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ISBN 5-7038-2090-1

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The textbook is devoted to basic problems and aspects of CAE/CAD/CAM systems. Mainapproaches to design procedures including methods and algorithms for modeling, simulation andsynthesis are considered. The information about workstations, networks, design frameworksand CALS components are given too.

The book is intended to students of technological universities, it may be recommended topostgraduates and industry specialists using CAE/CAD/CAM in their activity.

681.31(075.8) 32.97

.. , 2002ISBN 5-7038-2090-1 . .. , 2002

9

1. 121.1. 12

(12). (13). - (15).

1.2. 17 -

(17). (19). - (20). , - (20). (22).

1.3. 25

(25). (27). - (28). CALS- (30).

1.4. 31 (31). (34).

36

2. - 372.1. 37

, (37). (38). (41).

2.2. - 43

(43). (45). (46).

2.3. 47 (47). (48).

2.4. Ethernet 48 (48). (49). Ethernet (50).

2.5. 52 Token Ring (52). FDDI(55).

2.6. ,.... 56 (56). (58). (60). (61). (64).

2.7. 64 TCP (64). IP (67). TCP/IP (68).

(71). SPX/IPX (73). .25 Frame Relay (74). ATM(75). (78). (80).

83

3. 853.1. 85

(85). (86). (87).

3.2. 88 (88). - (89). (93). - (95). (96). (97).

3.3. 100 (100). - (104). - (105). (106). - (108). (108). (111).

3.4. 114 (114). (114). (117).

3.5. -- 118

(118). - (120). (124).

3.6. 125 (125). - (128). (130). (131). (133). GPSS (134). (140). (143).

3.7. 144

(144). (146). - ( ) (149).

151

4. 1534.1. 153

(153). (154). - (157).

4.2. 157 (157). (159). (160). (165). (166).

4.3. 171 (171). (172). (174). (175). (176). (177). (178).

4.4. 179

(179). (180). (182). (182). (183). (184). -

(185). (186). - (188). (190). - (190).

198

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5.4. 234 (234). (237). - (240). (243).

5.5. - 245

CASE- (245). (248). - IDEFO IDEF3 (250). IDEFIX (256). - UML (258). CASE- (260). (261). - (263). -- (268).

5.6. 271 (271). (272). (274). - (276). (278). (278). PDM (281). (286).

289

6. CALS- 291

6.1. CALS- 291 STEP (291). Parts Library, Parametrics, Mandate, IIDEAS (292). , CALS- (293).

6.2. 295 SGML (295). XML (296).

6.3. STEP- 299 STEP (299). (300). (301). , (302). (306). STEP (306).

6.4. Express 307 Express (307). (308). (308). (310). (311). -, , (311). (312). - (313). (314). (316). (316). - (317). STEP (ISO 10303-21) (319). Express (319).

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(TDM) (FDM) . -

( , . . ), -

.

, .

() , -, . . .

. -

, -

. , -

( ) N , 2N. , 16 1200 4 / 4800 /. ,, .

-

F (, 56

2.6.

Iog2 k , k )

V = Iog2k/t ( k < 1 + , ;t ,

,

-

.

: 12,5 - 6,25 . , - ,

, ,

, .

(STP Shielded Twist Pair) - (UTP Unshielded Twist Pair) . , , -

(). - 1 . 2 - 4 /. , . Ethernet (, 10Base-T) 3, Token Ring 4. - 5 6.

5 1 00 , 0,5 1 , - . UTP 100 . 5 100 1 00 24 , 1 0 1 00 1 .

6 7 , PIC, ,

. 6 5 , 0,5 , 100 22 . 7 , 8 , 100 20 , 600 - 50 .

,

( - ), . , .

.

, -

, .

(-) , .

.

57

2.

10 , 125 ... 200 . - : 0,83 ... 1,55 ; 0,7 /; 2 ; 4... 5 . 1 . - D ( ) X: , = 850 D = 5 , X, = 1300 D = 50 , .

, ,

Fiber Channel , - 133 1062 / 10 ( - SCSI 160 / ). - SDH (SONET) 155 622 /, - .

SDH (SynchronousDigital Hierachy). SDH - . , -

. .

STM-1. 270 , 1 . . ,

( -, ). .

.

, . ,

. -

1,5; 6; 45 140 / ( ) 2; 6; 34 140 / ( ). STM-1 155,52 /.

STM-1 STM-0, STM-4 STM-16 51, 622 2488 / .

.

.

(902 ... 928 2,4 ... 2,5 ) . - 5,725 ... 5,85 .

, , -

( ) , , -

58

2.6.

. -

.

-

. -

, -

, .

, -

. -

-

.

(), /, , -

.

-

-

. -

.

, ( 15...20 ). -: , .

RadioEthernet, -. . -

.

.

802/11 ,

.

(DSSS Direct Sequence Spread Spectrum). 11 (). , , .

-

( DSSS 802/11 11 /, 22 2,4 )., . ,

, 22 , , ,

.

, , , --

59

2.

, , -, -

, .

(FHSS Frequency HoppingSpread Spectrum). 802/11 79 . ( 20... 400 ) , -

, -

.

-

,

,

. , -

.

. ( 36 .) . ( 500 ) . - . -

. ,

, , , ,

, , , -

. ( ). ; -

, Lucent Technologies,Aironet, Multipoint Network.

,

. , -

, , . -

.

-

. , -

,

.

-

0,3 ... 3,4 ( - ), .

-

,

. -

60

2 6

,

.

,

, ,

.

/ , - :

Um ; ; v|/ .

Um, (AM),

() vy (). --

(QAM Quadrature Amplitude Modulation, -), , = 4 ... 8 (. . 16 ... 256 ). , ,

( 12 4).

2 3 .

