00, 150: 1.46/1.00, 180: 1.36/1.00 ko: Z/Z0 og xi ved mnd 36: 1.06/0.81, 48: 1.23/0.80, 60: 1.31/0.87, 72: 1.31/0.98, 96: 1.31/0.96, 108: 1.31/0.96, 120: 1.31/0.96, 138: 1.31/0.96, 150: 1.31/0.96, 180: 1.31/0.96 ko: tauD topp=8.3 ved mnd 33; des: tauD topp=13.4 ved mnd 39; ko: Lend(120)=0.786, koq: Lend(120)=0.801, koq: qmax=0.069 --- ren kapasitetssløyfe med gitt innstrømning (J=0.134): Z/Z_behov, bestilt kapasitet regnet med / ikke regnet med --- L2=24 kZ=0.5: bevilget regnes med : Zmax=1.00 amp(100-300)=0.003 amp(>300)=0.000; Hayes a=0, b=kZ/12, tau_Z=(L1+L2)/2: stabil hvis kZ < 1.26 L2=24 kZ=0.5: bare realisert : Zmax=1.03 amp(100-300)=0.003 amp(>300)=0.000; Hayes a=0, b=kZ/12, tau_Z=(L1+L2)/2: stabil hvis kZ < 1.26 L2=24 kZ=1.0: bevilget regnes med : Zmax=1.00 amp(100-300)=0.000 amp(>300)=0.000; Hayes a=0, b=kZ/12, tau_Z=(L1+L2)/2: stabil hvis kZ < 1.26 L2=24 kZ=1.0: bare realisert : Zmax=1.15 amp(100-300)=0.077 amp(>300)=0.003; Hayes a=0, b=kZ/12, tau_Z=(L1+L2)/2: stabil hvis kZ < 1.26 L2=36 kZ=0.5: bevilget regnes med : Zmax=1.00 amp(100-300)=0.004 amp(>300)=0.000; Hayes a=0, b=kZ/12, tau_Z=(L1+L2)/2: stabil hvis kZ < 0.90 L2=36 kZ=0.5: bare realisert : Zmax=1.07 amp(100-300)=0.052 amp(>300)=0.001; Hayes a=0, b=kZ/12, tau_Z=(L1+L2)/2: stabil hvis kZ < 0.90 L2=36 kZ=1.0: bevilget regnes med : Zmax=1.00 amp(100-300)=0.000 amp(>300)=0.000; Hayes a=0, b=kZ/12, tau_Z=(L1+L2)/2: stabil hvis kZ < 0.90 L2=36 kZ=1.0: bare realisert : Zmax=1.21 amp(100-300)=0.348 amp(>300)=0.183; Hayes a=0, b=kZ/12, tau_Z=(L1+L2)/2: stabil hvis kZ < 0.90