1、1.4、系統(tǒng)、模型和仿真三者之間具有怎樣的相互關系？答：系統(tǒng)是研究的對象，模型是系統(tǒng)的抽象，仿真通過對模型的實驗以達到研究系統(tǒng)的目的。2.2、通過因特網查閱有關蒲豐投針實驗的文獻資料，理解蒙特卡羅方法的基本思想及其應用的一般步驟。答：蒲豐投針實驗內容是這樣的：在平面上畫有一組間距為a的平行線，將一根長度為L（La）的針任意擲在這個平面上，求此針與平行線中任一條相交的概率?！辈钾S本人證明了，這個概率是：p=2L/（a) (為圓周率)利用這個公式可以用概率的方法得到圓周率的近似值。所以，蒙特卡羅方法的基本思想就是：當試驗次數(shù)充分多時，某一事件出現(xiàn)的頻率近似等于該事件發(fā)生的概率。一般步驟：（1）構造

2、或描述概率過程 （2）以已知概率分布進行抽樣 （3）建立各種估計量2.8、簡述離散事件系統(tǒng)仿真的一般步驟。（1）闡明問題與設定目標（2）仿真建模（3）數(shù)據(jù)采集（4）仿真模型的驗證（5）仿真程序的編制與校核（6）仿真模型的運行（7）仿真輸出結果的統(tǒng)計分析3.3、以第二章圖2-5所示的并行加工中心系統(tǒng)為對象，試分別畫出相應的實體流圖和活動循環(huán)圖，并比較它們兩者有何區(qū)別和練習。（1）實體流圖N零件到達是否有設備空閑進入隊列等待Y設置兩臺設備工作狀態(tài)均為忙碌零件開始加工零件加工完后離開設置完工設備狀態(tài)為“空閑”設置空閑設備工作狀態(tài)為忙碌零件開始加工零件加工完后離開設置該設備狀態(tài)為“空閑”是否兩臺設備都

3、空閑YN(2)活動循環(huán)圖加工安裝設備空閑設備就緒設備（I、II）循環(huán)等待工人循環(huán)3.6、以第二章中圖2-5所示的并行加工中心系統(tǒng)為對象，建立Petri網模型。t2P1設備II空閑零件離開加工好的零件t3P2加工完畢t2P3P1正在加工開始加工設備I空閑P0t1t1等待加工零件到達t0 P33.7、根據(jù)Petri網的運行規(guī)則，按照t3、t2、t1、t4的順序，重新分析圖3-20所示Petri網模型的運行過程，并將分析結果同例3-5相比較。t4t3P1t1P2P6P3P5t2P4(1)初始狀態(tài)t4t3P1t1P2P6P3P5t2P4(2)t3發(fā)生后t4t3P1t1P2P6P3P5t2P4(3)t2

4、發(fā)生后(4)t1不能發(fā)生 t4t3P1t1P2P6P3P5t2P4(5)t4發(fā)生后4.4、任取一整數(shù)作為種子值，采用第三題中得到的隨機數(shù)發(fā)生器生成隨機數(shù)序列的前200項數(shù)據(jù)，并對其統(tǒng)計性能進行檢驗。解：由第3題可得到一個隨機數(shù)發(fā)生器：a=5 b=9 c=3 m=512 xn=5xn-1+3 mod 512un=xn512 取種子值x0=，生成的隨機數(shù)序列前200項數(shù)據(jù)如下：n5xn-1+3xnun n5xn-1+3xnun 13230.264584580.21618820.2722932450.34134130.2812282040.42068200.2910235110.51031030.3

5、025585100.651860.3125535050.733330.3225284800.937581681680.3324033550.98433310.3417782420.1016581220.3512131890.116131010.369484360.125085080.3721831350.1325434950.386781660.1424784300.398333210.1521531050.401608720.16528160.03125413633630.1783830.4218182820.184184180.4314133890.192093450.4419484120

6、.202282280.452063150.2111431190.4678780.22598860.473933930.234334330.4819684320.843752421681200.4921631150.25603910.50578660.n5xn-1+3xnun n5xn-1+3xnun513333330.768283160.5216681320.771583470.536631510.782382380.547582460.7911931690.5512332090.808483360.65625561048240.8116831470.571231230.827382260.5

7、86181060.8311331090.59533210.84548360.601081080.851831830.61543310.869184060.621581580.8720334970.637932810.8824884400.6414083840.758922031550.6519233870.907782660.6619384020.9113333090.6720134770.921548120.6823883400.9363630.6917031670.943183180.708383260.951593570.711633970.962882880.5625724884880

8、.9714434190.7324433950.982098500.7419784420.992532530.7522131650.10012682440.n5xn-1+3xnun n5xn-1+3xnun10112231990.1264784780.1029984860.12723933450.10324333850.12817281920.37510419283920.1299634510.105196342701062138900.1311053290.1074534530.1321481480.10822682200.1337432310.1091103790.