-

V.32, V.34, V.90 V.92. , V.34 - 2,4 28,8 / 2,4 /.

1600 ... 2000 , - .

V34.bis 33,6 /. - 56 / , 2 V.90-92.

-

- (), PCM (Pulse Code Modulation).

, dt, - . , dt - : ,

. -

,

4 ( ) . , ( ) 8 , . . 64 ( 56 ).

61

2.

1 0 1 0 0 0 1 1 1 0 1 0 1 1

. .

. 2.7.

-

.

. 2.7. -

. -

, -

.

, .

-

1 ( DS-1). - 24 , DS-0 (Digital Signal-0). 8 28 = 256 , 64 / 1554 / 1. - 1 32 64 /, . . 2048/. ( DS-3), 28 1(45 /); 4, 6 , 4 -. -

.

1 (TDM). 24 , 192- . 24 . .

1 . DS-0 ( ) -, . . . -

, -

, 1, 1 .

(, DS-0). - , -

, .

, , ,

-

. DS-1 .

62

2.6.

, -

, (, ). -

. -

,

ISDN (Integrated Service Digital Network). ISDN .

ISDN 56 / 1,54 / ISDN (Broadband ISDN, B-ISDN) 155 ... 2048 /.

ISDN . 64 / ( 5-) 16 / (D-). 23 64 / D 16 /. ( ), . - , -

.

, 1, , ISDN .

ISDN . 2.8. ^- .

ISDN, S- . NT2 S- -, - . NT1 - (. 2.9) - U.

RS-232/V.35

. 2.8. ISDN

63

2.

,i "4

- , - , ( - ); 2 ,

; 3 - .

-

.

-

.

.

SPX/IPX Netware Novell SPX (Sequence

Packet Exchange) IPX (Internet Packet Exchange) - .

IPX ( - ), ( ) (- ). 30 546 . SPX 42 , . . 534 .

SPX ( ) - connect, con-nected () disconnected (). , .

-

IPX.

73

2.

.25 Frame Relay .25, , -

ITU (InternationalTelecommunication Union), . .25 1976 . , ,

, . -

.25 , .25.

.25 , . . , . -

.

.25: , , -

, . . , ,

( ), ( );

,

, ( 8 128);

() , ;

, ,

.

.25 - ( , , IP, ). - , . . .25 , .

( - ), .

.

( .25 , , Sprint, Infotel, .)

.25 . 2.10. .25 --

. 9,6 64 /. - .21, --.2 Ibis.

74

2.7.

. 2.10. .25

Frame Relay (FR) .25 ( 45 /) - , , -

, , . .

.

,

, . FR - .

FR , .

FR - , .

FR - ,

,

. ,

.25, , ( ). FR , .

FR - ,

.25. , -

.

ATM , ATM

(Asynchronous Transfer Mode), , - (, ) . , - -

75

2.

, , , -

, (, 6 ).

ATM (53 ), . ATM .

ATM , - .

.

, ,

-

.

.

,

.

. , -

, .

, -

5 . ATM .-,

(TDM) ( }. ,

. N , - .

, N. ATM , -

. ( ) - ( 32 ) /?- . - , -

. -

, -

. , -

. ,

.

-, -

( ) . .

( -). ( ) - .

76

2 7

-, .

TCP/ IP. - , -

-

. .

, (, , IP). . -

() , (1* - VPI/VCI () . , -

.

-, () , ^

( ATM), .

ATM (. 2.11). AAL , ( 64 ) , , , 48- , -

, , -

. -

, .

, ATM, - .

.

ATM- SDH } ' 4' L1 / 4), - ,

SDH ! FR ATM FR . .

*ft

2.

SDH, -. - STM-16, STM-4, STM-1. , ,

. FR ATM 3 .

ATM 51, 155,622 2488 / -1, -3, -12 -48 . , - , , TCP/IP .25, , - -

ATM, ATM. . -

(FR), 4 .

ATM ATM Forum . , ATM-, , TCP/IP, ,, Ethernet, Fast Ethernet, FDDI. , - IP-over-ATM (Multi-Protocol-Over-ATM), a IP- , - , ATM-.

TCP/IP ATM- ATM-. 53- , --.

, ATM - ( ). - -

.

,

( Fieldbus). ,

SCADA. -

, , ,

, .

,

.

78

2 7

. -

Fiber Channel, Fire Wire 1394, USB, Ethernet, a VMEbus, PCI .

,

, , .

Ethernet( 802.3).

() Fieldbus, - . Fieldbus - , . . -

: , , . Profibus, Interbus/S, CANbus . , -

,

. -

Infiniband, Fiber Channel, USB, FireWire 1394, - RS-232,RS-422,RS-485.

, , -

(, ) -- , VMEbus -pactPCI.

VMEbus 1987. ( IEEE 1014). - (IEEE 1101.10 1101.11). 21 , . 320 /. -

-, .

CompactPCI (PCI Peripheral Component Interconnect) - , 1990- . CompactPCI PCI, . 16. - 132 / 32- 264 / 64- .

(, - ) . - , OLE. (OLE for Process Control).

(, ) , - 1 ( ).

79

2.

. -

,

Ethernet , .

Profibus, 12 , 247 , - 1,5 . , Ethernet. Profibus, , , CAN. Fieldbus RS-485 , 1,2 , 32 .

, -

(internetworking), (). , , -

, , , , .

(repeater) , - , .

,

(, ) - - , , -

.

, , .

. , ,

.

. ,

10Base-T Token Ring.

.

(bridge) , , .

, , -

, . -

-

.

, -

. ,

, .

, .

.

,

.

, , ,

80

2.7.

.

: . .

,

,

.

. 2.12.

. , -

, , -

. -

. ,

.

