{VERSION 6 0 "IBM INTEL LINUX" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Headi ng 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 2 1 0 1 0 2 2 0 1 }{PSTYLE "Title" 0 18 1 {CSTYLE "" -1 -1 "" 1 30 0 0 0 0 0 1 2 0 0 0 0 0 0 0 }3 0 0 -1 12 12 0 0 0 0 0 0 19 0 }{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 " Times" 1 12 128 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 258 1 {CSTYLE "" -1 -1 "Times" 1 16 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Title" -1 259 1 {CSTYLE "" -1 -1 "Times" 1 24 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }3 1 0 0 12 12 3 0 3 0 2 2 19 1 }{PSTYLE "Maple Output" -1 260 1 {CSTYLE " " -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 18 "" 0 "" {TEXT -1 32 "Simulation de files d'attente 07" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "with(pldx): with(simul): xma cro(): seed=_seed;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {SECT 0 {PARA 3 "" 0 "" {TEXT -1 21 "A int\351grer dans simul" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 393 "compar_histo:= proc(ex::lis t, th::list) global mihis; local nn, mi; nn:= nops(th);\nif map2(op,1, ex) <> map2(op,1,th) then error `: les deux structures n'ont pas le m \352me support` fi;\nmihis:= [seq(Weight( op(1,th[j]), min(op(2,th[j]) ,op(2,ex[j]))), j=1..nn)]; \ndisplay(xhisto(mihis, color=grey, args[ 3..-1]), xhisto(ex, color=cyan, args[3..-1]) \n, xhisto(th, color=yell ow, args[3..-1]));\nend: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "kernelopts(ASSERT=true);" }}}{EXCHG }{EXCHG }{EXCHG }{EXCHG }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 50 "La variabilit\351 est la cause du ph\351nom\350ne d'atten te" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 56 "Tr\350s faible variabilit \351 : il ne se produit pas d'attente" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "2: arv:= 20-%+2*%*ra; 1: srv:= 15-%+2*%*ra;\nraz_file(); # _seed :=123 ; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "xprint(new_clie nt);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "to 6 do evol_file() ; agenda, charge; od;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 65 "Faible v ariabilit\351 : la probabilit\351 d'une attente est tr\350s faible" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 133 "4: arv:= 20-%+2*%*ra; 2: srv:= 15- %+2*%*ra; \nraz_file(): # _seed:=1234; \nto 10000 do evol_file(); od : agenda, charge; eval(durees);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "[seq(durees[k], k=0..nops([indices(durees)])-1)]: evalf(%/add( k,k=%),3);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 69 "Quand la variabilit \351 augmente, la probabilit\351 d'une attente augmente" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 135 "10: arv:= 20-%+2*%*ra; 7: srv:= 15-%+2*%*ra; \nraz_file(): # _seed:=1234; \nto 10000 do evol_file(); od: agenda , charge; eval(durees);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 " [seq(durees[k], k=0..nops([indices(durees)])-1)]: evalf(%/add(k,k=%), \+ 3);" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 20 "Etude d'une file U/U" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 69 "Quand la variabilit\351 augmente, la probabilit\351 d'un e attente augmente" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 167 "15: arv:= 20 -%+2*%*ra; 10: srv:= 15-%+2*%*ra; \nraz_file(): _seed:=123456; \nto 40000 do evol_file(); od: \nwhile nops(agenda)>1 do evol_file(); od: \+ 'numcli'= numcli; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "dur:= [seq(Weight(k, durees[k]), k=0..nops([indices(durees)])-1)];" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 117 "durtot:= nbr(dur); \nhisto_ dur:= [seq(Weight(k-1/2..k+1/2, durees[k]*numcli/durtot), k=0..nops([i ndices(durees)])-1)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "ma p2(op,2,dur)/durtot: evalf(%,4);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 145 "aut:= \+ stats[transform, tally] ([seq(autres[k], k=1..numcli)]);\nhisto_aut:= \+ stats[transform, tallyinto](%, [seq(k-1/2..k+1/2, k=0..nops(dur)-1)]); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 35 "map2(op,2,aut)/numcli: evalf(%,4); " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "[op(2,aut[1]), round(op(2,hi sto_dur[1]))];\nmap(proc(z) z= evalf(z/numcli,2) end, %);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "compar_histo(histo_aut, histo_dur, \+ area=count, axes=boxed, tickmarks=[[0,2,4,6],%]);" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 21 "coeff(eval(srv), ra);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 76 "att:= [seq(attentes[j], j=1..numcli)]:\nsej:= \+ [seq(sejours[j], j=1..numcli)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "moy(sej), moy(att), var(sej), var(att);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 30 "att_cond:= subs(0.