91103983980.1356731610.11119934570.1368082960.11222882400.4687513714834590.1131203179011489838601151933397011619884520.1416231110.11722632150.142558460.1181078540.1432332330.11927327302812512013683440.1457232110.12117231870.1461058340.12

10、29384260.1471731730.1232133850.1488683560.12442842801252143950n5xn-1+3xnun n5xn-1+3xnun1511073490.17648480.093751522482480.177243243017812181940.1541098740.1799734610.155373373015618683320157166312701586381260

11、1596331210160608960.18751857632510.16148348301622418370016318533170.1887482360.16415885201652632630.1907982860.16613182940.19114334090.16714734490.19220480016822482000.193330.16910034910.1941818019593930.171205350.1964684680.17228280.1

12、9723432950.1731431430.19814784540.1747182060.19922732250.175103390.20011281040.對上述數(shù)據(jù)進行參數(shù)檢驗如下：經計算可知，u=1ni=1nui=0. s2=1n-1i=1n(ui-u)2=119916.=0.因此可知統(tǒng)計量v1=12n(u-12)=-1. v2=180n(s2-112)=0.假定顯著性水平=0.05，則查表可知z2=1.96 v1z2，v2z2故可以認為：在顯著性水平=0.05時，該隨機數(shù)序列un總體的均值和方差與均勻分布U（0,1）的均值和方差沒有顯著性的差異。4.5、三角分布的概率密度函數(shù)為fx=2

13、x-ab-am-a axm 2b-xb-ab-m mxb 0 其他試寫出其相應的分布函數(shù)，并采用反變換法給出生成該三角分布隨機變量的算法步驟。解：根據(jù)密度函數(shù)f(x)可計算得到x的分布函數(shù)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 采用反變換法生成該三角分布隨機變量的算法步驟如下：計算其反函數(shù)令u=F(x),則其反函數(shù)x=F-1u=b-am-au+a 0um-ab-ab-b-ab-m1-u m-ab-au1則數(shù)列Xn即為所求的指數(shù)分布的隨機變量5.2、根據(jù)第4章復習思考題第6題中

14、得到的結論，生成標準正態(tài)分布N（0,1）的前200項數(shù)據(jù)，并根據(jù)這些數(shù)據(jù)分別繪制相應的相關圖、散點圖和直方圖，以檢驗樣本數(shù)據(jù)的獨立性及其分布形式是否為正態(tài)分布。解：由已知條件可生成如下的隨機數(shù)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

15、-0.6781.2900.3720.356-0.8651.0810.9100.466-0.424-0.5730.4260.304-0.433-0.6350.9760.8070.0770.3040.9910.256-0.005-0.0530.9520.0530.2972.3160.7050.8170.3370.5430.9730.466-0.231-1.2260.3000.750-0.002-0.0080.3510.7760.2290.7060.0740.1980.727-1.7800.0640.358-1.473-0.2450.4870.511-1.197-1.0920.3730.9861.3

16、980.1020.0410.2310.3081.6020.0050.9262.908-0.2170.1000.257-0.088-0.8690.7760.680-0.306-0.8250.8090.724-0.106-0.4960.0850.1321.4970.0440.7560.627-0.5250.1480.1740.405-1.5450.3680.5520.712-0.263-0.8220.5550.1810.4550.5140.9700.687-0.095-0.4880.5290.7970.3240.6040.8060.262-0.050-0.5040.1780.8671.2400.5

17、340.1150.0601.937-0.9310.7620.738-0.056-0.2660.9860.9260.1480.3150.9040.545-0.432-0.4580.5010.675-0.5360.1990.4900.1460.728-1.9430.0380.7960.727-0.6680.6720.732-0.105-0.4820.5850.1520.598-1.1150.8920.378-0.343-1.1630.2000.2060.4930.0830.3340.325-0.6721.3220.3000.8020.4960.0190.6960.271-0.114-1.0590.

18、9040.0390.4361.0050.7090.454-0.7941.2100.5170.257-0.046-0.4730.2910.8020.502-0.0060.7890.676-0.310-0.8230.7550.9490.710-0.3150.6190.722-0.173-0.7140.9680.369-0.173-1.2490.8500.557-0.5330.2240.8730.441-0.485-0.1190.2180.8591.1010.3260.2800.703-0.465-0.1860.7070.376-0.5910.7530.3300.0861.2782.1830.977

19、0.286-0.048-0.4670.5340.407-0.9350.5390.9980.8950.0530.1550.8110.9090.543-0.1150.5750.706-0.289-0.8090.4010.1111.0360.4600.8970.386-0.351-1.1100.0960.7780.3690.5210.7840.666-0.354-0.7170.6570.258-0.048-0.4880.7650.700-0.226-0.8350.8590.0030.552-1.0870.6790.9290.793-0.3710.0420.518-2.498-0.0260.9120.

20、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.