, , ,

(AS Autonomous System). AS .

. AS AS, (). , .

-

-

. , ,

, . -

-

, . . .

.

,

.

. 2.12. : ; ; ;

FDDI ;

81

2.

(router) , . -

-

, , .

,

IP- . - , -

, . . ,

.

(, -) . - -, -

- . ,

, -

. IP-- -

.

( out-through), - ,

( store-and-forward). , -

.

, -

.

, ,

, .

. , ODS Infinity - Optical Data Systems Ether-net, Token Ring, FDDI, Local Talk, 48, 48, 2 6 . - ( ), . -

.

.

,

, , .

,

, .

, ,

- .

82

. ,

.

.

,

. .

() , - , .

, -

. -

( - IEEE 802/10), . () .

Cisco. - Catalyst 1024 FDDI, E, TR,ATM. .

(gateway ) ,

. -

. ,

Ethernet SNA, - . , -

.

1. .2. ?3. ? ?4. -

.

5. (TDM) (FDM) ?

6. / - ?

7. 10Base-5, 500 .

8. ?9. RadioEthernet?

10. 4b/5b 8b/10b - ?

11. Token Ring?12. Ethernet ?

Gigabit Ethernet.

83

2

13. 4 130?

14. - ?

15. - ( 36 . ).

16. 1 ?17. , -.18. -

TCP?19. IP- , ?20. ?21. ,

ATM.22. ?23. ?

3.

3.1.

, , -

.

,

.

-

-

. , ,

.

,

, -

, -

. .

( , -, ) - -

. ,

,

.

, ,

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85

3

/. () , ,

, .

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- . -

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.

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, .

.

,

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.

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.

.

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,

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.

. ,

.

,

|0|

3.1.

, -

. ,

, ,

.

-

.

-

(). , - : -, ,-, .

-

.

,

,

. -

, ,

. -

.

-

(. 3.1) . ,

, -

. -

.

|

t

. 3.1.

87

3.

,

, ,

, .

3.2.

.

,

.

, .

.

,

(), , ().

-

.

()., -

,

. -

. -

, , ,

(), . - : - -

.

, .

VK(dV/dt,\,t) = , (3.1)

Ft(V) = 0, (3.2)

88

3.2.

V = (v,, v2, ..., ) ; t . , -

(, -) (, ). ,

(, ), .

, -

.

.

.

. -

.

- -

.

: , , - R, , L. - . 3.2, .

:

= iR ( ); = Cdu/dt;

(3.3)(3.4)

- Ldi/dt, (3.5) (, ); / .

R

L

-DI-

. 3.2. : , , ;

89

3.

. 3.3.

-

.

(3.3) (3.5) (. . R, , L ), R, , L , . -

.

() (). , ,

:

= , (3.6)" f = 0, (3:7)

.

- ; J9 , q-e .

. . 3.3 , /

= 1

(

/(/

)) im= /^^/

/(

)) - /?-; '^ /

; /

;

;

; R^viR^ - , /?6 RK ;/' = Bi - i , ;

' .

,

, 1

, /

, /. - , .

. -

.

.

, ,

. -

,

.

90

3 2.

, ,

F= Mdu/dt, (3.8) F ; ; .

,

. ( - )

G = e, (3.9) G ; ; = /// - ; / / - G. , G = F/S, F , S , (3.9),

dF/dt = (SE/l) d(U)/dt

dF/dt = gu, (3.10) g = SE/l (, , - Z,M); = d(&l)/dt .

-

, -

,

, -

.

, -, : , , , (); -, , -, .

-

-

, , -

, .

. 3.2, . -

. ,

( ) , (3.4) (3.5) /, (3.8) (3.10) MnL

u, -

. ( ),91

3.

L ZM ( ), R Rrp== du/dF ( ).

-

: ( ), {ID) (3D) . , 3D - , , -

.

, -

, -

.

. -

. , -

-

.

/ - ( ):

pdU/dt = -dP/dx-2aU,

; U ; ; . U = Q/S, Q ,S , , - ,

dQ/dt =5/(/) - 2aQ/p, '

= LrdQ/dt + RTQ. (3.11)

;Z

r= A/pAS , -

; RT= 2 aAl/S , - .

. -

:RT= 8//(4), ; - -

^> -^v> | - [ =1 - ' = R

rQ\Q\ R=0,31(nru /\Q\)M.

. 3.4. (3.11) , . 3 .4.

92

3 2

/,=/2

. 3.5.

,

,

(3.12) (3.12) , Q - U d&l/dt Q US,

JAP/ = CrQ,

Cr = E/(S I) .

. -

: -, -

.

, . 3.5. ; g ; U / '- ; j = 1 , / = 2 - .

. , -

,

VHDL-AMS, across quantity, through quantity.

.

, . . ,

.

(3. 1) (3.2).

93

3.

Jtl =U [VR.

. 3.6. () ( ) -

-

, . -

,

. , -

, . -

( - ,

).

. 3.6. , -

, -

. ,

, -

.

. -

() , . . - 1 , - , ( - ). . 3.6, , . 3.6, , .

Ux 1^

,

1

-

+

= 0; (3.13)1

-

1

= 0, (3.14) ; 7 -.

94

3.2,

3.1

RI

R2

R3

R4

J

1

-1

00

-1+1

2

0

-1

0+ 1

0

00

-1+1

0

- -

,

. -

. -

. -

- q- , -

= +1 - ,

= -1 . -

= 0. . 3.6 -

. 3.1

.

( ). , , ,

.

, , -

; , , ; , . -

.

. 3.7, - , ,

51,52 1,2. . 3.7, - , -

, , -

, ; , . 3.7, , .

\L

. 3.7. : - ; -

95

3

(3. 1) (3.2) , -

. -

, , -

.

