Теория массового обслуживания. Сивохин А.В - 211 стр.

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211
> diff((PSi[5]), t):
6. Решение дифференциальных уравнений для
вероятностей состояний pi(t) при заданных
начальных условиях
> ODESystemInit:=
{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),
seq(diff(p[n+si](t), t)=-
Lambda*p[n+si-1](t)-
(Lambda+n*Mu+si*Nu)*p[n+si](t)+(n*Mu+(si+1)*Nu)*
p[n+si+1](t), si=1..s),
diff(p[16](t), t)=diff(1-(sum(p[i](t),
i=0..n+s)), t),
p[0](0)=1.0, seq(p[i](0)=0.0,
i=1..n+s+1)
};
ODESystemInit :=
?
?
?
d
dt
p
0
t( ) = -5.08 p
0
t( ) + 4.12 p
1
t()
,
d
dt
p
10
t( ) = -5.08 p
9
t( ) - 56.33 p
10
t( ) + 57.38 p
11
t()
,
d
dt
p
14
t( ) = -5.08 p
13
t( ) - 80.85 p
14
t( ) + 81.90 p
15
t(),
d
dt
p
3
t( ) = 5.08 p
2
t( ) - 17.44 p
3
t( ) + 16.48 p
4
t(),
d
dt
p
1
t( ) = 5.08 p
0
t( ) - 9.20 p
1
t( ) + 8.24 p
2
t(),
d
dt
p
2
t( ) = 5.08 p
1
t( ) - 13.32 p
2
t( ) + 12.36 p
3
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( ) - 31.81 p
6
t( ) + 32.86 p
7
t(),
d
dt
p
7
t( ) = -5.08 p
6
t( ) - 37.94 p
7
t( ) + 38.99 p
8
t(),
d
dt
p
8
t( ) = -5.08 p
7
t( ) - 44.07 p
8
t( ) + 45.12 p
9
t(),
d
dt
p
9
t( ) = -5.08 p
8
t( ) - 50.20 p
9
t( ) + 51.25 p
10
t(),
d
dt
p
11
t( ) = -5.08 p
10
t( ) - 62.46 p
11
t( ) + 63.51 p
12
t(),
d
dt
p
12
t( ) = -5.08 p
11
t( ) - 68.59 p
12
t( ) + 69.64 p
13
t(),
d
dt
p
13
t( ) = -5.08 p
12
t( ) - 74.72 p
13
t( ) + 75.77 p
14
t(),
d
dt
p
15
t( ) = -5.08 p
14
t( ) - 86.98 p
15
t( ) + 88.03 p
16
t(),
d
dt
p
16
t( ) = -
d
dt
p
0
t()
?
?
?
?
?
?
-
d
dt
p
1
t()
?
?
?
?
?
?
>   diff((PSi[5]), t):
6. Решение дифференциальных уравнений для
вероятностей состояний pi(t) при заданных
начальных условиях

> ODESystemInit:=
         {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),
           seq(diff(p[n+si](t), t)=-
Lambda*p[n+si-1](t)-
(Lambda+n*Mu+si*Nu)*p[n+si](t)+(n*Mu+(si+1)*Nu)*
p[n+si+1](t), si=1..s),
          diff(p[16](t), t)=diff(1-(sum(p[i](t),
i=0..n+s)), t),
           p[0](0)=1.0, seq(p[i](0)=0.0,
i=1..n+s+1)
         };
                 ? d                                    d
ODESystemInit := ?    p0(t) = -5.08 p0(t) + 4.12 p1(t),    p10(t) = -5.08 p9(t) - 56.33 p10(t) + 57.38 p11(t),
                 ? dt                                   dt

       d                                                     d
         p (t) = -5.08 p13(t) - 80.85 p14(t) + 81.90 p15(t),   p (t) = 5.08 p2(t) - 17.44 p3(t) + 16.48 p4(t),
       dt 14                                                 dt 3
       d                                                d
          p1(t) = 5.08 p0(t) - 9.20 p1(t) + 8.24 p2(t),   p (t) = 5.08 p1(t) - 13.32 p2(t) + 12.36 p3(t),
       dt                                               dt 2
       d                                                 d
         p (t) = 5.08 p3(t) - 21.56 p4(t) + 20.60 p5(t),   p (t) = -5.08 p5(t) - 31.81 p6(t) + 32.86 p7(t),
       dt 4                                              dt 6
       d                                                   d
          p7(t) = -5.08 p6(t) - 37.94 p7(t) + 38.99 p8(t),   p (t) = -5.08 p7(t) - 44.07 p8(t) + 45.12 p9(t),
       dt                                                  dt 8
       d                                                   d
         p (t) = -5.08 p8(t) - 50.20 p9(t) + 51.25 p10(t),   p (t) = -5.08 p10(t) - 62.46 p11(t) + 63.51 p12(t),
       dt 9                                                dt 11
       d                                                       d
          p12(t) = -5.08 p11(t) - 68.59 p12(t) + 69.64 p13(t),   p (t) = -5.08 p12(t) - 74.72 p13(t) + 75.77 p14(t),
       dt                                                      dt 13

       d                                                       d              d          ? d p (t)?
          p15(t) = -5.08 p14(t) - 86.98 p15(t) + 88.03 p16(t),    p16(t) = -?
                                                                            ?    p0(t)?
                                                                                      ? -?    1 ?
       dt                                                      dt           ? dt      ? ? dt      ?




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