9, 9. 9.. Nt () [, t] t Nt () { Nt ( ) t [, T]} t< t< t< t + N ( ( t+ ) i+ N( t) i, N( t) i,, N( t) i N + + N ( ( t ) i ( t ) i ) (9-) { Nt ( ) t [, T)} 9- t t + t, t,, t t
t { Nt ( ) t [, T] } t< t,, t( 3) N( t) N( t), N( t3) N( t),, N( t) N( t ) t [, T], t ( t) Nt ( ( ) ),,, (9-)! > [ t, t),[ t, t3),,[ t, t) ( t) t! Nt () ( t) t ( t) ENt ( ( )) t! ( )! t ( t) i t t t (9-3) i i ENt ( ( )) (9-4) t Nt) ( DNt ( ( )) t (9-5) 9. 3 47 3 ( + 8 + 34+ 3 9 + 4 6).87 3 9-3 4 8 34 9 6 9-
3.87.6 / (.6 t) Nt ( ( ) )!.6t { Nt ( ) t [, T)} () t< t < < t( 3) N( t) N( t), N( t3) N( t),, N( t ) N( t ) () [, ss+ t] [, T ] Ns [ ( + t) Ns ( ) ] Nt [ ( ) N() ] N ( () ), Nt ( ( ) ) (3) ϕ() t ( N() t ) ϕ() t lim t t { Nt ( ) t [, T]} [, T ] [, ss+ t] [, s] [, s] [, ss+ t] [, ss+ t] t s { N ( t)} { ( N t) } { N ( t)} +{ ( N t) } + 9.. τ { } τ
{ τ } µ t ( τ t) t (9-6) t < µ > t µ µ pt () t (9-7) t < τ µ t E( τ ) tp( t) dt µ t dt + + + µ t + µ t t + dt (9-8) µ µ (9-9) E( τ ) { Nt ( )} ET ( ) µ µ τ ( ) D τ (9-) µ { Nt)} ( t T t t { } { T } T { Nt)} ( { T } µ t T ( t) t (9-) t <
9. 6 5 7 3 4 5 3 39 55 58 6 63 65 68 8 8 85 89 97 99 3 3 33 5 6 6 8 6 3 4 3 3 4 8 4 8 5 + + + 33 5.3 5 5 5.3 5.3.88 5.3.88 { Nt)} ( (.88 t) Nt ( ( ) )!.88t,,, { T }.88t t t T ( ) t < 7 7 T 9- s T s + s t T ( s) T ( s) dt s T s T s+ t( t> ) T s+ t + t ( s + t) T ( st, s+ t) T ( s+ t) dt T s T s+ t s+ t
( s+ t) T ( st, s+ t) t T ( s+ tt s) T ( t) s T ( s) s T ( s+ tt s) T ( s+ tt s) T ( t) Erlag pt () ( )! µ ( µ t) µ t t t < µ > (,,, ) (9-) τ τ E( τ), D( τ) µ µ (9-3) ξ, ξ,, ξ µ τ ξ + ξ + + ξ µ 9..3. t t+ ( t) t
µ t+ ( t) t ( t+ ( t)),( µ t+ ( t)),( t+ ( ))( µ t+ ( t)) t ( t) t i t+ t i + i t+ ( t) t+ t i µ t+ ( t) ξ t t i () [,T ) t ξ() t {( ξ t) t [, T)} {( ξ t) t [, T )} ξ() t I {,,,, m} I {,,, } t ξ() t t+ t ξ ( t+ t) + t+ ( t) + + ) > t t t ξ(t t I ( t) {( ξ t) t [, T)} t t µ t ( t) t t t t t t. T + lim (ξ( t ) ) T + 3 π, π µµ µ (,, ) {( ξ t) t } I {,,,, m} I {,,, } π <+, + π s Ii I, lim ( ξ( t) ) t + lim ( ξ( s + t) ξ ( s) i) > I {,,,, m} t +
p ( π ) p π p p,,, m µ I {,, } p ( π ) p π p p,, µ (,,, ) t ( ξ ( t) ) I t, I t 3 t + 9. 9.. 9-. 9-
() α { T } T ( t) t < α t α () { T T } t T ( t) t t < [, t ) Nt () Nt () ( t) t Nt ( ( ) ),,,! (3) { T T } ( t) t pt () ( )! t t < (4) { T T } (a) (b) s (c) s. 9-9- τ
() τ β, τ ( τ t) τ τ < β β () { τ τ } ( τ t) t µ t < t (3) { τ τ } pt () ( t) ( )! µµ µ t t < t (4) { τ τ 3. } 9..