, , -

,

V - V - ; = tn - t

n_l

. -

t ( t t

n),

FT(VJ = 0; (3.15)Z

n= (-_,)//*

Vn

, Z = dV/dt. , ,

-

.

2 + , ( , -

, -

), . -

, -

( ) .

.

. -

.

( , ), - W . - , -

96

3 2

. , ( ,

2/2), -, . . , .

,

, . . ,

dWIdt W, - .

-

.

, -

.

-

(. . - , ,

, -

). -1, . , , ,

2 . -

, -

.

.

. -

,

. , -

, (3.13) (3.14)

U + M

3.

1 =

+, (3.18) , -

(; , - /

.

( ) -, -

.

(3.18) (3.16) (3.17), :

1= MT(GnU

n+ ) = -

+ =

=

, (3.19) =

- ; =

. -

, ( - 1), , -(-1)(-1).

(3.19) (), , - -

. -

,

.

, .

, -

R. -

.

-

in = Cdu/dt \ = ( -.. ,)/*,

g = 11 = const

g=C/hn.

= gun ,.

:

= !(/-/ _,)/ L = const

98

3.2.

-

,

dU/dt I = - ,

; \ U - .

.

, ( ) -, , , -

,

.

, -

, -

.

.

, -

. (. 3.2), -: UHCT(I) , ; (/) ; 1

(1) , ; L ;

- i ^.

UHCT, I, , 1 . , -

, . . I, . ( ) . : IL - ; I, ,.- ; G

x, GL, G, -

, , .

(3.17)

3.2

L

1(1)

21

3,

(1)12

22

32

( / )

23

33

99

3.

I, (3.18), 1

= (91

/51) - . (3.16),

U,= -

- 12 - 13 = - 1] - 12 (/1)1 - ,3.

, I 1L:

- (

) /

+ M12RI) + (2)) I, + (31) KI == (

)(,13-,); (3.20)\ = - 21 + M22RI + 23) + ,; (3.21)I = - ,(31 + M32RI + 33) + (3.22)

R = (5UHCT/9I). - .

. 1 . -, AL -. 2. , , , 1

/5 Gi5 - . 3. , , ,

, -

(3.20)-(3.22).

3.3.

-

. ( -) , - ,

, . -

, , , -

-

, , ,

, . .

100

3.3.

, -

,

():

, -

. -

, (3. 1 5), , -

.

-

, . -

-

.

( -, , ) - (, ). -

.

tn:

; hn = t

n + , - t

n

( hn ).

: < / V / A | = ( V - V ,)/A,1 v -1 ' '

= *-*_,. -

:

dVldt = AV (3.23) V0 - h. ; V .

101

3.

. Vn + 1 -

V0:V_

+ 1 = (E + /zA)"V0. (3.24)

= + (3.25) :

= T-'diag^JT.

- ; diag{A,B } - - ,

. ,

, ,

, -

. (3.25) :

(3 .23) V( /) > 0 / > , ,

+ 1->->,

( + /zA)" V0 -> , V0* 0, ( + )" -> 0, ^ 0, . - 0 -

- |1 +

| < 1. (3.26),

.

.

( (3.23) ), -

^-^,,

(3.26) - 1 < | 1 - / | < 1 < < 2

, (3.27) .

,

(3 .27), .

102

3 3

(3.27), -, ,

. , -

.

(3.27) . ,

-

(3.27) , ,

, 1

.

(3.27) . -

. , ^ -

, . . -

.

=

/

. , .

,

> 105 . - .

-

. (3.24)

h > 0. , - -.

. -,

h > 0. ^ - -

.

, .

; -, , -, -

^-

. -

-

.

103

3.

, -

,

. ,

.

, - -

, . . , - , -

V( t) , , - ; |V(/>+1)(t)| ( + 1) V(/), - ; - / .

- , . .

, h . V(f) - t

n + l, ( + 1)- + (d2V/dt 2)AV2! - (d3 V/dt 3)#/3! + ... (3.28)

( + 2)- V(/;

+ 2) = Vfc + 1) + (dVldt)ht + (d2\/dt2)h2x/2\ + (d3V/dt3)h3x/3\ + ..., (3.29) h

n h , -

tn+ . (3.28) (3.29), h = = /?

V(tn + 2) = V(tn) + 2(dV/dt)h + 2(d3V/dt3)h3/3\ + ...,

. . , (3.28) (3.29),

h3. , .

, ,

. -

,

,

.

-

. ,

() d, -.

, , ,

.

104

3.3.

.

, . -

, -

(). . , ,

(3.19). .

, -

, , -

, -

. , (3.19) . -

.

F(X) = 0. (3.30) F(X) \k ,

F(X) = F(Xt) + (SF/dX)(X - Xt) + (X - Xt)T(S2F/dX2)(X - XJ/2 + ... = 0.

, X:

, (3.31) ^ = (5F/3X)|t. (3.31) (3.30), Xt+ ,.

0

, ,

.

. -

,

. -

. -

, -

.

105

3.

-

, , = 0 = 0 (3.30) , a

0 X

= 0 . -

,

, -

.

, -

,

.

h. , h = . h - .

,

.

. -

. k-w. - xk

= (3.32) at] / > k > k

3.3.

.

, ,

, , 1-

2.

-

, -

, , , .

.

11*1 14*4

(3.33) , , , -

. ,

, .

. 3.3 . . .

. 3.3 3.4, - + . , , .

, -

.

. -

-

, ,

.

( ) -.

3.3 3.4

107

3.

-

. -

( ) -.

. , -

(200 200) 320 . 9 ,

28 .

(3.33) a, k 0 akj * 0 , ,

(3.33). - , -

, , -

, .

,

.

(3.33) - .

. ,

. , -

.

-

. -

, d/dt -'.

, -

, .

. -

.

,

-, ,

. .

-

X Q . , . ,

108

3.3.

. . , ,

.

-

,

X Q, - . -

-

, , ,

,

. .

.

, -

, . . ^ .

. 1, , . -

.

-

.

-

,

yj . TV -- xt ( X Q), , -

AJC,, , -

!,= (, ~.,)/.,

jt J I I '] *

-

. , ,

./^ 1 . - , -

,, BJt. .

, -

, .

-

() . - -

:,

:. -

,

109

3.

. 3.8.

(. 3.8). -

, Y < , ,

.

-

- ( ). - ./V , - ,

-. -

jc(. - ,

N , : ; :

-

, , ,

.

, -

, , ./V - , .

, -, -

-

- xt.

, *( ,

-

^ xt , ( ). - . -

,

. !

110

3.3.

, . -

,

,j [1 : ]., < (. .sign(.8,,) = ) ^ > sign(5,,) = 1,

= + * ,I I I '

, , , -

,

,

, -

, , -

.

-

. 3.9. -

-

F(X) = . -

= .

. 3.9. : V0(/0) - ;h /?

- ; UBH(/) - ; N NU - ; - ;8 - , ; 1 - ; - .

111

3

V:=V0;t:=to;h:=hHm

, * =

/V :=+

. 3.9. -

, jV> ^

. -

5 , [2, ml] , .

N , ml, m2, ,

-

.

, . -

, -

. . 3.10.

112

3.3.

_>.

t

i

1

*

*

-

. .

( ) .

.

-

, -

. ,

. ,

, , -

.

- , -

, (. . 3.9). - (. . 3.10)- , - . 3.9. . -

,

,

.

-

, ,

- . .

3.

3.4.

,

. ,

. -

JCj, x2, 3 t.

-

.

:1)

- ; - ; - ; t - ; X - - ; g - , - ;

2)

at N- ; D - ;

3) , :

4) div = / (

) . ; q ; Jpu 3 ; gp gn -- ; ; - ;

.

,

, , -

.

- -

.

-

-

114

3.4.

. ,

.

-

: () . - , . . -

.

-

.

IF(z)=/(z)

L ; F(z) ; z == (,, 2, 3, f) ; /(z) y(z) - .

-

--

.

.

, -

.

. 3 . 1 1 . , -

. ,

. , ,

,

. , -

dVldx k,

h(dV/dx) = 4+ , - V-, 2h(8V/dx) = Vk+ , - Vk_ ,; HpVIQ*) = Vk^-2Vk + Vk_ ,, h .

. 3 . 1 1 - :

-

2*2W = V^^ + F t_, ,+

Vk VB (, k, x ); h .

115

3

-1 1 -1

--

1 1 -2 1

(kt

^

).t -1u

. 3.11.

,

F(z). , - qt

U(z.) = QT

3.4.

-

( ), - , ,

.

.

,

= 0,5 I 8TarfR, (3.36)R

= (en, s22, s33, s)2, 813, 823) - - ; = (, 22,

,

, ,3, ?3) - ; R - . stj

etj= 0,5(5)^/5* +dW}/dx), (3.37) Wt *,

= 0,5SW, (3.38) S (3.37) ; W = (w , w , \v ).

D, , . 3.5:

a = De. (3.39) , , ,

.

(3.39) (3.38) (3.36), 3 = 0 , 5 j \ V T S T D S W d R .

R

W(X), X = (,, xz, 3).

(3.34), - :

U(X) = NQ, N ; Q -. 3.5

+2

X000

+2

000

,+ 2000

000

200

0000

20

00000

2

117

3.

W(X) U(X), = 0,5|QTNTSTDSNQrfR=0,5QT( J(SN)TDSNrfR)Q=0,5QTKQ, (3.40)

R R

= J(SN)TDSNc?R .R

/dQ = /dQ - /dQ = , (3.40),

KQ = , (3.41) = 9A/5Q . , , , -

(3.41). ,

(3.41) . .

,

.

3.5. -

- ,

, -

.

-

. , -

.

--

, .

, . .

, -

.

--

.

-, . .

, (3.42) . F,

x - .

, (3.42) ,

FBX .

118

3 5 -

, (3.42) , - , . . -

. , (3.42) - .

,

, -

. (3.42) -, ,

() (),

() .

h(p)- .

, -

.

--

. -

,

(3.42).

, : ,

. -

.

(. 3.12), - ht(p), h2(p) h3(p).

= h}(p)h2(p)/(l -

. 3.12.

119

3

, :1) ,

, -

;2) ;3) ;4) -

;5) -

.

- -

. ,

, ,

.

( 1) (- 0), . - . -

- .

-

.

- -

, -

. , -

, , () = a or b, () = a and b, ()> = not , - , b . .

. 3.13. -

, , -

, .

I

. 3.13.

120

3.5. -

1 & ( \

~

&

R & (L

&

. 3.14. ./US'-

.

,

, .

.

-

, (. 3.14): = not (R and ); Q = not ( and ); = not (A and Q); = not (S and ).

,

.

y(t (3.43) t3 ; / . (3.43), , -

(), t + tm. -

,

.

-

.

-

(-) . ,

. ,

, -

.

-

.

,

. ,

, .

121

3.

-

&

. 3.15. : ;

.

. 3.15, - ,

. 3.15, . , , -

, , . 3.15, , , .

.

.

, 1 , - . - , ,

. 3.6. , ,

.

,

, ( ) ( ) . , -

: 0-0-0, 1-1-1, 0--1, 1--. - 0--0 1--1 - , . . .

3.6

01

0 10 0 00 0 1

0 10 1 11 1 1

0 11 0

-

-

122

3.5. -

3.7

1

0

01

00

(. 3.15, ) - . 3.7.

