Теория массового обслуживания. Сивохин А.В - 253 стр.

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253
(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),
p[0](0)=1.0, seq(p[i](0)=0.0,
i=1..n+m)
};
ODESystemInit :=
?
?
?
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
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
15
t( ) = 5.08 p
14
t( ) - 20.60 p
15
t(), p
0
0( ) = 1.0, p
1
0( ) = 0., p
2
0( ) = 0., p
3
0( ) = 0., p
4
0( ) = 0., p
5
0( ) = 0.,
p
6
0( ) = 0., p
7
0( ) = 0., p
8
0( ) = 0., p
9
0( ) = 0., p
10
0( ) = 0., p
11
0( ) = 0., p
12
0( ) = 0., p
13
0( ) = 0., p
14
0( ) = 0.,
p
15
0( ) = 0.
?
?
?
> # PSiInit:=dsolve(ODESystemInit);
7. Визуализация решений дифференциальных
уравнений для вероятностей состояний pi(t)
при заданных начальных
условиях
> # p[1](t):=rhs(PSiInit[2]):
# p[2](t):=rhs(PSiInit[4]):
# p[3](t):=rhs(PSiInit[1]): 
(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),
           p[0](0)=1.0, seq(p[i](0)=0.0,
i=1..n+m)
         };
                 ? d
ODESystemInit := ?    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
           p0(t) = -5.08 p0(t) + 4.12 p1(t),   p (t) = 5.08 p0(t) - 9.20 p1(t) + 8.24 p2(t),
        dt                                   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
           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
           p8(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                                                  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
           p12(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                                                      dt 13
        d
          p (t) = 5.08 p14(t) - 20.60 p15(t), p0(0) = 1.0, p1(0) = 0., p2(0) = 0., p3(0) = 0., p4(0) = 0., p5(0) = 0.,
        dt 15
        p6(0) = 0., p7(0) = 0., p8(0) = 0., p9(0) = 0., p10(0) = 0., p11(0) = 0., p12(0) = 0., p13(0) = 0., p14(0) = 0.,

                   ?
        p15(0) = 0.?
                   ?

>   # PSiInit:=dsolve(ODESystemInit);
7. Визуализация решений дифференциальных
уравнений для вероятностей состояний pi(t)
                                                        при заданных начальных
условиях

>   #      p[1](t):=rhs(PSiInit[2]):
#         p[2](t):=rhs(PSiInit[4]):
#         p[3](t):=rhs(PSiInit[1]):
                                                           253

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