06第六章 排队论

CBAZYX/////XYZABCFCFS/////ZYXMMDkEkGGI1//MMcMD//csLqLsWqWbTnn,2,1,0nNNn,,1,0ccn,,1,0ttn)(tPnnnP)(tN),0[t0t),(21ttPn))(,[1221tttt)0(n)0,(})()({),(121221nttntNtNPttPn),(21ttPnt),[ttttt)(),(1tottttP)(to0tt0t),[ttt2)(),(nntotttPn)(),0(tPtPnn)()()(000tPtPttPnkkknnntPtPttP0,2,1),()()()(1)(0tottPttotPttPttP)()()()(000ttotPtPttPttPnnnn)()()()()(1t)()(00tPdttdP,2,1),()()(1ntPtPdttdPnnn1)0(0P),2,1(0)0(nPntetP)(0tnnetUtP)()()(0tU)(tUn,,2,1),()(1ntUdttdUnn1)(0tU0)(tUn,2,1,!)()(nenttPtnn)}()()({sNtsNtNttNE)]([ttN)](Var[T),0{[}{tPtTPtetP)(}0)(tFT0,00,1)(}{ttetFtTPt0,)(tetft1ETtetG1)(tetg)(}{}{lim}|{lim00tTtPttTtPttTttTPtt),[ttt)(tot1),(ba),(baU)1,0(UX)1,0(UXabaY)(),(baU2),(2N)(Exp0,00,)(ttetft121)()|(sXPtXstXP,),(G1n),n,),(W1)1,0(),(B0,1xpp1)(BernpKk,2,1,0,!kkePkk)(PoissonpnKknkppCPknkknk,,1,0,)1(),(pnBnkn,),(pnB))1(,(pnpnpNnpnp),(pnB)(Poisson)(tNt}0),({ttN}0),({ttN}0),({ttN)(tNntN)(tn,2,1,0nntN)(tn,2,1,0n}0),({ttN)(tN})({)(ntNPtpn,2,1,0n,2,1,0,npnnnnnnnnnnnnpppppppppppn)()()(21011112223311111220000110101pp01201121001121212)(1pppppp0123012232112232323)(1ppppppn01101111111)(1ppppppnnnnnnnnnnnnnnnn11021nnnnnC,2,1n0pCpnn,2,1n10nnp1101pCnn1011nnCp1nnC1nnCsMM///1//MMV}{nNPpn,2,1,0nN,2,1,0,nn,2,1,0,nn1nnC,2,1n0ppnn,2,1n1111111010nnnnpnnp)1(,2,1nn11)32()32()1(324323210nnnnsnnpLqL)()1()1(201LpLpnLnnqTtetTP)(}{0t1sWqTVVTTq1)()()(qqsWVETETEWqW)(1sqWWsLsWssWLqLqWqqWLBIBI1)1(:BI)1(:1IB1111BsWB/1//MM4101.014.06.04.0110p38.0)4.01(4.0)1(333p4.01}1{0pNP67.01sL(min)10)h(467.0ssLW267.04.014.0122sqLL(min)4)h(4267.0qqLW3679.0}10{1)15161(10eeTPmodel:s=1;lamda=4;mu=10;rho=lamda/mu;Pwait=@peb(rho,s);p0=1-Pwait;Pt_gt_10=@exp(-1);end///sMMs}{nNPpn,2,1,0nNsn,2,1,0n,1,,,,2,1,ssnssnnnsss1ssnsssssnnCsnnnsnn,!)/(!)/(,,2,1,!)/(snpsssnpnpsnnnn,!,,2,1,!001100)1(!!snssnsnpnsn0)1(!),(pspscsssnnqLsnsnsssnnqsnsppsnL)(!)(012010)1(!!sssnnsssspddspssqscL1),(ss010010)1(!!psspnnpsnpssssnnsnnsnn)1()!1()!1(11110sssnnsnpssLsLqLssLW1sqqWLWmin/9.0min/4.0///sMM3s25.21325.2ss0748.0)3/25.21(!3)25.2(!2)25.2(!1)25.2(!0)25.2(132100p70.1)3/25.21(!33/25.2)25.2(0748.023qL95.325.270.1qLL89.19.070.1qqLW39.49.095.3ssLW57.00748.0)3/25.21(!3)25.2()25.2,3(3c/3//MM/1//MM3.039.0321/3//MM/1//MM/3//MM/1//MM/3//MM/1//MMmodel:s=3;lamda=0.9;mu=0.4;rho=lamda/mu;rho_s=rho/s;P_wait=@peb(rho,s);p0=6*(1-rho_s)/rho^3*P_wait;L_q=P_wait*rho_s/(1-rho_s);L_s=L_q+rho;W_q=L_q/lamda;W_s=L_s/lamda;endssMM///slostPe)1(lostPeQAlost1PQ2lost)1(PQAesL/esL0qLsLs/sW/1sW0qWee1s1/1//MM6.025.11model:s=1;lamda=0.6;mu=1/1.25;rho=lamda/mu;Plost=@pel(rho,s);Q