(. 3.16). , , . -

-

,

{0, 1, , , ), - , , -

.

,

: 0-0-0, 1-1-1,0-a-l, 1-P-0. 0-

3.

-

() . -

/0, /15 /2,... . . -

, -

.

.

. -

: - , -

.

2... 3 % - , -

-

.

-

.

,

.

-

npmfepe (. . 3.14). . 3.8 -

.

( ) - , , Q,P,A, - .

-

R, S . , - , -

.

,

, -

. , -

,

.

,

, -

.

.

124

3.6.

3.8

( 0) 1 2 3 4

R000000

S011111

011111

111*111

Q11110*0

0001*11*

110*000

-

: 1) - , -

(); 2) ( ) 0; 3) k, k - 1.

, (. . 3.14) Q Q,, - : S, , Qt 0,- \,- 2 > - 3. :

= not (S and ); = not (R and ); =not (A and Q);Q=not ( and P). ( ) .

,

, ,

.

-

. - -

, .

(. . 3.14) : 16- , . 3.8, -. . 3.8 , - . , , 0 5 , -

.

3.6.

-

, , , -

,

. .

(-125

3.

). , -

( ) , () , .

, ,

, , , -

, . , , , -

-

. , ,

. -

,

(). -

, , -

, ,

, . .

(), (), - . -

. -

, . ,

.

-

. , -

.

.

, , -

true () false (), - , .

, , -

.

, -

, , , -

, . -

.

FIFO ( ), LIFO ( ) .

126

3.6.

.

, . -

, . -

,

, .

, -

. -

.

, . .

, ,

,

. -

, -

.

.

, , -

.

-

.

, -

, .

, -

- -

,

, -

. , , -

. -

,

, .

-

, -

-

.

() . -

. (, ), . -

, -

.

127

3.

,

. -

.

-, , ,

FIFO.-, -

.

-, -

, . . ,

, ( ), .

. -

.

S, -

( ). , , ,

( ) ( ).

, F =limP (*,)/*, (

> 0, { (fj) - St S t

r

'

(3.44)

N . . 3.17 -

1,,..., S4, . 3.9 -

.

3.9

5iSi554

Si-Ki2-Ki3-Ki4

V2100

52Vu

-Vi\0

K42

5Vn0

-F340

54

0F34

-F42

128

3 6

, -

, . .

() - -

. -

, . 3.17. -

. , ,

.

.

St t} S - St f,, . .

(0 = (,) - (0 = IP ,(gp ( - (,(0, (3.45),/eJ *

P(t) P(f) - S S - t, ,(^,) ?,) ?,; ,(f,)P (0 S 5 , , - ; J S .

(3.45) /, t > ,

*L(V )- I V ..v j i 1 ' i ik

J *

dP/dt = 0 , /- -

Z ( F y , P ) = P Z F t . (3.46)j * Vt ( (3 .46) (3 .44),

N N

Jl J ' I;=1 t-1

\

129

3

. .

.

, -

, -

, -

.

NW , , Q

m , T

w ,

.

. 3.18 , Sk k . . .

,

i= 1,2,3,..., 0.

^^^

2= (( + )/, - 0)/ = (1 + ), - 0 =

3.6.

3.10

SoSi5SiS*

So-

000

Si

-.-

00

S20

--

0

500

--

S4

000.

--

:

Nm - Z Pkk = ,+ 22+ 3 + ... = (\ - \\

- );= 2 + 23 ... = Z (k- \)Pk = ^

:

N = ^av av

2av=^

:

-

,

. -

.

, ,

(). .

- -

.

( - ) , .

, SMPL . - , SOL, GPSS.

--

, -

. , GPSS , -

, . .

5- 131

3.

, ,

-

, , .

, -

tk -. . -

, .

tk .

() . .

, .

,

, .

,

, . -

, , , -

() .

,

, ,

, , ,

. .

, -

,

(). , , -

.

, -

, . -

, , -

tk. , ,

,

, . . -

,

. -

, -

.

132

3.6.

-

.

, . -

() -, . ,

-

(, ), . -

, -

, -

.

-

.

,

. . . -

. -

(), (). , - (), , . .

,

.

(), . - ,

. X.

(. 3.19):

. 3.19.

133

3.

1) X; , X, X , ^

X;2) ,

, X, ; - ;

3) , - , ,

; ,

, ; ;

4) . , tt, -

, -

, .

GPSS GPSS (General Purpose Simulation System), -

, . (-) GPSS ( ), , . GPSS ,

,

.

GPSS : [],

, ,

, 19-, .

, , -

, , , ...

, , -

, , -

. , , 1 , FN , ( L -, L 12), , RN1 , [0, 1], S ,F , Q .

134

3.6.

$,, QSORD ORD FN$COS COS.

, -

.

GENERATE A,B,C,D,E ,

: 1) [ - , + ] ; 2) , , ; ; D ; - . D , -. :

GENERATE 6,FN$EXP,, 15 , 15 , 6 ;

GENERATE 36,12 , -

[24, 48]., ,

:

FUNCTION A,B ,

/^/^/...^^ , ,

, _ Y - , .:

FUNCTION RN1.C120,0/0.2,0.22/0.4,0.51/0.5,0.6/0.6,0.92/... . .

() , 12 , (RN1), - [0,1];

FUNCTION *4,D61,2/2,5/3,11/4,20/5,18/6,12/7,9

(D) , - , .

SPLIT A,B,C . -

, ( ) .135

3.

,

.

1, - 2, 3, 4,... . .

ASSEMBLE A

, 1 ,

GATHER A ,

.

SEIZE A ,

RELEASE A .