=NULL, att):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "(nbr, moy, var)(att_cond);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 150 "bb:= (max@op)(att):\n4: les _interv:= [-10..0.001, 0.001..%, seq(%*j..%*j+%, j=1..floor(bb/%))];\n att_tal:= stats[transform, tallyinto](att, les_interv);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "nbr(att_tal);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 524 "att_tal := [Weight(-27 .. -10,10286), Weight (.0 .. 4,2309), Weight(4 .. 8,2030), Weight(8 .. 12,1715), Weight(12 . . 16,1261), Weight(16 .. 20,798), Weight(20 .. 24,541), Weight(24 .. 2 8,325), Weight(28 .. 32,226), Weight(32 .. 36,172), Weight(36 .. 40,87 ), Weight(40 .. 44,104), Weight(44 .. 48,45), Weight(48 .. 52,35), Wei ght(52 .. 56,17), Weight(56 .. 60,17), Weight(60 .. 64,11), Weight(64 \+ .. 68,7), Weight(68 .. 72,5), Weight(72 .. 76,5), Weight(76 .. 80,1), \+ Weight(80 .. 84,0), Weight(84 .. 88,2), Weight(88 .. 92,1)];" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "xhisto(att_tal, area=4, tic kmarks=[[-18.5=`none`,seq(k*20=k*20, k=0..5)],[0=0,0.05=0.05,0.1=\"0.1 0\"]]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "autt:= [seq(autr es[k], k=1..numcli)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "au tt0:= subs(0=NULL, autt): att0:= subs(0.=NULL, att):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "nops(autt0), nops(att0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "moy(sej); moy(dur) ; %%/%;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 8 "r\351siduel " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "resi:= [seq(resid[k], k= 1..numcli)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "moy(resi); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "resi0:= subs(0=NULL, re si): (nbr, moy)(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "2: l es_interv0:= [seq(%*j..%*j+%, j=0..floor(25/%))];" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 59 "resi_tal:= stats[transform, tallyinto](resi0 , les_interv0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "1680./nb r(resi_tal);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "display(xh isto(resi_tal, area=2), plot((25-x)/25^2*4, x=0..25),\ntickmarks=[[$0. .2]*10,[0,0.1,0.173]]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "25*0.08/2; 3877=a*0.1+b, 6124=a*.173+b, z=a*0+b; solve(\{%\});\n2115. =a*10+b, 4038=a*25+b, z=a*0+b; solve(\{%\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 128 "subsop(1=NULL, aut): a:= nbr(%);\nb:= op(2, aut [2]);\nsubsop(1=NULL, 2=NULL, aut): c:= nbr(%)* (moy(%)-1);\nss:= conv ert(sej, `+`);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "numcli*15 +c*15+a*x=ss; solx:= (op@solve)(\{%\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "macro(H=Heaviside):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "eval(srv), eval(arv);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "piecewise(x<5,0,x<25,1/20,0): fs:= unapply(convert(%, H),x);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "Int(x*fs(x), x=-infinity. .infinity); value(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 107 "p iecewise(x<5,0,x<35,1/30,0): fa:= unapply(convert(%,H),x);\nInt(x*fa(x ), x=-infinity..infinity); value(%);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 167 "forget(int, H): Int(fs(t+alpha)*fa(t), t=5..35);\n(y joli@xjoli@expand)(%); xplif(%, [t-5, positive, t-35, negative, alpha, positive]);\nvalue(%); gg:= unapply(%, alpha);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 89 "Int(gg(t), t=0..20):%= value(%);; Int(t*gg(t), t=0..20)/Int(gg(t), t=0..20): %= value(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "Int(t*t*fs(t), t=0.. infinity)/Int(t*fs(t), t=0.. \+ infinity); value(%)*1.;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "subsop(1=NULL, 2=NULL, aut): nbr(%);\n(op(2, aut[2])*``(20/3.)