21、5060.0290.4140.366-0.8810.9710.4350.330-0.6211.0240.2110.740-0.110-0.4930.5230.8970.905-0.2640.6030.523-0.9950.0390.5900.585-0.8860.6830.4970.1110.909-1.1410.5930.559-0.9540.3130.7740.2310.0870.8860.7310.587-0.6770.9260.5460.8070.3850.4320.9640.0950.2232.1360.1090.712-0.500-0.0040.8830.1900.1841.668

22、0.0160.1851.1521.4940.5800.666-0.5270.1520.1620.1950.646-1.4320.6780.548-0.8420.9200.2950.541-1.5130.0850.1730.1850.741-1.8330.8520.9480.535-0.0700.2510.432-1.5120.0890.5450.9671.0780.1210.7240.9510.765-0.3160.5700.9410.986-0.0320.2600.1670.819-1.7210.8840.8210.2130.6110.0420.8982.0180.0490.4210.128

23、0.912-1.0720.0300.2050.745-1.7800.6820.8210.3730.4490.4720.479-1.213-1.1810.5850.362-0.6711.2520.8230.311-0.231-1.5180.9900.7720.0180.0830.7290.1630.4121.0000.8080.9260.582-0.1930.2320.382-1.256-1.3870.0900.9121.863-0.3270.8520.573-0.5080.0490.0140.693-1.021-0.1110.7010.8880.642-0.3780.1690.8861.419

24、0.2420.2870.2320.1841.5640.0420.9152.1640.3590.1670.9391.752-0.3550.1220.341-1.112-0.9440.0950.9442.0330.0670.5110.629-0.7970.9210.8360.9740.591-0.1230.4760.1520.707-1.8710.2850.8020.502-0.0060.8080.695-0.221-0.8390.0690.0812.0190.2560.4430.265-0.117-1.0900.2650.8100.599-0.3760.2010.454-1.7171.2280.

25、4080.9361.2290.3620.0940.1750.991-0.1070.4340.1440.797-1.8830.0760.0152.2612.8870.7190.367-0.5450.3930.6600.0200.904-1.5890.8790.0260.502-0.0350.3020.1640.793-1.8340.4600.554-1.177-0.9730.9590.306-0.100-0.9060.2130.2280.2481.7200.7210.9000.654-0.3760.0760.8341.1370.4550.9440.252-0.005-0.0510.5330.20

26、40.3221.6050.7570.595-0.6200.6950.5190.1520.665-1.6700.3820.7660.1330.5410.4960.8420.644-0.4600.1550.7760.3090.6650.8930.1210.3451.7010.6540.0370.896-1.5640.5320.8430.617-0.3910.8500.542-0.5510.3490.2230.719-0.344-0.6750.6790.7670.0910.3950.1710.725-0.302-0.7600.9460.593-0.278-1.0080.3500.598-1.183-

27、0.9240.9650.0080.2653.0870.5070.451-1.111-0.8060.8390.8920.4600.1200.9490.0340.3162.3770.7890.643-0.429-0.4060.7710.686-0.285-0.8480.4460.9511.2110.3060.6750.488-0.8830.8040.4920.479-1.181-1.0990.0460.671-1.183-0.8140.5760.742-0.053-0.2500.4330.7950.3620.5170.9070.9710.4350.0960.0950.732-0.245-0.789

28、0.4150.2290.1751.5300.7700.9900.721-0.1380.9110.571-0.389-0.6830.3180.406-1.256-1.3420.1360.530-1.9630.267所以，由上述數(shù)據(jù)可生成如下圖形：由圖形可知，樣本數(shù)據(jù)大體符合正態(tài)分布的形式，雖然從圖形上來看，X1 的分布與標準正態(tài)分布的形式有一定的差距，但其偏差應該在誤差范圍內，所以可以認為樣本數(shù)據(jù)是獨立的、正態(tài)分布。5.4、分析終態(tài)仿真與穩(wěn)態(tài)仿真這兩種仿真方式的異同。答：相同點：都是對系統(tǒng)進行仿真及輸出分析的方式不同點：終態(tài)仿真結果與系統(tǒng)初始條件有關，而穩(wěn)態(tài)仿真的最終結果是不受初始條件影響的；終

29、態(tài)仿真主要研究的是在規(guī)定時間內的系統(tǒng)行為，穩(wěn)態(tài)仿真更側重于對系統(tǒng)長期運行的穩(wěn)態(tài)行為的關注。5.5、對圖2-1所示的簡單加工系統(tǒng)，進行獨立的重復仿真10次，每次仿真運行的長度為200，初始條件為初始隊長q(0)=0,且鉆床設備處于空閑狀態(tài)。仿真運行的結果如下：平均等待時間Dj200: 10.427 14.469 12.780 8.703 12.727 9.206 8.053 28.039 6.228 13.931平均隊長Qj200: 2.098 2.718 2.389 1.596 2.585 1.755 1.724 6.523 1.227 2.779試計算求解該簡單加工系統(tǒng)平均等待時間Dj200

30、和平均隊長Qj200這兩個性能指標的置信度為0.90的置信區(qū)間。解：1-=0.9 =0.1 t29=1.8331（1） 求Dj200的置信區(qū)間由已知數(shù)據(jù)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平均等待時間Dj200的置信度為0.90的置信區(qū)間為（8.913,15.999）（2） 求Qj200的置信區(qū)間由已知數(shù)據(jù)可得，Q=Qj=2.539 S2=19110(Qj-12.456)2=2.230Q -t2(9)S10=2.539-1.8331*0