ADVANCE A,B , GENERATE.D 1. WST - , -

[7,11] , -:

SEIZE WSTADVANCE 9,2RELEASE WST

D

ENTER A,B , () ().

LEAVE A,B , -

:

STORAGE A , .

136

3.6.

-

, -

.

.

,

.

QUEUE A

DEPART A -

.

, -

.

TESTXXA,B,C , ,

, XX , XX {E,NE,L,LE,G,GE}; ; NE ; L ; LE ; G ;GE (XX 13 14).D 2. , 4, . :

TESTLE Q$STR,K4,LBLQUEUE SIRSEIZE POINTDEPART STRADVANCE 50,16RELEASE POINT

LBL TERMINATE 1

D 2 TERMINATE A

.

.

, -

START ,

. .

137

3.

3. GPSS SIMULATE

START END.

D

TRANSFER ,B , .

TRANSFER. :TRANSFER P,B,C

,

.

TRANSFER FN,B,C , -

.

TRANSFER PICK,B,C , -

[, ]. TRANSFER A,B,C

,

1 - .

LOOP A,B () , , .

D 4. , [20,40], WGR1, WGR2 WGR3, . WGR1,WGR2 WGR3 0,05, 0,1 0,125 . - ,

1000 .:

SIMULATE FUNCTION RN1.C12

0,0/.2,.22//.4,.51/.5,.6/.6,.92/.7,1.2/.8,1.61/.9,2.3/.95,3/.99,4.6/.999,6.9/1,GENERATE 30,10SEIZE WGR1

138

3.6.

ADVANCE 20,FN$EXPRELEASE WGR1SPLIT 1,MET1SEIZE WGR2ADVANCE 10,FN$EXPRELEASE WGR2TRANSFER , MET2

MET1 SEIZE WGR3ADVANCE 8,FN$EXPRELEASE WGR3

MET2 ASSEMBLE 2TERMINATE 1START 1000,, 1000END.

D -

X .

F(T) = \p(f) dt=l- exp(- X 7).

. 3.20 , - , ,

[0, 1] , (3 = (1/)1(1/(1 - )) (3.47)

. (3.47) ADVANCE (. 4) 1/.

GPSS.

ASSIGN A,B , -

. F(T)ASSIGN A+,B 1

, -

ASSIGN -. -

- ' in

3.

X = S , X = R ;

GATE_XXA,B XX = LR = 1 XX = LS = 0 - ( GATE, ), XX . -

VARIABLE A

,

3 VARIABLE K216-S$MEM2 3 216 2. , , ,

LBL MATCH NUMB ,

NUMB MATCH LBL .

,

, .

TABLE A,B,C,D ; ; ; ; D .

TABULATE A /- , . z'- , .

-

( ). , - , I . , ,

, , -

, ; I - , ,

.

, : () .

140

3.6.

.

. -

, . ,

-

.

.

( ), -

. -

.

(. 3.21) : , - N, > Kt, N, '- , , , /- ; '- /- }, } , '- .

. 3.21 , (2, 2,3, 1). - : (1,0,1,4).

-

, . ,

, -

, . -

() , - , .

.

, -

. -

. , . 3.22 ,

/ (2. - .

,

- ,

. ., .

.

,

. ; - .

.

-

, , (-) . , , .

141

3.

. 3.21. . 3.22.

.

1. WS WS .

. 3.23. -: /, - WS, t2 , /3 - /, , t4 - ; 4 - WS:

, WS - -

/2; -, 4 , ,

{ -

tr

. 3.23. ( 1) 2.

, /- ; ; , -

, . . 3.24 - . , , ,

, .

2 -

. : tt , /2 , /3 , t4 .

,

/, -, , -

.

/, , f2, 6. , -

-

-

. t2 - , -

v_y. 3.24. ( 2)

142

3 6

. 3 , ( 4 ), ty 2, 5 6 , . 14 - .

,

, .

, ,.

, .

-

.

.

-

, .

, , -

, , , .

( -) , . -

/^ - . -

.

, 1 --. , ,

.

, . .

= const,

Nt /'- ; : .

- , -

, , Mt.

.

,

, , .

.

0 .

0, . , ,

( -> /. .

,

(, Mt 143

3.

. 3.25. ( 1)

. 3.26. ( 2) , -

Mt). - , . . . -

- -

.

.

1. . 3.25. , -

. ,

, , .

2. . 3.26., -

, , , .

3.7.

() -. -

, , -

144

3 7

, . . , -

,

(, , . .).

, -

( ), - , -

. -

. -

, ,

.

.

(2D) (3.D) . - 2)- - - ,

. -

2D-, 31)- - ,

, -

. .

31)- (), , () .

, . -

-

. -

,

.

-

, , ,

.

,

.

(, , ), -, ( , -), .

,

.

-

.

1. , , .

145

3.

2. , ; - .

3. , - () , ; .

4. () - . ,

, , , . -

- , , -

. , -

.

-

.

-.

-

, . . , .

-

. ,

.

-

-

.

, , -

. ,

, -

.

-

. ,

, , -

. -

.

, -

.

:1) ,

( ); , ;

2) , - .

146

3. 7.

-

-

, -

.

-

5-. ,

3.27. -

.

. ,

, , .

-

x(t) = axt3 + b

xt2 + c

xt + d

x ;

y(t) = ay t3 +X by t2 + cy t + dy ; (3.48)z(t) = a.t3 + b_t2 + cj + d_,

1 > t > 0. -, . .

(3.48). (

) . -

-

.

5- - (. . ) , - , -

.

, -

.

(3.48) , -, (3.48) (=0(=1 - , 4 , -,

dx/dt = t2 + 2b + ,X X 'dy/dt = , 2 + 2byt + ,dz/dt = 3a.t2 + 2b.t + .