+%*``( 17.22222222/2))/(7478+2237);\nexpand(%); " }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 6 "PolKin" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "a:= unapply(lambda*exp(-lamb da*t),t);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 52 "GeM gen\350re les mo ments de la variable inter-arriv\351es" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 149 "Sum(z^n/n!*Int(t^n*a(t), t=0..infinity), n=0..infinity);\n(xj oli@xfubini)(%); (yjoli@xvalval)(%); xplif(%, [lambda-z, positive]);\n GeM:= unapply(%, z);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }{SECT 1 {PARA 4 "" 0 "" {TEXT -1 32 "Le nombre de clients est Poisson " }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "Definition des probabilit\351s Pr" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 206 "recur:= Pr(k+1, T)=Int(Pr(k ,t)*a(T-t), t=0..T);\nSum(s^k*Pr(k,t), k=0..infinity); defGK:= %= GK(s ,t);\niniPr_k0:= Pr(0,0)=1, Pr(k+1,0)=0;\niniPr_0T:= Pr(0,T)=xplif(Int (a(t),t=T..infinity), [lambda, positive]);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 65 "xavance(defGK); iniGK:= ((rhs=lhs)@value@subs)(t=0, iniPr_k0, %);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 146 "recur; m ap(ZZ-> Sum(s^(k+1)*ZZ, k=0..infinity),%); %- subs(t=T, xavance(defGK) );\n(yjoli@xjoli@expand@xfubini)(%); eqdi:= subs(defGK, iniPr_0T, %); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "diff(eqdi, T); (normal@ yjoli@xjoli)(%+lambda*eqdi); eqd:= collect(%, [diff, GK]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 112 "pdsolve(eqd); subs(T=0, iniGK, %); valGK:= (expand@subs)(solve(\{%\}, _F1(s)), %%);\nseries( combine(rhs (%)),s,4); " }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 30 "Nombre de clients dans la file" }} {EXCHG {PARA 0 "" 0 "" {TEXT -1 140 "X(n) est le nombre de clients arr iv\351s durant le s\351jour, probabilit\351 p\nZ(n) est le nombre de c lients arriv\351s durant le service, probabilit\351 q" }}{PARA 0 "" 0 "" {TEXT -1 73 "Si X(n)=0 alors X(n+1)=Z(n+1)\nSinon \+ X(n+1)=Z(n+1)+X(n)-1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "def Gp:= Sum(p(k)*s^k,k=0..infinity)=Gp(s);\ndefGq:= Sum(q(k)*s^k,k=0..inf inity)=Gq(s);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "recur:= p( k)= p(0)*q(k)+Sum(p(j+1)*q(k-j), j=0..k);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 106 "recur: map(ZZ-> Sum(s^(k)*ZZ, k=0..infinity),%);\n (yjoli@xjoli@expand)(%); recur1:= subs(defGp, defGq, %); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "lhs(defGp), lhs(defGq); " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "(xcombipo@xavance@combine@ex pand)((lhs(defGp)-p(0))/s), lhs(defGq);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 127 "subs(k=j, n=k, xcauchy(%)) = ((rhs(defGp)-p(0))/s)*rhs(defGq) ;\nsubs( (yjoli@xjoli)(%), recur1);\nvalGp:= (op@solve)(%, \{Gp(s)\}); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "Gq(s)=Int(g(t)*GK(s,T), t=0..infinity); valGq:= (xcombipo@subs)(valGK, T=t, %);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 117 "paramsg:= Int(g(t),t = 0 .. infini ty)=1, Int(g(t)*t,t = 0 .. infinity)=M1(g),\n Int(g(t)*t^2,t = 0 .. in finity)=M2(g);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 186 "subs(val Gq, valGp);\nrhs(%); exp(lambda*t*s-lambda*t): subs(%=mtaylor(%, s=1,3 ), %%);\nmap(yjoli@xjoli@expand, %); (factor@subs)(paramsg, %);\ntmp:= (factor@subs)(s=1, lambda=rho/M1(g), %);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 41 "valp0:= (expand@op@solve)(tmp=1, \{p(0)\});" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 183 "subs(valGq, valGp);\ndiff(r hs(%),s): exp(lambda*t*s-lambda*t): subs(%=mtaylor(%, s=1,3), %%):\nma p(yjoli@xjoli@expand, %): (factor@subs)(paramsg, %):\ntmp:= (factor@su bs)(s=1, valp0, %);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 118 "col lect(subs(lambda=rho/M1(g), tmp), [M1], factor);\nsubs(M2(g)=1/mu^2+Va r(g), M1(g)=1/mu, %): collect(%, Var, normal);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 173 "Int(t^1*a(t), t=0..infinity):%= xplif(%, [lam bda, positive]);\ncollect(subs(lambda=rho/M1(g), M2(g)=2/mu^ 