µ µ S ρ L L W
W 6 6 / / / / / M D E G M / M // M / G/ S/ s ( 9-3) s 9-3 L W (9-4)
L W (9-5) 9.3 9.3. M / M / S SS ( ) M / M / S/ / S M / M / M / M / S M / M / 9- a S > M / M / S 9- c 9-3 M / M / S S 9-4 S M / M / M / M / S M / M / S { T } T ( t) t t < t { τ } ( τ t) t µ t < t µ
s ξ () t 9.4 t { ξ( t)} I {,,, } t t ( ξ( t) ) t t( t+ ( t))! t+ ( t) τ t µ t+ ( t) S t Sµ t+ ( t) µ µ Sµ,,,,,, S S+, S+, 3 π S ρ! s S ρ S! S > S (9-6) ρ (9-7) Sµ s S S ρ! S! S s π ρ + S+ s + π π S+ π
s! S! + ρ S S ρ S S+ ρ < π <+, π + 3 ρ < 3 ( Sρ) ( Sρ) ( ) ( + ) S S π! S! ρ (9-8) π ( Sρ)! S S ρ S! S > S (9-9) / M M / S (,., ) L L WW, L L ρ L p Sρ + ( ρ) p s (9-) L ρ p + ( ρ) S ps (9-) W W 9.4 9.5 L W W L W W ρ W L + p s (9-) µ ( ρ) W ρ L ( ρ) p S (9-3) S M / M / ρ < 9-8 µ
ρ p ( + ) ρ ρ p ρ p ( ρ) ρ,, (9-4) L ρ µµ ( ) ρ ρ L µ ρ W ρ µµ ( ) µ ( ρ) W µ µ ( ρ ) (9-5) (9-6) (9-7) (9-8) 9.3 3 3 4 5 6 4 7 7 8 9 4 4 4 36 36 48 48 6 6 7 7 84 33 5 6 4 3 96 84 96 8 8 5 5 8 8 M / M / 4+ 7 + 7 + 3 8+ 4 9+ 5 4+ 6.97.97 3.657 / 3 µ
(6 33 8 3 5 4 54 6 66 4 78 3 9 µ + + + + + + + + + 4 + 35 + 65 + 9 ) 3.7.59 µ.89 /ρ.348 µ 9.4 ~ 9.8 ρ.348.65.348 L ρ.86 µµ ( ) ρ W.8 µ W.8 µµ ( ) 9.4 5 M / M / W
/ 5 6 3 µ µ / 5 5 ρ S µ µ 6 W 9.8 S ( ρ) ( ρ) ( + )!! ρ ( + ( ) 6) 6 6 9.9, + ( ρ) s ( ).6! 6 9. ρ 5 W + p + µ ρ 5 3 6.6 ( ) 6 6.34 M / M /3.45.7 s 3 W 5.53 M / M / S ( S ) S M / M / 9.5 S M / M / ( 5, µ 4) M / M / M / M / 9.8 ~ 9.3 9-3 M / M / M / M / 5 M / M /
9.5 ~ 9.8 9-3 9-3 L 4 W M / M / W.6667 M / M / W.47 9-3 µ L L p W W p () M / M / 5 4.86.7586.47.57 () M / M /.5 4.6667.47.6667.467 9.3. M / M / S/ M / M / S/ S S > S ξ () t t { ξ( t)} I {,,,, } {( ξ t)} µ µ Sµ,,,,,,, s S+, s+,, µ M / M / S 9.3 p ( S) ( + S ρ S i 3 i ) (9-9) i i! i S S! p ( S) p s S ρ p S!,,, S S+, S+,, (9-3)
