3.2.1
3.1 . λ. , , , , , . , μ-1 .
, , .
; ; ;
3.1
, , . , : , , ( ), , , . , , .
, .
, . Q.514 :
F(t+)=1-e-(Mc-λ) t (3.16)
F(t+) () t.
F(t+), t, λ. (3.16), .
(, ) :
π = 
=λ/μ ;
[0]= 
φ=0, =0, V-1, φv=1,
π=Ev(A)= 
(3.17)
, π . (3.17), , .
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=90 . μ-1=3 (μ=20-1, =5,5 -1. F(t+) t=0,6 V=10 . λ=Α*μ=1800 -1=0,5 -1.
Pascsal.
program 3.l6;
uses crt;
const e=3.27;
var Ft,ly,t,mc:real;
begin
clrscr;
writeln('e=',e:4:2);
write('inter ly=');read(ly);
write('inter t=');read(t);
write('inter mc=');read(mc);
Ft:=1-exp((-(mc-ly)*t)*ln(e));
writeln('Ft=',Ft:4:4);
end.
inter ly=0.5
inter t=0.6
inter mc=3
Ft=0.9714
program 3.17;
uses crt;
const v=10;
var Pi,A,ly,u,sum,fi,fv:real;
z:array[1..v] of integer;i:integer;
begin
clrscr;
write('inter ly=');read(ly);
write('inter u=');read(u);
writeln('inter v=',v);
A:=ly/u;
writeln('A=',A:4:4);
sum:=0;
fi:=1;
fv:=1;
for i:=1 to v do
fi:=fi*i;
sum:=sum+exp(i*ln(A))/fi;
fv:=fv*i;
Pi:=exp(v*ln(A))/fv;
writeln('Pi=',Pi:4:10);
end.
inter ly=0.5 inter u=3
inter v=10 Pi:=0,0000000001.
3.2 - 3.16
3.3 3.17
3.2.2
, , , .
, , , , , , . , , ( ) . () ( ) , . () , , . , , . , , - . , ( ) .
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: ( λ, μ, A=λ/μ) , . k kω, θ, AL=ω/θ. , , , : , , , . , V- .
= 
: A=λ/μ , AL=ω/θ. B=EV(A+AL), A0= λ(1-B)tm, tm- . , tm 
μ-1, A0=A[1-EV(AL=a)]-A[EV(AL+A)-EV(A)].
, ( 3.4) , , . .
3.4 -
N , h , j- Vj (j= 
). , , , , .
, , ( ), N 
100α/μ ( ) N>100α/μ. α, μ, a0=α/μ. λ=Nα, μ, 0=λ/μ. , i- j- , . , j. , j=kja0(Aj=kjA0). . .
, , .. , . , .. (, ), , , . , , , , . ra.r.,, rc.
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, V - , , V , (, ), , , . .
. . , . , , 5 - .
. . , , , ( ) .
.
N=n, j=h, Vj=V, s=1, n ; s . , ..=..=0, > , ( ) , . : d () , , V-d. , (3.16)
, (3.18)
- y (V-y) .
d- ;
d .
BASIC. p = V = 1, B = 25,56 , = 3.
10 INPUT A, B, V
20 V1 = V
30 A1 = B
40 GOSUB 220
50 D = 1
60 W = 1
70 Z = E1
80 IF V <= 0 GOTO 160
90 W = (W * A) / D
100 V1 = V - D
110 GOSUB 220
120 H = W * E1
130 Z = Z + H
140 D = D + 1
150 IF D <= V GOTO 90
160 V1 = V
170 A1 = A
180 GOSUB 220
190 P = Z / Z1
200 PRINT "P="; P
210 STOP
220 I1 = 1
230 W1 = 1
240 Z1 = 1
250 IF V1 <= 0 GOTO 280
260 W1 = (W1 * A1) / I1
270 Z1 = Z1 + W1
280 E1 = W1 / Z1
290 I1 = I1 + 1
300 IF I1 <= V1 GOTO 260
310 RETURN
320 END
? 2,5,1
= 0,879.
.
3.2.3
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. , , . , .
n . 3.5. S0, S1, ,Sn - , (S0 ; S1 , ; Sn n ); λ=1/ μ=1/t T ( ) tc . Pn , :
S0 ; S1 , ; Sn n
3.5
Pn=(Rn/n!)/ 
(3.19)
R= λ/ μ . tc, R=tc/ .
( n) n n N n n(R) n(R)=F[En-1(R),n,] , .
.
, , . , Ei , i , n(ΣEi=N) pi I ( 3.6).
1 ; 2
3.6
, : 1 2 ( 3.6).
λ μ 1,2, :
dE1/dt=-λE1+ μE2;
dE2/dt=λE1+ μE2.;
dE1/dt=dE2/dt=0;
2=Nρ+(1+ρ),
ρ=λ/μ.
ij :
 |
i = 1, j- i;
0, .
j :
| i | ||
| 1-i | pi |
pi i.
i=2 N xij=xi
D[x2]=(0-p2)2(1-p2)+ (1-p2)2,
D2=E2(1-E2/N)=Nρ(1+ρ)2.
2+3 
(, ). n N , ρ, :
n=(Nρ+K 
,; (3.20)
2,2- 70 ;
= 2,31 100 .
K , ( ) . , (3.2) Nρ , R (3.16).
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(3.17) (3.17) n=n(N, Pn), En(R). ρ=0,05 ( 0,05 ) , n ( ) 1%.
.
( ) E2 D2 (2) :
()= 
n, 2=Nρ/(1+ρ) n-E2:
; (3.21)
(3.17) (3.18) 
1-2F(K).
=-n;
n (3.16) 
(3.17), , .
(3.18) (3.17) =2,22,31, ( =0,10,014), N 
20 0,04 
0,01, . , <0,03n n=(0.010,015)n - n 11,5% 3% 0,0004. , .
Pascal , 3.7 .
program laura1;
uses crt;
const n=10;
var Pn,Rn,Rj,ly,nu,sum,R,f,f2:real;
a:array[1..n] of integer;j:integer;
begin
clrscr;
writeln('inter number of chanel n=',n:1);
write('inter ly =');readln(ly);
write('inter nu =');readln(nu);
R:=ly/nu;
writeln('result R=',R:4:10);
f:=1;
for j:=1 to n do
f:=f*j;
writeln('fa=',f:4:10);
Rn:=exp(n*ln(R))/f;
writeln('result Rn=',Rn:7:10);
sum:=0;
f2:=1;
for j:=1 to n do
begin
f2:=f2*j;
Rj:=exp(j*ln(R));
sum:=sum+(Rj/f2);
writeln('sum=',sum:7:10);
end;
Pn:=Rn/sum;
writeln('Pn=',Pn:7:10);
end.
n=10
n=0,0000151088
3.7