2, M1(g)= 1/mu, tmp), [M1], factor);\n(normal@subs)(rho=lambda/mu, %);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 164 "valGq;LapG:= Gq(s)= Lap(g)( lambda-lambda*s);\nLapH:= subs(g=h, Gq=Gp, %);\nsubs(LapH, LapG, solve (z=lambda-lambda*s,\{s\}), valGp):\nPolKin:= collect(%, [p(0)], normal );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "Int(g(t)*exp(-z*t), t =0..infinity);\nseries(%,z,4);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 189 "Lap(g)(z)=1-M1( g)*z+M2(g)*z^2/2-M3(g)*z^3/6;\nsubs(%, subs(g=h, %), lambda=rho/M1(g), (lhs-rhs)(PolKin) );\nseries(%, z, 4): subs(p(0)=1-rho, %);\ntmp:= ma p(collect,%, [M3(g), M2(g)], normal);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 175 "``(1):=1: (op@solve)(coeff(tmp,z), \{M1(h)\}); lhs(% )=M1(g)*\ncollect(collect(expand(rhs(%)/M1(g)), [M2, M1], ``@normal), \+ ``, ``);\n(factor@yjoli@subs)(``(M2(g)/(M1(g)^2))=2, %);" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {SECT 1 {PARA 3 "" 0 "" {TEXT -1 20 "Etude d'une file M/M" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "arv:= proc() -20*ln(ra()) end; srv: = proc() -15*ln(ra()) end;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 141 "raz_fi(); _seed:=123456; \nto 10000 do evol(); od; agenda, cha rge; \nfor j while nops(agenda)>1 do evol() od; agenda, charge;\nnumcl i*2; j-1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 294 "aut:= stats[transform, tally] ([se q(autres[k], k=1..numcli)]):\nhisto_aut:= stats[transform, tallyinto]( %, [seq(k-1/2..k+1/2, k=0..nops(%)-1)]):\ndur:= [seq(Weight(k, durees[ k]), k=0..nops([indices(durees)])-1)]:\nhisto_dur:= [seq(Weight(k-1/2. .k+1/2, durees[k]), k=0..nops([indices(durees)])-1)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 135 "` comparaison dur, aut`; display(x histo(histo_aut, color=pink), xhisto(histo_dur, color=green), xtickmar ks=map2(op,1,dur), axes=boxed);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 124 "sdur:= nbr(dur); saut:= nbr(aut); \nadd( (op(2, aut[j])/saut- op(2, dur[j])/sdur)^2 /(op(2, dur[j])/sdur), j=1..15);\n%*numcli;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 37 "sej:= [seq(sejours[j], j=1..numcli)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 162 "bb:= (max@op)(sej);\n10: seq(%*j.. %*j+%, j=0..floor(bb/%)-5): les_interv:= [%, rhs(%[-1])..ceil(bb*1.3)] ;\nexper_sej:= stats[transform, tallyinto](sej, les_interv):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 161 "Law:= unapply(1-exp(-t/60),t); fu:= proc(z) local \+ a,b; a,b:= op(op(1,z));\nevalf(Law(b)-Law(a))*numcli; subsop(2=%, z) e nd;\ntheor_sej:= [seq(fu(k), k=exper_sej)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "nbr(theor_sej), numcli, nbr(exper_sej);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "display(xhisto(exper_sej, co lor=pink),xhisto(theor_sej, color=green)) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "add( (op(2, exper_sej[j])-op(2, theor_sej[j]))^2 / (op(2, theor_sej[j])), j=1..15);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "dist:=3: dat1:= sej[1..-1-dist]: dat2:= sej[1+dist..- 1]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "plots[pointplot]([seq([dat1[ k],dat2[k]],k=1..nops(dat1))]);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 " 1/(1-cov(dat1,dat2)^2/var(dat1)/var(dat2));;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "aut: = [seq(autres[j], j=1..numcli)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "aut_tal:= stats[transform, tally](aut); xhisto(%, are a=count, numbars=17); pl1:=%: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 107 "Sum((1-p)*p^k, k=0..infinity); normal(value(%));\nSum(k*(1-p) *p^k, k=0..infinity); val_m:= normal(value(%));" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 29 "moy_sej/15.; moy(aut_tal)*1.;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "moy(aut_tal)=val_m; pi:= solve(%)*1 .;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "kx:=17: [seq(Weight( k,numcli*(1-pi)*pi^k), k=0..kx)]:\nxhisto(%, area=count, numbars=kx, c olor=pink): pl2:=%:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "plot s[display](pl1, pl2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }}{MARK "9 0 0" 0 }{VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }