系统建模与仿真课后作业

1.4、系统、模型和仿真三者之间具有怎样的相互关系？答：系统是研究的对象，模型是系统的抽象，仿真通过对模型的实验以达到研究系统的目的。2.2、通过因特网查阅有关蒲丰投针实验的文献资料，理解蒙特卡罗方法的基本思想及其应用的一般步骤。答：蒲丰投针实验内容是这样的：在平面上画有一组间距为a的平行线，将一根长度为L（La）的针任意掷在这个平面上，求此针与平行线中任一条相交的概率。”布丰本人证明了，这个概率是：p=2L/（a) (为圆周率)利用这个公式可以用概率的方法得到圆周率的近似值。所以，蒙特卡罗方法的基本思想就是：当试验次数充分多时，某一事件出现的频率近似等于该事件发生的概率。一般步骤：（1）构造或描述概率过程 （2）以已知概率分布进行抽样 （3）建立各种估计量2.8、简述离散事件系统仿真的一般步骤。（1）阐明问题与设定目标（2）仿真建模（3）数据采集（4）仿真模型的验证（5）仿真程序的编制与校核（6）仿真模型的运行（7）仿真输出结果的统计分析3.3、以第二章图2-5所示的并行加工中心系统为对象，试分别画出相应的实体流图和活动循环图，并比较它们两者有何区别和练习。（1）实体流图N零件到达是否有设备空闲进入队列等待Y设置两台设备工作状态均为忙碌零件开始加工零件加工完后离开设置完工设备状态为“空闲”设置空闲设备工作状态为忙碌零件开始加工零件加工完后离开设置该设备状态为“空闲”是否两台设备都空闲YN(2)活动循环图加工安装设备空闲设备就绪设备（I、II）循环等待工人循环3.6、以第二章中图2-5所示的并行加工中心系统为对象，建立Petri网模型。t2P1设备II空闲零件离开加工好的零件t3P2加工完毕t2P3P1正在加工开始加工设备I空闲P0t1t1等待加工零件到达t0 P33.7、根据Petri网的运行规则，按照t3、t2、t1、t4的顺序，重新分析图3-20所示Petri网模型的运行过程，并将分析结果同例3-5相比较。t4t3P1t1P2P6P3P5t2P4(1)初始状态t4t3P1t1P2P6P3P5t2P4(2)t3发生后t4t3P1t1P2P6P3P5t2P4(3)t2发生后(4)t1不能发生 t4t3P1t1P2P6P3P5t2P4(5)t4发生后4.4、任取一整数作为种子值，采用第三题中得到的随机数发生器生成随机数序列的前200项数据，并对其统计性能进行检验。解：由第3题可得到一个随机数发生器：a=5 b=9 c=3 m=512 xn=5xn-1+3 mod 512un=xn512 取种子值x0=，生成的随机数序列前200项数据如下：n5xn-1+3xnun n5xn-1+3xnun 13230.264584580.21618820.2722932450.34134130.2812282040.42068200.2910235110.51031030.3025585100.651860.3125535050.733330.3225284800.937581681680.3324033550.98433310.3417782420.1016581220.3512131890.116131010.369484360.125085080.3721831350.1325434950.386781660.1424784300.398333210.1521531050.401608720.16528160.03125413633630.1783830.4218182820.184184180.4314133890.192093450.4419484120.202282280.452063150.2111431190.4678780.22598860.473933930.234334330.4819684320.843752421681200.4921631150.25603910.50578660.n5xn-1+3xnun n5xn-1+3xnun513333330.768283160.5216681320.771583470.536631510.782382380.547582460.7911931690.5512332090.808483360.65625561048240.8116831470.571231230.827382260.586181060.8311331090.59533210.84548360.601081080.851831830.61543310.869184060.621581580.8720334970.637932810.8824884400.6414083840.758922031550.6519233870.907782660.6619384020.9113333090.6720134770.921548120.6823883400.9363630.6917031670.943183180.708383260.951593570.711633970.962882880.5625724884880.9714434190.7324433950.982098500.7419784420.992532530.7522131650.10012682440.n5xn-1+3xnun n5xn-1+3xnun10112231990.1264784780.1029984860.12723933450.10324333850.12817281920.37510419283920.1299634510.105196342701062138900.1311053290.1074534530.1321481480.10822682200.1337432310.10911037901103983980.1356731610.11119934570.1368082960.11222882400.4687513714834590.1131203179011489838601151933397011619884520.1416231110.11722632150.142558460.1181078540.1432332330.11927327302812512013683440.1457232110.12117231870.1461058340.1229384260.1471731730.1232133850.1488683560.12442842801252143950n5xn-1+3xnun n5xn-1+3xnun1511073490.17648480.093751522482480.177243243017812181940.1541098740.1799734610.1553733730156186833201571663127015863812601596331210160608960.18751857632510.16148348301622418370016318533170.1887482360.16415885201652632630.1907982860.16613182940.19114334090.16714734490.19220480016822482000.193330.16910034910.1941818019593930.171205350.1964684680.17228280.19723432950.1731431430.19814784540.1747182060.19922732250.175103390.20011281040.对上述数据进行参数检验如下：经计算可知，u=1ni=1nui=0. s2=1n-1i=1n(ui-u)2=119916.=0.因此可知统计量v1=12n(u-12)=-1. v2=180n(s2-112)=0.假定显著性水平=0.05，则查表可知z2=1.96 v1z2，v2z2故可以认为：在显著性水平=0.05时，该随机数序列un总体的均值和方差与均匀分布U（0,1）的均值和方差没有显著性的差异。4.5、三角分布的概率密度函数为fx=2x-ab-am-a axm 2b-xb-ab-m mxb 0 其他试写出其相应的分布函数，并采用反变换法给出生成该三角分布随机变量的算法步骤。解：根据密度函数f(x)可计算得到x的分布函数如下：Fx=0 , &xa(x-a)2(b-a)(m-a) , axm (x-m)(2b-x-m)(b-a)(b-m)+ m-ab-a , &mxb1 &xb 采用反变换法生成该三角分布随机变量的算法步骤如下：计算其反函数令u=F(x),则其反函数x=F-1u=b-am-au+a 0um-ab-ab-b-ab-m1-u m-ab-au1则数列Xn即为所求的指数分布的随机变量5.2、根据第4章复习思考题第6题中得到的结论，生成标准正态分布N（0,1）的前200项数据，并根据这些数据分别绘制相应的相关图、散点图和直方图，以检验样本数据的独立性及其分布形式是否为正态分布。解：由已知条件可生成如下的随机数U1U2X1X20.3820.1011.1191.4530.5960.8990.817-0.4210.8850.9580.4780.0410.0140.407-2.429-0.5850.8630.1390.3501.6130.2450.0451.609-1.5650.0320.1641.3471.5650.2200.0171.731-2.8310.2850.343-0.8731.0480.5540.357-0.6781.2900.3720.356-0.8651.0810.9100.466-0.424-0.5730.4260.304-0.433-0.6350.9760.8070.0770.3040.9910.256-0.005-0.0530.9520.0530.2972.3160.7050.8170.3370.5430.9730.466-0.231-1.2260.3000.750-0.002-0.0080.3510.7760.2290.7060.0740.1980.727-1.7800.0640.358-1.473-0.2450.4870.511-1.197-1.0920.3730.9861.3980.1020.0410.2310.3081.6020.0050.9262.908-0.2170.1000.257-0.088-0.8690.7760.680-0.306-0.8250.8090.724-0.106-0.4960.0850.1321.4970.0440.7560.627-0.5250.1480.1740.405-1.5450.3680.5520.712-0.263-0.8220.5550.1810.4550.5140.9700.687-0.095-0.4880.5290.7970.3240.6040.8060.262-0.050-0.5040.1780.8671.2400.5340.1150.0601.937-0.9310.7620.738-0.056-0.2660.9860.9260.1480.3150.9040.545-0.432-0.4580.5010.675-0.5360.1990.4900.1460.728-1.9430.0380.7960.727-0.6680.6720.732-0.105-0.4820.5850.1520.598-1.1150.8920.378-0.343-1.1630.2000.2060.4930.0830.3340.325-0.6721.3220.3000.8020.4960.0190.6960.271-0.114-1.0590.9040.0390.4361.0050.7090.454-0.7941.2100.5170.257-0.046-0.4730.2910.8020.502-0.0060.7890.676-0.310-0.8230.7550.9490.710-0.3150.6190.722-0.173-0.7140.9680.369-0.173-1.2490.8500.557-0.5330.2240.8730.441-0.485-0.1190.2180.8591.1010.3260.2800.703-0.465-0.1860.7070.376-0.5910.7530.3300.0861.2782.1830.9770.286-0.048-0.4670.5340.407-0.9350.5390.9980.8950.0530.1550.8110.9090.543-0.1150.5750.706-0.289-0.8090.4010.1111.0360.4600.8970.386-0.351-1.1100.0960.7780.3690.5210.7840.666-0.354-0.7170.6570.258-0.048-0.4880.7650.700-0.226-0.8350.8590.0030.552-1.0870.6790.9290.793-0.3710.0420.518-2.498-0.0260.9120.9540.4110.1630.5940.558-0.9550.3080.9680.483-0.253-1.2060.2560.8180.680-0.5720.4960.8510.697-0.5370.6680.9270.804-0.3680.4520.1680.621-1.2990.0620.0052.3572.5510.5410.618-0.8210.8880.4930.579-1.045-0.2900.6020.9300.911-0.2040.5340.1320.757-2.0110.0820.576-1.9870.0900.8290.0660.561-0.8640.2710.700-0.5060.0290.4140.366-0.8810.9710.4350.330-0.6211.0240.2110.740-0.110-0.4930.5230.8970.905-0.2640.6030.523-0.9950.0390.5900.585-0.8860.6830.4970.1110.909-1.1410.5930.559-0.9540.3130.7740.2310.0870.8860.7310.587-0.6770.9260.5460.8070.3850.4320.9640.0950.2232.1360.1090.712-0.500-0.0040.8830.1900.1841.6680.0160.1851.1521.4940.5800.666-0.5270.1520.1620.1950.646-1.4320.6780.548-0.8420.9200.2950.541-1.5130.0850.1730.1850.741-1.8330.8520.9480.535-0.0700.2510.432-1.5120.0890.5450.9671.0780.1210.7240.9510.765-0.3160.5700.9410.986-0.0320.2600.1670.819-1.7210.8840.8210.2130.6110.0420.8982.0180.0490.4210.1280.912-1.0720.0300.2050.745-1.7800.6820.8210.3730.4490.4720.479-1.213-1.1810.5850.362-0.6711.2520.8230.311-0.231-1.5180.9900.7720.0180.0830.7290.1630.4121.0000.8080.9260.582-0.1930.2320.382-1.256-1.3870.0900.9121.863-0.3270.8520.573-0.5080.0490.0140.693-1.021-0.1110.7010.8880.642-0.3780.1690.8861.4190.2420.2870.2320.1841.5640.0420.9152.1640.3590.1670.9391.752-0.3550.1220.341-1.112-0.9440.0950.9442.0330.0670.5110.629-0.7970.9210.8360.9740.591-0.1230.4760.1520.707-1.8710.2850.8020.502-0.0060.8080.695-0.221-0.8390.0690.0812.0190.2560.4430.265-0.117-1.0900.2650.8100.599-0.3760.2010.454-1.7171.2280.4080.9361.2290.3620.0940.1750.991-0.1070.4340.1440.797-1.8830.0760.0152.2612.8870.7190.367-0.5450.3930.6600.0200.904-1.5890.8790.0260.502-0.0350.3020.1640.793-1.8340.4600.554-1.177-0.9730.9590.306-0.100-0.9060.2130.2280.2481.7200.7210.9000.654-0.3760.0760.8341.1370.4550.9440.252-0.005-0.0510.5330.2040.3221.6050.7570.595-0.6200.6950.5190.1520.665-1.6700.3820.7660.1330.5410.4960.8420.644-0.4600.1550.7760.3090.6650.8930.1210.3451.7010.6540.0370.896-1.5640.5320.8430.617-0.3910.8500.542-0.5510.3490.2230.719-0.344-0.6750.6790.7670.0910.3950.1710.725-0.302-0.7600.9460.593-0.278-1.0080.3500.598-1.183-0.9240.9650.0080.2653.0870.5070.451-1.111-0.8060.8390.8920.4600.1200.9490.0340.3162.3770.7890.643-0.429-0.4060.7710.686-0.285-0.8480.4460.9511.2110.3060.6750.488-0.8830.8040.4920.479-1.181-1.0990.0460.671-1.183-0.8140.5760.742-0.053-0.2500.4330.7950.3620.5170.9070.9710.4350.0960.0950.732-0.245-0.7890.4150.2290.1751.5300.7700.9900.721-0.1380.9110.571-0.389-0.6830.3180.406-1.256-1.3420.1360.530-1.9630.267所以，由上述数据可生成如下图形：由图形可知，样本数据大体符合正态分布的形式，虽然从图形上来看，X1 的分布与标准正态分布的形式有一定的差距，但其偏差应该在误差范围内，所以可以认为样本数据是独立的、正态分布。5.4、分析终态仿真与稳态仿真这两种仿真方式的异同。答：相同点：都是对系统进行仿真及输出分析的方式不同点：终态仿真结果与系统初始条件有关，而稳态仿真的最终结果是不受初始条件影响的；终态仿真主要研究的是在规定时间内的系统行为，稳态仿真更侧重于对系统长期运行的稳态行为的关注。5.5、对图2-1所示的简单加工系统，进行独立的重复仿真10次，每次仿真运行的长度为200，初始条件为初始队长q(0)=0,且钻床设备处于空闲状态。仿真运行的结果如下：平均等待时间Dj200: 10.427 14.469 12.780 8.703 12.727 9.206 8.053 28.039 6.228 13.931平均队长Qj200: 2.098 2.718 2.389 1.596 2.585 1.755 1.724 6.523 1.227 2.779试计算求解该简单加工系统平均等待时间Dj200和平均队长Qj200这两个性能指标的置信度为0.90的置信区间。解：1-=0.9 =0.1 t29=1.8331（1） 求Dj200的置信区间由已知数据可得，D=Dj=12.456 S2=19110(Dj-12.456)2=37.353D -t2(9)S10=12.456-1.8331*3.7353=8.913D +t2(9)S10=12.456+1.8331*3.7353=15.999平均等待时间Dj200的置信度为0.90的置信区间为（8.913,15.999）（2） 求Qj200的置信区间由已知数据可得，Q=Qj=2.539 S2=19110(Qj-12.456)2=2.230Q -t2(9)S10=2.539-1.8331*0