/ = 0 / = 1 2 3, (. 3.27).

(3.49)

147

3.

3.11 3.12

-13

-31

3-6

30

-3300

1000

-1/61/2

-1/21/6

1/2_j0

2/3

-1/21/21/21/6

1/6000

= (/3, t2, t, 1) -, . 3.11,G^ P

xi ,, 2, 3 4, Gy, G, . , .

5- , - 0, ,, 2, ..., .

( [+] ^ -, -

,.,, ,+ ,, , + 2. 5- [(, Pj+1] , (3.49),

. 3.12, - G

x, G ,^ G. ,_1; , + 1, , + 2.

, -

, -

-. -,

[ , +1] , [Q(, Q, + ]].

Q/+ , t = 1 dX(t)ldt\t__ , = [3t\ 2t, 1, 0] [*_*, *+|, xi+2F= [3, 2, 1 , 0] [,_ , , xi+], x+2]T= (-);d2x(t)ldt\^ = [6t, 2, 0, 0] [^^^^- [6,2, 0, 0] [*,_,,*, ,++2]= -2+

[Q|+1 Qi+2] Qi+| t = 0 0 = [0, 0, 1,0] [^,,^=(-2;

Uo = [0. 2, 0, 0] [ > xi+],xi+2, xi+3] = - 2 , +1+ , +

. .

. ,

Qi+1 [Q^ QI+1]

= [1, 1, 1, 1] 4x , [Qi+1 Q,+2], +]

.

5- , (3.48) .

148

3. 7.

( )

, ( ) , , , , .

, , .

^ ,. -

= , (3.50) .

- 1 3, -, ,

W. ID (3.50), . 3.13, a W- 1.

. 3.14 3.15 ,

,

,

.

3.14 3.13 3.1510

A*i

01

2

001

00

0

0

001

COS

-sin 0

sin COS

0

001

(3.50) , (3.50). ,

= = , '

=

;

;

.

.

= + , 1 > > 0 ( - -

). : = (, yd), = (xb, yb); () . ,

, :

149

3.

1) : = - ;Ay:=yb-ya; := ;: = ;2)d = 2Ay- Ax;3) d> , { : = +1; d := d+ 2( - )}; d:=d+2 Ay;4)jc: = *+ 1;5) 3, .

. 3.28. .

, -

.

= *,, = 2, =, = 2 (. 3.28). -

. , ABCD - = 2

.

R:1) JCP > 2 XR > 2,

;2)

< 2 XR < x2, ;

3) jcp < 2 XR > 2, , R = 2, = yf + (yR - )(2 --XP)/(XR-xf); ;

4)

> 2 XR < 2, = 2, =yR + (yf-yR)(x2- *(~ XR)' R ;

-

.

,

AEFD, = 2 AGFD(. . 3.28). , - AGHFD. ,

, .

.

z-, z- , . -

, z z = 0.150

-

z, . . - , -

z- (). z. , (- z- S), z (. . ) S. z- - .

.

-

-

'

1

N

1 1 J

/^ ''

fi \9 Ai

iI

tii

iii

i'o

. 3.29.

(. 3.29). , '

'

*; = x.dlz,

'

".

d > " . ,

.

,

cos ,

. -

. -

, -

. ,

.

1. .2. . 3.30 , ,

. i3. -

-

. 3.30.4.

(- ), . 3.31, F , .

R, * 1 1 1-J * /"*

? 'if2

1'.. 3.30.

151

3

. 3.31.

5. (. . 3.30) -

.

6. -

. 3.30.7. ?8.

dx/dt = 10 - 2

= 0 h - 2, (3.27). .

9. ?10.

?11. ?

12. - -

?13. -

?14. -

f(x) (. 3.32, - /,).

15. . 3.33.

16. .

. 3.32. -

17. .18. .19. ,

-

"k. - , . 2, - .

20. GPSS , - .

.

1 2, 1 3.21.

, , -

. -

GPSS.22. GPSS , -

. 3.24 .23. -

?24. ,

D.. 3.33. - 25.

-?

152

4.

4.1.

, -

-

. ; -

. ,

, -

. -

-

. .

. 1, -. , -

. -

, ,

, -

. , . .

. ,

,

, . . . -

,

,

. .

-

, -

153

4.

.

, . . -

. -

, -

-

. ,

. -

, , . . -

.

-

( ), - ( -). .

: - Y X, - . -

. ,

,

,

.

,

,

. , -

, -

. -

,

, .

-

extrF(X), (4.1)XeD^.

,= {|0,/() = 0}, F(X) ; X () -; () vj/(X) -; D^ - . (4.1) -

.

154

4.1.

, -

, -

, (4.1), -, F(X).

-

-

, -

, (4.1) . ,

\ ! , -

- 4.1.

.

.

-

,

(4.1). -, -

. -

(. 4. 1 ). -

7, 2, >>, < } 2 < . .

-

, -

. ,

, .

, -

, , -

. (. . 4.1) .

. 4.1. }, X, . , , , -

-

. , ,

, -

. , . . -

. , -

, 2,

.

155

4.

() - ( ) , -

F(X) = ^(), (4.2)

; . (4.2) ,

> , < 0. ' j j j

-

. , (4.2) .

, -

)=^(). (4.3)

, (4.3), - .

,

, -

. -

'- -

S '- . ( , -

,

< ):J S = (T-yj)IT,

S = (T-y ) / 8 ,J V 1 J J' J>

, 5 '- , , . -

[1: ] 1 . (4.1) -:

F(X) = max min S (X), (4.4)XeD

x 6[1 ] '

156

4.2.

D^ :

-

.

. 4.2.

. 4.2,

-

. -

, -

,

-

.

-

,

-

,

. -

, .

, , -

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157

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159

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