=1-Plost;lamda_e=Q*lamda;A=Q*lamda_e;L_s=lamda_e/mu;eta=L_s/s;end4343570.195435.2.21sssMM///42008h2040min80120min13min9511402008.0120602.04060160601220060140212505.0lostP3LINGOmodel:lamda=200;mu=60/3;rho=lamda/mu;Plost=@pel(rho,s);Plost0.05;Q=1-Plost;lamda_e=Q*lamda;A=Q*lamda_e;L_s=lamda_e/mu;eta=L_s/s;min=s;@gin(s);end153.6596.35185.6764.23LINGO5@pelLINGOmodel:lamda=200;mu=60/3;rho=lamda/mu;@pel(rho,s)=0.05;end33555.14s@pel(rho,s)ssLINGOmodel:lamda=200;mu=60/3;rho=lamda/mu;s=15;Plost=@pel(rho,s);Q=1-Plost;lamda_e=Q*lamda;A=Q*lamda_e;L_s=lamda_e/mu;eta=L_s/s;end6sMM//6.1KMM/1//1VKKN}{nNPpn,2,1,0nK1KKnKnn,01,,2,1,0,nKn,,2,1456KnKnCnnn,0,,2,1,270ppnnKn,,2,11,111,1111110KpKKnn281sLKnnKnnsnpnpL110011201)1(1])1(1[)1(KKKKKKp2912111010KnKpnnpLKnKnnKnns30qL)1()1(01pLpnLsKnnq311,)1(2)1(1,1)1(11KKKKLKKq321KKKp1)1()1(0ppKeeKp)1(ksesspLLW)1(KqeqqpLLW1qsWW1K1/1//MM1K110p11p11pLs1)1(01ppe1essLW0qL0qW4/1//MM18.025.1125.14K122.025.1125.1111550p298.0122.025.14044pp702.0)298.01(1)1(4pe44.225.1125.1)14(25.1125.155sL56.1)122.01(44.2)1(0pLLsq48.3702.044.2essLW23.28.0148.31sqWWmodel:sets:state/1..4/:p;endsetslamda=1;mu=1/1.25;rho=lamda/mu;k=4;lamda*p0=mu*p(1);(lamda+mu)*p(1)=lamda*p0+mu*p(2);@for(state(i)|i#gt#1#and#i#lt#k:(lamda+mu)*p(i)=lamda*p(i-1)+mu*p(i+1));lamda*p(k-1)=mu*p(k);p0+@sum(state:p)=1;P_lost=p(k);lamda_e=lamda*(1-P_lost);L_s=@sum(state(i)|i#le#k:i*p(i));L_q=L_s-(1-p0);W_s=L_s/lamda_e;W_q=W_s-1/mu;endKsMM///sKKnKnn,01,,2,1,0,Knsssnnn,0,Knspsssnpnpsnnnn,!0,!001,)1(!!1,)1(!)1(!11011010ssnsnssnssKssnsKsnsnpKnpn,,2,1,0,KsnnqpsnL)(1,!2)1)((1],)1)(1(1[)1(!0120ssssKsssKssssssKsKpsKspKsnnKsnnKsnnqpsnppsnL)(spsnLpsnpnpsnnssnnsnnKnn1010100)(1100!)(snnqsnsnpsLLe)1(KepessLW1seqqWLWKsnsnnsnnKsnnsnnsssnnppsnps!!10010KsnsKKsnnsnnKsnsnnsnnssssnpssnp!!!!)!1(100111110)1()!1(0KsKKppss)1(KqqspLsLL5/2//MM25.042s5K008.0)2/41(!2])2/4(1[441112520p512.02!2008.042555p])2/4)(125)(2/41()2/4(1[)2/41(!2)2/4(4008.02512522qL18.213.4)512.01(418.2)1(5pLLqs23.4)512.01(213.4)1(5pLWss23.2223.41sqWW95.118.213.4qsLLsmodel:sets:state/1..5/:p;endsetslamda=2;mu=0.5;rho=lamda/mu;s=2;k=5;lamda*p0=mu*p(1);(lamda+mu)*p(1)=lamda*p0+2*mu*p(2);@for(state(i)|i#gt#1#and#i#lt#s:(lamda+i*mu)*p(i)=lamda*p(i-1)+(i+1)*mu*p(i+1));@for(state(i)|i#ge#s#and#i#lt#k:(lamda+s*mu)*p(i)=lamda*p(i-1)+s*mu*p(i+1));lamda*p(k-1)=s*mu*p(k);p0+@sum(state:p)=1;P_lost=p(k);lamda_e=lamda*(1-P_lost);L_s=@sum(state(i):i*p(i));L_q=L_s-lamda_e/mu;W_s=L_s/lamda_e;W_q=W_s-1/mu;endKsMM///Ks0!pnpnnsn,,2,1100!snnnp10!!),(snnssnspsB),(sBsnnsnnpnnnps