Теория массового обслуживания. Сивохин А.В - 251 стр.

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251
d
dt
p
6
t( ) = -5.08 p
5
t( ) - 25.68 p
6
t( ) + 20.60 p
7
t(),
d
dt
p
7
t( ) = -5.08 p
6
t( ) - 25.68 p
7
t( ) + 20.60 p
8
t(),
d
dt
p
8
t( ) = -5.08 p
7
t( ) - 25.68 p
8
t( ) + 20.60 p
9
t(),
d
dt
p
9
t( ) = -5.08 p
8
t( ) - 25.68 p
9
t( ) + 20.60 p
10
t(),
d
dt
p
10
t( ) = -5.08 p
9
t( ) - 25.68 p
10
t( ) + 20.60 p
11
t(),
d
dt
p
11
t( ) = -5.08 p
10
t( ) - 25.68 p
11
t( ) + 20.60 p
12
t(),
d
dt
p
12
t( ) = -5.08 p
11
t( ) - 25.68 p
12
t( ) + 20.60 p
13
t(),
d
dt
p
13
t( ) = -5.08 p
12
t( ) - 25.68 p
13
t( ) + 20.60 p
14
t(),
d
dt
p
14
t( ) = -5.08 p
13
t( ) - 25.68 p
14
t( ) + 20.60 p
15
t()
> diff(p[n+m](t), t)=Lambda*p[n+m-1](t)-
n*Mu*p[n+m](t);
d
dt
p
15
t( ) = 5.08 p
14
t( ) - 20.60 p
15
t()
> ODESystem:=
{diff(p[0](t), t)=-
Lambda*p[0](t)+Mu*p[1](t),
seq(diff(p[k](t), t)=Lambda*p[k-1](t)-
(Lambda+k*Mu)*p[k](t)+(k+1)*Mu*p[k+1](t),
k=1..n-1),
diff(p[n](t), t)=Lambda*p[n-1](t)-
(Lambda+n*Mu)*p[n](t)+n*Mu*p[n+1](t),
seq(diff(p[n+si](t), t)=-Lambda*p[n+si-
1](t)-
(Lambda+n*Mu)*p[n+si](t)+n*Mu*p[n+si+1](t),
si=1..m-1),
diff(p[n+m](t), t)=Lambda*p[n+m-1](t)-
n*Mu*p[n+m](t)
};
ODESystem :=
?
?
?
d
dt
p
2
t( ) = 5.08 p
1
t( ) - 13.32 p
2
t( ) + 12.36 p
3
t(),
d
dt
p
5
t( ) = 5.08 p
4
t( ) - 25.68 p
5
t( ) + 20.60 p
6
t(),
d
dt
p
14
t( ) = -5.08 p
13
t( ) - 25.68 p
14
t( ) + 20.60 p
15
t(),
d
dt
p
0
t( ) = -5.08 p
0
t( ) + 4.12 p
1
t(),
d
dt
p
1
t( ) = 5.08 p
0
t( ) - 9.20 p
1
t( ) + 8.24 p
2
t(),
d
dt
p
3
t( ) = 5.08 p
2
t( ) - 17.44 p
3
t( ) + 16.48 p
4
t(),
d
dt
p
4
t( ) = 5.08 p
3
t( ) - 21.56 p
4
t( ) + 20.60 p
5
t(),
d
dt
p
6
t( ) = -5.08 p
5
t( ) - 25.68 p
6
t( ) + 20.60 p
7
t(),
d
dt
p
7
t( ) = -5.08 p
6
t( ) - 25.68 p
7
t( ) + 20.60 p
8
t(), 
d                                                   d
   p6(t) = -5.08 p5(t) - 25.68 p6(t) + 20.60 p7(t),   p (t) = -5.08 p6(t) - 25.68 p7(t) + 20.60 p8(t),
dt                                                  dt 7
       d                                                  d
         p (t) = -5.08 p7(t) - 25.68 p8(t) + 20.60 p9(t),   p (t) = -5.08 p8(t) - 25.68 p9(t) + 20.60 p10(t),
       dt 8                                               dt 9
       d                                                      d
          p10(t) = -5.08 p9(t) - 25.68 p10(t) + 20.60 p11(t),   p (t) = -5.08 p10(t) - 25.68 p11(t) + 20.60 p12(t),
       dt                                                     dt 11
       d                                                     d
         p (t) = -5.08 p11(t) - 25.68 p12(t) + 20.60 p13(t),   p (t) = -5.08 p12(t) - 25.68 p13(t) + 20.60 p14(t),
       dt 12                                                 dt 13
       d
         p (t) = -5.08 p13(t) - 25.68 p14(t) + 20.60 p15(t)
       dt 14

> diff(p[n+m](t), t)=Lambda*p[n+m-1](t)-
n*Mu*p[n+m](t);
                                        d
                                          p (t) = 5.08 p14(t) - 20.60 p15(t)
                                        dt 15

> ODESystem:=
         {diff(p[0](t), t)=-
Lambda*p[0](t)+Mu*p[1](t),
          seq(diff(p[k](t), t)=Lambda*p[k-1](t)-
(Lambda+k*Mu)*p[k](t)+(k+1)*Mu*p[k+1](t),
k=1..n-1),
          diff(p[n](t), t)=Lambda*p[n-1](t)-
(Lambda+n*Mu)*p[n](t)+n*Mu*p[n+1](t),
         seq(diff(p[n+si](t), t)=-Lambda*p[n+si-
1](t)-
(Lambda+n*Mu)*p[n+si](t)+n*Mu*p[n+si+1](t),
si=1..m-1),
         diff(p[n+m](t), t)=Lambda*p[n+m-1](t)-
n*Mu*p[n+m](t)
         };
             ? d
ODESystem := ?    p2(t) = 5.08 p1(t) - 13.32 p2(t) + 12.36 p3(t),
             ? dt
       d                                                  d
          p5(t) = 5.08 p4(t) - 25.68 p5(t) + 20.60 p6(t),   p (t) = -5.08 p13(t) - 25.68 p14(t) + 20.60 p15(t),
       dt                                                 dt 14
       d                                   d
         p (t) = -5.08 p0(t) + 4.12 p1(t),   p (t) = 5.08 p0(t) - 9.20 p1(t) + 8.24 p2(t),
       dt 0                                dt 1
       d                                                  d
          p3(t) = 5.08 p2(t) - 17.44 p3(t) + 16.48 p4(t),   p (t) = 5.08 p3(t) - 21.56 p4(t) + 20.60 p5(t),
       dt                                                 dt 4
       d                                                  d
         p (t) = -5.08 p5(t) - 25.68 p6(t) + 20.60 p7(t),   p (t) = -5.08 p6(t) - 25.68 p7(t) + 20.60 p8(t),
       dt 6                                               dt 7



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