ρ ρ < S µ L L L p (9-3) L s p S+ (9-3) ( ) (9-33) W W S M / M // ρ + ρ + ρ ρ (9-34) ρ ( ρ) ρ + + ρ ρ (9-35) ρ( ( + ) ρ ) + ρ + ( ρ)( ρ ) L L ρ ( + ρ) ρ ρ ρ ( ) ( + ) + + + ρ ρ ρ ρ (9-36) (9-37) 9.6 6 4.5 M / M /6/ 6 S 6 4
.5 µ µ ρ 4 Sµ 6 3 ρ S 9.9 9.3 i 6 5 (6 ) (6 ) 3 3 +.36 i! i i 6! 6 (6 ) ( Sρ) 3 6.! 6! S 6 6 6.988 M / M // 5 6 9.33 ( ) 4.988 3.95 6 9.7 5 5, S, ( ) µ / µ / ρ µ 9.34 9.35 ρ
3 4 5 + 6 + 6 5 ( > S) 9.33 ( ) ( 5 ) ( ) 5 6 / 9.35 ρ L W 6 5. 5 6 6 9.3.3 M / M / S/ m/ m S m, M / M / S/ m m 9-5 s 9-5 S m m S,m S S
, µ µ 3 ξ() t t { ξ( t)} I {,,, m} {( ξ t)} µ ( m ) µ Sµ,,,, m,,, S S+, S+,, m 3 p S m m! + S µ S+ SS! µ (9-38) p m p µ m! S SS! µ p,,, S S+, S+,, m (9-39) m L L S+ L L m S ( m L) W W S p m m! i ( m i)! µ (9-4) p m! p ( m )! µ (9-4)
µ L m ( p) (9-4) L L ( p ) (9-43) 9.8 4 LL,, WW, M / M / S/ m/ m S 4, m,, µ, ρ 3 3 9.38 9.39 3 4 + + + + + µ µ µ 3 µ 4 µ 5 6 7 5! 6! 7! + + 3 5 4!4 µ 6 4!4 µ 7 4!4 µ + 8 9 8! 9!! + + 4 5 6 8 4!4 µ 9 4!4 µ 4!4 µ (+3.3333+5+4.4444+.596+.963+.54+.8+.45+.75+.6) - (8.44).54 3.3333.87 µ 5.7 µ L L 3.49 4.45 5.73 6.93 7.98 8.4 9.75.4.6.3 -
L.66 4 4+ 5 6 3 7 4 8 5 9 6 L + + + + +.7 ( m L) (.66).458 3 W W L.66 W.684.458 W L.7.69.458 ( + + + ).53 3 9.9 µ. µ 3 6 3 3 3 M / M //6/ 6. µ 9.4 9.4.48, p.9,.5 3.58, 4.8, 5.35 6.3. 9.4 9.43 L.855 L.335
( ) ( ) m L 6.855 5.45 W ( I) L.335 5.45 M / M /3//. µ.4,.7,.6, 3.6 4.88, 5.47, 6.3, 7. 8.48, 9.9,.7,. p., p 3, p 4,..., p L p.3 L 3 p.337 3+ M / M /3// ( ).3 7.87.337 W ( ) 7.87 () ( ) W.335.337 3.453 W 5.45 7.87 9.3.4 M / G /
M / G / ( ) E τ τ D ( τ ) ρ ρ < µ µ ρ (9-44) L ρ + L + D( ) ( ρ) ρ τ D( ) ( ρ) ρ + τ (9-45) (9-46) 9.4 9.5 L W W L 9. 7 6 X, X, X 3, X 4 3 4 τ X + X + X + X 4 X i ( i,,3,4) /t i t t X ( ) t < 9.3 E( τ ) 4 4 8 D( τ ) 6 µ E ( τ 8 )
7.667 6 7 ρ 8.933 µ 6 9.45 L.933+ ( ) 7.933 + 6 6 9.544.933 ( ) ) L 9.544 W 77.6 (.67.3